Mathematics, Time, and the Oscillatory Architecture of Earth
A Booklet Of Eight Individual Papers
A TSTOEAO Project
John Swygert
August 25, 2026
Ivory Tower Publishing
Copyright © John Swygert 2026
TSTOEAO.com
IvoryTowerJournal.com
SecretarySuite.com
Contents
The Planetary Control Experiment
The Master Time Architecture
The Oscillatory Earth Architecture
Oscillatory Earth Architecture — Formal Simulation Specification
Earth-System Simulation Registry & Preregistration — Phase 1
Oscillatory Earth — Phase 1 Implementation Package
Oscillatory Earth — Phase 1 Data Acquisition & Provenance Record
Oscillatory Earth — Phase 1 Frozen Data Archive — Batch 1
The Planetary Control Experiment
Is Mathematics Universal, or Is Mathematical Culture Shaped by the World That Observes It?
DOI: To be assigned
John Swygert
August 25, 2026
Abstract
Mathematics is often called the language of the universe, but that slogan conflates mathematical truth with mathematical notation, measurement, historical discovery, and cognitive salience. This paper proposes a planetary control experiment in thought and simulation. Arithmetic and structural invariants may be universal, while the mathematical concepts privileged by a civilization may depend strongly on the physical environment from which that civilization observes reality. Earth supplies a distinctive hierarchy of rotation, lunar, seasonal, orbital, and planetary cycles. Mercury presents a 3:2 spin-orbit resonance; Venus has a sidereal rotation longer than its year and a solar day of roughly 117 Earth days; the Jovian system displays the 4:2:1 Io-Europa-Ganymede resonance. A civilization developing independently on each world would face different measurement problems and might therefore privilege different ratios, radices, calendars, geometries, and metaphors while discovering the same underlying mathematical relations. The paper distinguishes universal invariants from planetary numerical salience, reframes mathematics as a potential Rosetta Stone rather than an instantly shared language, and develops testable hypotheses about environmental selection in mathematical culture. A final speculative section asks whether biological morphology - including digits and joint structure - could ever become statistically coupled to recurrent environmental and behavioral counting demands. That extension is explicitly treated as a high-risk hypothesis requiring evolutionary and developmental evidence, not as an established claim.
Keywords: philosophy of mathematics, SETI, alien communication, planetary environment, numerical salience, radix, calendar, orbital resonance, cognitive evolution, mathematical culture
Core distinction
Arithmetic invariants may be universal; numerical salience can be environmental. A civilization can discover the same mathematical truths while arriving through a different sequence of observations, units, symbols, favored ratios, and conceptual metaphors. |
1. The Slogan and the Problem
The statement ‘mathematics is the language of the universe’ contains an important truth and an important ambiguity. If two physical systems instantiate the same ratio, the relation does not change because the observer speaks another language. Prime numbers do not acquire different divisors on Venus. Yet nothing follows from this about whether an extraterrestrial civilization would use our symbols, conceptual categories, units, proof traditions, coordinate systems, bases, or even the same ordering of mathematical discoveries.
Mathematical relation ≠ mathematical representation ≠ measurement system ≠ mathematical culture
The alien-contact question is therefore not merely whether mathematics is true everywhere. It is whether independently evolved minds would parse those truths into sufficiently similar concepts that mathematics functions as an immediate common language. Recent philosophical work on mathematical SETI explicitly questions that assumption: even if mathematical facts are universal, historically and biologically contingent minds may not instantiate the same concepts in the same way.
Figure 1. The planetary control experiment separates universal relations from the environmentally selected path through which a civilization encounters and encodes them.
2. Universal Invariants and Local Salience
A useful distinction is between invariance and salience. The prime factorization of 60 is invariant. The practical importance of 60 is not. Sixty remains 2²×3×5 on every planet, but a civilization has to encounter problems for which those divisors are valuable before sexagesimal structure becomes culturally prominent. The same distinction applies to 12, 20, 360, 432, π, prime sequences, symmetry groups, and orbital ratios. Their mathematical properties are universal; the probability that a culture notices, names, ritualizes, or builds metrology around them can be environmentally conditioned.
Universal structure + local observation + cognition + history → mathematical culture
3. The Planetary Control Experiment
The thought experiment is simple. Hold intelligence broadly constant while changing the world from which the sky is observed. Do not ask what imaginary inhabitants ‘would definitely believe.’ Ask instead what recurrent physical relationships their environment makes easiest to notice, count, predict, and coordinate around. This turns the Solar System into a conceptual control set for studying mathematical salience.
Figure 2. Rotation and orbital periods differ radically among terrestrial planets. A native calendar problem on Venus or Mercury would not begin with the same hierarchy familiar on Earth.
World/system | Salient physical cycles | Possible mathematical pressure | What is controlled |
Earth | ~24-hour solar day; 365.24-day year; large Moon; axial seasons | Day–month–season–year nesting; lunisolar reconciliation; quartering and subdivision | Earth-based calendars naturally emphasize solar/lunar reconciliation and seasonal recurrence. |
Mercury | ~58.6-day sidereal rotation; ~88-day orbit; 3:2 spin-orbit resonance | 2, 3, 6 and resonance relations could be observationally conspicuous | A stable integer spin-orbit ratio is part of the planet’s basic time architecture. |
Venus | 243-Earth-day retrograde rotation; 225-day orbit; ~117-day solar day; minimal seasons | Day/year categories become non-Earthlike; retrograde sky motion | A ‘day’ longer than a ‘year’ in sidereal terms challenges Earth-derived intuitions about calendar hierarchy. |
Mars | ~24.6-hour sol; ~687-Earth-day year; ~25° axial tilt | Earth-like daily rhythm but very different annual count | Some mathematical pressures may converge with Earth while others diverge. |
Jovian moon system | Io, Europa, Ganymede in 4:2:1 resonance | Repeated small-integer orbital ratios | Persistent resonance is an environmental demonstration of integer relation and phase coupling. |
Figure 3. Illustrative environmental ratios. These are not predictions of alien culture; they are candidate measurement pressures for a comparative model.
4. Would Base-60 Work Everywhere?
Yes in the mathematical sense, not necessarily in the historical sense. Any civilization capable of discrete arithmetic can in principle use a radix of 60. Its divisor structure does not depend on gravity, atmosphere, or orbital period. But the reasons for choosing it are contingent. On Earth, sexagesimal arithmetic became extraordinarily useful for fractions, angles, and astronomical period relations. On another world, a different collection of recurrent ratios could make another radix more efficient or culturally obvious.
This distinction suggests a measurable quantity: environmental radix fitness. For a specified set of naturally important periods on a planet, one can score candidate bases by how compactly they express the ratios, subdivisions, and least-common-multiple problems generated by those periods.
Radix fitness(B) = weighted compactness of environmentally salient ratios in base B
A simulation could evaluate bases 2 through 120 using the same coding-length metric for each planet. If base 60 repeatedly performs well across very different planetary cycle sets, that would support a more universal computational advantage. If its advantage is strongly Earth-specific, it would support environmental selection. Either result is informative.
5. Earth Mathematics as an Earth-Conditioned Selection from Mathematics
The claim is not that gravity changes arithmetic. Rather, physical environment may select which subset of mathematical possibility becomes useful first. Human mathematical history is filled with such selection: counting bodies and goods; surveying land; reconciling lunar and solar calendars; predicting eclipses; dividing circles; navigating; keeping accounts; and later describing mechanics, fields, probability, computation, and relativity. The mathematical universe may be enormous while any civilization explores it along a path shaped by survival and observation.
Mathematical possibility space → environmental problems → culturally explored subspace
This makes the phrase ‘our mathematics’ meaningful without implying mathematical relativism. Theorems do not become locally true. The sequence of discovery, preferred notation, canonical examples, unit systems, and intuitive metaphors can nevertheless be local.
6. Mathematics and Alien Communication
An extraterrestrial civilization would not instantaneously understand the string 2+2=4, because the glyphs and operator conventions are human. Communication would require establishing a mapping. Prime-number pulses, repeated geometric ratios, symmetry, or physically anchored frequencies may provide starting points precisely because they contain structure unlikely to be accidental. Mathematics is therefore better described as a possible Rosetta Stone than as a preinstalled spoken language.
SETI literature has long treated mathematics and physics as promising common ground, while also recognizing the anthropocentric assumptions hidden in that approach. A sufficiently different intelligence might represent quantity geometrically, topologically, temporally, chemically, or in conceptual structures for which our arithmetic notation is not primary. Translation may still be possible because invariant relations constrain both descriptions.
Their representation ↔ shared invariant ↔ our representation
7. Mathematics, Gravity Wells, and the Metaphor of “Dancing Numbers”
A useful metaphor is to imagine mathematical relations passing through different physical environments and acquiring different visible expressions. The numbers themselves do not twist under gravity in the sense that the integer 8 becomes another integer. What changes are the measurable quantities: clock rates, trajectories, resonances, material behavior, stable structures, and characteristic scales. General relativity makes this distinction especially vivid. Proper time depends on worldline and gravitational potential, yet the mathematical relationships used to describe that dependence remain internally consistent.
Thus the ‘dancing numbers’ image can be made scientifically precise: invariant mathematics is instantiated through environment-dependent observables. The same equations can produce different characteristic values when boundary conditions, mass distributions, density, pressure, temperature, and gravitational fields change.
Invariant law + different boundary conditions → different realized numerical world
8. A High-Risk Extension: Could Morphology and Counting Co-Evolve?
Human counting traditions have often been linked to bodily affordances: ten fingers encourage decimal grouping; twelve finger phalanges can be counted with the thumb; five repetitions of twelve yield sixty. This raises a provocative evolutionary question. Could long-term environmental and behavioral demands related to quantification exert selection on morphology or neural representation, such that organisms on different worlds evolve different counting affordances?
At present, there is no evidence that human finger-joint anatomy evolved because Earth’s astronomical cycles favored base 12 or base 60. Tetrapod limb patterning has deep developmental and evolutionary causes that predate human mathematics by hundreds of millions of years. Therefore the strong claim - ‘digits evolved to encode planetary mathematics’ - is unsupported. The scientifically viable descendant hypothesis is subtler: once a morphology exists, cultures exploit it for counting; over much longer evolutionary times, recurrent manipulative, communicative, and quantitative behaviors could in principle feed back on neural or morphological traits. Testing that would require comparative biology, developmental genetics, cognitive archaeology, and evolutionary modeling.
Critical guardrail
The finger/phalange idea is retained as a speculative research direction, not as evidence for the planetary-control hypothesis. Its current value is that it generates testable questions about how bodily affordances bias numerical culture. |
9. Fractal and Relational Interpretation
The broader intuition can be expressed without claiming literal fractal identity. At multiple scales, physical systems create recurrent ratios: atomic transitions, rotations, orbital resonances, waves, biological rhythms, and ecological cycles. Intelligence detects regularity by compressing recurrence into symbols. Different scales and environments therefore produce different numerical saliences while remaining connected through common operations such as ratio, symmetry, periodicity, optimization, and transformation. What repeats is not necessarily the same number; it is the relational grammar.
Environment → recurrence → relation → compression → symbol
10. Proposed Simulation Program
Construct a planetary observables vector for each Solar System body: rotation, solar day, orbital period, axial tilt, moon periods, major resonances, seasonal forcing, and other stable periodicities.
For candidate radices B = 2…120, calculate the representation length and exact-divisibility cost of the most salient ratios for each world.
Generate synthetic calendars optimized under different objectives: agricultural season tracking, eclipse prediction, navigation, ritual recurrence, and administrative simplicity.
Compare whether the same bases repeatedly emerge under different worlds or whether optimal systems diverge strongly by environment.
Test communication schemes between independently optimized mathematical cultures to estimate how many examples are required to infer one another’s notation and units.
Keep biological embodiment as a later module, initially modeling only fixed digit/joint affordances rather than assuming evolutionary adaptation.
11. Falsifiable Predictions
Prediction | Domain | Test |
P1 | Environmental selection | Different planetary cycle sets produce statistically different optimal radix distributions under equal optimization rules. |
P2 | Universal arithmetic advantage | Certain radices (especially highly composite ones) perform well across many worlds despite differing cycles. |
P3 | Translation gap | Independent mathematical cultures can recover shared relations but require explicit mapping of notation and units; recognition is not instantaneous. |
P4 | Embodiment bias | Given identical environmental data, agents with different counting affordances converge on different early numeral systems more often than on different mature mathematics. |
P5 | Invariant convergence | As technical sophistication grows, independently simulated cultures increasingly converge on deeper structural mathematics even if their elementary notation diverges. |
12. What Would Count as a Strong Result?
The most interesting outcome would not be that aliens ‘use different math.’ It would be a layered result: elementary notation and numerical salience vary strongly with environment and embodiment; intermediate mathematical tools vary with engineering and observational history; deeper structural relations increasingly converge because the same universe constrains successful prediction. Such a result would reconcile mathematical realism with cultural contingency.
Universal constraints + contingent paths = convergent structure without identical mathematical culture
Conclusion
Mathematics can be universal without being an instantly universal language. The truths represented by arithmetic, ratio, symmetry, and physical law may not depend on where an observer lives, while the numerical structures that become culturally obvious can depend profoundly on the observer’s world. Earth gave humanity one particular sky, one rotation, one Moon, one seasonal architecture, and one network of planetary cycles. Mercury, Venus, Mars, and the Jovian system offer dramatically different control conditions. Thinking comparatively exposes a neglected possibility: civilizations do not merely discover mathematics; they navigate the mathematical possibility space along paths selected by environment, embodiment, and history. The planetary control experiment converts that philosophical idea into a research program. It asks which mathematical structures are universal attractors of intelligence and which are local signatures of the world doing the observing. That distinction matters for the history of mathematics, comparative cognition, SETI, and any serious attempt to imagine what truly alien intelligence would find obvious.
References
NASA Science. “Venus: Facts.” Rotation ~243 Earth days, orbit ~225 Earth days, solar-day interval ~117 Earth days. https://science.nasa.gov/venus/venus-facts/
NASA Technical Reports Server. “Spin-Orbit Resonance of Mercury.” Mercury’s stable 3:2 spin-orbit relation. https://ntrs.nasa.gov/
NASA Science. “Europa: Facts” and “Ganymede: Facts.” Io-Europa-Ganymede 4:2:1 orbital resonance. https://science.nasa.gov/jupiter/jupiter-moons/
Lemarchand, Guillermo A. “Counting on Beauty: The Role of Aesthetic, Ethical, and Physical Universal Principles for Interstellar Communication.” arXiv:0807.4518 (2008).
Mathematical SETIbacks (preprint, Philosophy of Science Archive). Discussion of why universal mathematical truth does not automatically make mathematics a universal communicative language. https://philsci-archive.pitt.edu/24162/
Vakoch, Douglas A., ed. Archaeology, Anthropology, and Interstellar Communication. NASA, 2014. Essays emphasize the translation and anthropological problems hidden in assumptions of mathematical universality.
Clement, Matthew S., Sean N. Raymond, Dimitri Veras, and David Kipping. “Mathematical Encoding within Multi-Resonant Planetary Systems as SETI Beacons.” arXiv:2204.14259 (2022).
Chrisomalis, Stephen. Numerical Notation: A Comparative History. Cambridge University Press, 2010. Comparative history of numeral systems and notation.
The Master Time Architecture
A Comparative Relational Framework for Ancient Calendars, Cosmological Ages, Numerical Bases, and Planetary Timekeeping
DOI: To be assigned
John Swygert
August 25, 2026
Abstract
Human civilizations have represented time through strikingly different calendars, numerical bases, sacred chronologies, regnal schemes, astronomical cycles, and cosmological ages. These systems are usually studied within separate disciplines and cultural traditions. This paper proposes a Master Time Architecture: a comparative framework that preserves each system in its native units and arithmetic before converting it into a common scale. The central hypothesis is not that every ancient chronology encodes one literal master period, but that all terrestrial systems were constructed from the same observational platform - Earth - and therefore may exhibit overlapping ratios, recurrence structures, and preferred numerical families. Particular attention is given to sexagesimal mathematics and to the 432 family (43,200; 432,000; 4,320,000), whose apparent decimal similarity becomes more structurally interesting when expressed through powers and multiples of 60. The paper develops rules for preventing retrospective pattern matching, distinguishes arithmetic convenience from physical observation without treating them as mutually exclusive, and specifies a visualization and simulation-ready data architecture. The result is a falsifiable program for determining which cross-cultural correspondences arise from shared terrestrial observation, which reflect cultural transmission, which follow naturally from highly factorable number systems, and which remain unexplained.
Keywords: comparative chronology, sexagesimal mathematics, base 60, Maya Long Count, Sumerian King List, Yuga, calendar cycles, astronomical time, 432, cultural astronomy
Working principle
Base-60 may be understood, in a deliberately compact phrase, as a form of mathematical shorthand for spacetime recordation: not because sexagesimal notation is a physical law of spacetime, but because a highly divisible radix efficiently records nested astronomical and temporal relations. The phrase is used here as a heuristic, not as a claim that spacetime itself is base-60. |
1. The Problem: Many Clocks, One Planet
Ancient time systems are normally encountered one at a time. A student learns that the Maya counted k’in, uinal, tun, katun, and baktun; Mesopotamian scribes used sexagesimal arithmetic; Chinese chronology employed a sixty-term stem-and-branch cycle; Egyptian civil time used a 365-day year; Indian cosmology developed enormous nested yuga intervals; Hebrew texts organized sacred time through seven-day, seven-year, and Jubilee structures. In isolation, these systems can appear unrelated. The methodological error is to compare their modern translations before reconstructing what each culture was actually counting.
The Master Time Architecture reverses that order. It asks four questions for every interval: What was the native unit? What arithmetic or radix generated it? What observable cycle, ritual structure, or cosmological claim did it represent? And only then: what is its equivalent duration in a common modern unit? This preserves the difference between a culture thinking in ‘twelve šar’ and a modern reader seeing ‘43,200 years.’
Figure 1. Proposed causal and representational sequence. Mathematical convenience and terrestrial observation are treated as potentially linked stages rather than competing explanations.
2. Native Units Before Modern Conversion
A translation of a duration into modern solar years can be numerically correct while conceptually misleading. The Sumerian King List is the clearest example. Oxford’s ETCSL renders antediluvian reigns of 28,800, 36,000, and 43,200 years; the Ashmolean Museum explicitly characterizes the document as a mixture of myth, legend, and historical information. Yet these extraordinary values are not arbitrary decimal integers. They sit naturally inside a sexagesimal numerical tradition. The 43,200-year reign of En-men-lu-ana is 12 × 3,600: twelve šar if šar is taken as the 3,600-unit value used in discussions of the list. The cognitive object ‘12 large units’ is far simpler than the decimal phrase ‘forty-three thousand two hundred years.’
43,200 = 12 × 3,600 = 12 × 60²
This does not prove that the reign was an astronomical code, nor that the person named in the list was actually a planet, star, dynasty, or cycle. It does establish a guardrail: extraordinary ancient durations should not be interpreted literally until their native arithmetic and literary category have been reconstructed.
Tradition | Arithmetic structure | Representative intervals | Primary function | Interpretive caution |
Mesopotamian / Sumerian | sexagesimal; mixed notation | 60; 600; 3,600; large regnal totals | Scribal arithmetic, administration, astronomy, mythic chronology | King List antediluvian reigns are mathematically structured; literal historicity is not established. |
Egyptian | decimal counting; 365-day civil calendar | 30-day months + 5 epagomenal days; later Sothic realignment ~1460 Julian years | Civil administration, Nile/Sirius seasonal observation | The long Sothic cycle follows drift between a 365-day civil year and the solar/Sirius year. |
Hebrew / Biblical | primarily decimal language with strong 7-structures | 7-day week; 7-year sabbatical; 7×7-year Jubilee framework | Ritual, agriculture, covenantal chronology | Long patriarchal ages should be kept separate from calendrical 7-structures until tested. |
Greek / Hellenistic | decimal language with inherited Near Eastern astronomy | Metonic 19-year lunisolar relation; later Callippic refinements | Lunisolar reconciliation, eclipse/planetary astronomy | Shows how observed cycles generate compact integer approximations. |
Iranian / Zoroastrian | cosmological millennial structure | 12,000-year cosmic history often expressed as 4 × 3,000 | Mythic-cosmic chronology | Iranica notes a mythological cosmic calendar; historical events were fitted inside it. |
Indian / Purāṇic | decimal notation with nested astronomical/cosmological ratios | Kali 432,000; Dvāpara 864,000; Tretā 1,296,000; Kṛta 1,728,000; Mahāyuga 4,320,000 | Cosmological ages; 4:3:2:1 structure; divine/human-year conversion | The 432 family is explicit, but its relation to Mesopotamian sexagesimal structures requires historical and statistical testing. |
Chinese / East Asian | decimal notation; combinatorial 10×12 stem-branch architecture | 60-term sexagenary cycle | Day/year naming, calendrical ordering, Jupiter-associated traditions | 60 appears by least-common-multiple structure, not necessarily by direct Mesopotamian inheritance. |
Maya | vigesimal with calendrical modification | 20 k’in = uinal; 18 uinal = 360-day tun; 20 tun = katun; 20 katun = 144,000-day baktun | Absolute chronology plus ritual/solar cycles | A powerful example of mixed-radix timekeeping generated around a 360-day tun inside a largely base-20 system. |
Aztec / Central Mexican | 20-based counting with paired calendrical cycles | 260-day ritual cycle; 365-day solar cycle; 18,980-day / 52-year Calendar Round | Ritual, civic time, New Fire cycle | The 52-year recurrence is a least-common-multiple phenomenon: 73×260 = 52×365. |
3. Why 60 Matters
Sixty is not merely a cultural curiosity. It is highly composite: 60 = 2² × 3 × 5 and therefore divides evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. For repeated subdivision of circles, days, fractions, and astronomical intervals, this property is extraordinarily useful. Babylonian mathematical astronomy later exploited sexagesimal place-value notation and period relations in highly developed predictive schemes. Modern survivals - 60 seconds, 60 minutes, 360 degrees - remind us that a useful representational architecture can outlive the civilization that developed it.
60 = 2² × 3 × 5
The proposed shorthand phrase ‘base-60 as spacetime recordation’ is therefore strongest when stated precisely: a divisible radix can compress recurring temporal and angular relationships into smaller integer structures. It records the geometry and recurrence of observed motion efficiently. This is a claim about representation, not about the ontology of spacetime.
4. The 432 Family
The recurrence of 432-related values warrants structured study because it can be described without mystical assumptions. The Sumerian King List includes 43,200; traditional Purāṇic chronology gives Kali Yuga as 432,000 human years and a Mahāyuga as 4,320,000. In decimal notation these values look like shifted versions of the same motif. In sexagesimal arithmetic they also remain unusually compact.
43,200 = 12 × 60²
432,000 = 2 × 60³
4,320,000 = 20 × 60³
Figure 2. The 432 family remains structurally simple under sexagesimal decomposition. Decimal resemblance alone is weak evidence; cross-base simplicity is the more interesting observation.
The crucial test is comparative. Highly factorable numbers recur because they are useful. Cultural transmission between ancient mathematical traditions also occurred over long periods. Therefore the existence of matching integers cannot by itself demonstrate common geophysical knowledge. A meaningful result requires showing that the observed cross-cultural network of ratios is denser, simpler, or more astronomically informative than would be expected from ordinary arithmetic conventions and documented transmission.
5. Earth as the Shared Observational Frame
Every terrestrial civilization, regardless of language, began from the same planet. Their latitude, climate, horizon, political history, and observational precision differed; the underlying platform did not. They encountered the same solar year, the same Moon, the same planetary synodic phenomena, the same precessional sky, and the same terrestrial rotation. This does not force calendars to become identical. It does create a common source from which different mathematical encodings can overlap.
Shared terrestrial observables + different cultural transforms → partially overlapping time architectures
This is the central hypothesis of the paper. Cross-cultural overlap is predicted even without direct cultural contact because multiple observers are sampling the same physical system. Cultural diffusion, meanwhile, can strengthen or reshape that overlap. The empirical task is to estimate how much correspondence is expected from shared observation, how much from arithmetic, and how much from transmission.
Figure 3. Selected ancient and astronomical intervals converted to Earth days and displayed logarithmically. The purpose is not to imply equivalence, but to make scale, nesting, and clustering visible without allowing the largest values to dominate the page.
6. Personification, Kingship, and the Ontology Problem
Ancient texts often express celestial, environmental, political, and cosmological entities as persons or gods. Consequently, a named figure in a mythic chronology cannot automatically be classified as an ordinary biological individual. The Sumerian King List itself begins with kingship descending from heaven, contains mythic material, and includes Dumuzid, a figure with divine associations. The proper research question is therefore not ‘Were these people really forty thousand years old?’ but ‘What category of quantity did the text intend the reign to represent, and did that category change across textual layers?’
Possible interpretations - literal regnal duration, dynastic aggregation, symbolic magnitude, ritual number, astronomical interval, literary idealization, or personified cosmic phase - must be treated as competing models. No model should be selected merely because it produces a desirable numerical match.
7. Biblical Longevity as a Separate Test Case
The long lifespans in Genesis raise a related but distinct problem. Calendar conversion is one possible hypothesis, but simply dividing every age by twelve or another convenient factor is methodologically weak. The stronger procedure is to preserve each age, identify internal arithmetic structure, test whether special values cluster around calendrical or astronomical quantities, compare textual variants, and determine whether the genealogy uses multiple numerical classes. Enoch’s reported 365 years is especially conspicuous in a calendrical context, but a conspicuous value is a clue, not a conclusion.
8. The Master Dataset
Field | Purpose |
Tradition / text / artifact | Keeps each claim tied to a specific historical source. |
Earliest attested date and textual layer | Separates original evidence from later elaboration. |
Native interval and native unit | Prevents modern-year translation from replacing the original mathematical object. |
Radix / mixed-radix structure | Records base 10, 12, 20, 60, combinatorial systems, or uncertain structure. |
Prime factorization | Allows objective comparison of divisibility and numerical simplicity. |
Modern duration in days | Provides one common physical scale. |
Observational referent | Solar, lunar, planetary, seasonal, eclipse, ritual, regnal, mythic, or unknown. |
Evidence class | Observed, computed, literary, ritual, theological, reconstructed. |
Uncertainty interval | Prevents false precision. |
Known transmission pathways | Controls for cultural borrowing. |
Candidate mathematical links | Stored only after the primary record is frozen. |
9. Statistical Guardrails Against Numerology
A dataset containing many cultures, units, divisors, multiples, and uncertain dates can generate apparently astonishing coincidences by chance. The architecture therefore needs preregistered comparison rules. At minimum, the analysis should freeze the source list before searching for matches; use one common unit for physical comparison; distinguish exact relations from approximate ones; penalize additional transformations; and compare observed network density against randomized datasets that preserve the marginal distribution of interval sizes and cultural grouping.
Match score = simplicity × precision × independence × observational relevance
A proposed link should become weaker when it requires arbitrary unit changes, large tolerances, multiple ad hoc multipliers, or historically impossible transmission. It should become stronger when the relation is exact in native arithmetic, independently attested, tied to an observable recurrence, and reproduced across sources not derived from one another.
10. Visualization Architecture
The visual layer is not decoration; it is part of the method. Four complementary views are recommended: (1) a logarithmic duration map, as in Figure 3; (2) factor trees and radix decompositions for each culturally salient number; (3) a network graph in which nodes are native intervals and edges represent exact integer ratios, least-common-multiple relations, or documented derivation; and (4) stacked cultural timelines that keep source dates separate from the durations those sources describe. The reader should be able to zoom from a one-day unit to multi-million-year cosmological ages without losing the relational structure.
11. Simulation-Ready Hypotheses
H1 - Shared-observer hypothesis: independently developed terrestrial calendars will exhibit more overlap in astronomical ratio structure than matched random numerical systems because they sample the same sky and planet.
H2 - Sexagesimal compression hypothesis: intervals associated with Mesopotamian and downstream astronomical traditions will show unusually low description length when represented in base 60.
H3 - 432-family hypothesis: the cross-cultural recurrence of 432-related quantities will remain statistically unusual after controlling for high divisibility, powers of 10, and documented cultural transmission.
H4 - Translation-distortion hypothesis: some apparently extraordinary ancient durations become structurally simpler when analyzed in native units, reducing the need for literal biological interpretation.
H5 - Mixed-origin hypothesis: the best model will require all three mechanisms - shared observation, mathematical convenience, and cultural transmission - rather than any single universal explanation.
12. What This Paper Does Not Claim
This framework does not claim that all ancient cultures possessed a hidden master calendar; that 432 is a universal physical constant; that mythic kings were planets; that biblical patriarchs were necessarily calendrical abstractions; or that cross-cultural numerical resemblance proves forgotten global contact. Those remain hypotheses of very different evidential strength. The paper instead creates the architecture required to test them without collapsing mythology, mathematics, astronomy, and geophysics into one undifferentiated story.
Conclusion
The most productive way to compare ancient time systems is to stop beginning with modern years. The native unit is part of the meaning. A Sumerian value such as 43,200 becomes twelve units of 60²; a Maya baktun is 144,000 days inside a mixed vigesimal calendar; a Chinese sixty-cycle emerges from paired periodic sequences; the Egyptian Sothic interval arises from calendar drift; and the Indian yuga system explicitly scales enormous ages through fixed ratios. These structures need not be manifestations of one hidden clock to be related. They are different mathematical responses to recurrence, measurement, inheritance, and cosmology from a shared terrestrial observational frame. The Master Time Architecture therefore treats ancient chronologies as a relational dataset. Its next task is empirical: freeze the corpus, normalize without erasing native structure, map the factor network, simulate expected coincidences, and determine which apparent correspondences survive rigorous controls. If a deeper architecture exists, this method is designed to reveal it; if it does not, the same method should show where the resemblance ends.
References
Ashmolean Museum, University of Oxford. “Sumerian King List.” https://ashmolean.web.ox.ac.uk/sumerian-king-list
Electronic Text Corpus of Sumerian Literature (ETCSL), University of Oxford. “The Sumerian King List (c.2.1.1).” https://etcsl.orinst.ox.ac.uk/
ORACC / ePSD2. “The Sumerian King List.” https://oracc.museum.upenn.edu/epsd2/literary/Q000371
Smithsonian National Museum of the American Indian. “Maya Calendar Converter / Living Maya Time.” https://maya.nmai.si.edu/calendar/maya-calendar-converter
Smithsonian National Museum of the American Indian. “The Meaning of 2012.” https://maya.nmai.si.edu/2012-resetting-count/meaning-of-2012
Morley, Sylvanus G. Introduction to the Study of the Maya Hieroglyphs. Bureau of American Ethnology Bulletin 57. Smithsonian Institution. (Calendar Round arithmetic: 18,980 days = 52×365 = 73×260.)
Encyclopaedia Iranica. “Zoroaster ii. General Survey.” (Discussion of the 12,000-year Zoroastrian cosmic calendar.) https://www.iranicaonline.org/articles/zoroaster-ii-general-survey/
Encyclopaedia Iranica. “Astrology and Astronomy in Iran.” https://www.iranicaonline.org/articles/astrology-and-astronomy-in-iran/
Indian National Centre for the Arts (IGNCA). The Yugas, chapter reproduced in archival PDF. Values: 432,000; 864,000; 1,296,000; 1,728,000; 4,320,000 years. https://ignca.gov.in/Asi_data/8341.pdf
Encyclopedia of ancient/modern calendrical literature: Metonic cycle = 235 synodic months ≈ 19 tropical years; Egyptian 365-day civil year and Sothic realignment ≈ 1,460 Julian years.
Leviticus 25:8–12. Seven sabbaths of years and the Jubilee framework.
The Oscillatory Earth Architecture
Coupled Cycles, Drifting Periods, Thresholds, and Scale-Dependent Regularity in a Dynamical Planet
DOI: To be assigned
John Swygert
August 25, 2026
Abstract
Earth is often described through isolated cycles: annual seasons, El Niño-Southern Oscillation, solar variability, polar motion, orbital precession, obliquity, eccentricity, glacial pacing, abrupt paleoclimate events, and still longer geological changes. Studied separately, these processes can appear to form an untidy collection of unrelated periods. This paper proposes an Oscillatory Earth Architecture: a multiscale dynamical framework in which Earth is treated as a spinning, deformable, dissipative body whose atmosphere, ocean, cryosphere, hydrology, mantle, core, biosphere, orbital geometry, and external forcing exchange energy, momentum, and mass across nested timescales. The central claim is deliberately weaker than a single-master-cycle hypothesis. Earth should be expected to exhibit frequency bands, quasi-periodic recurrences, beat phenomena, phase locking, drifting periods, state-dependent responses, and threshold transitions rather than clock-perfect repetition. A key methodological principle is scale dependence: structures that appear irregular at fine temporal resolution may become regular when viewed through progressively coarser windows, while apparently regular macro-patterns may fragment when magnified. The paper specifies a simulation-ready state-vector model, preregistered tests for periodicity versus stochastic recurrence, wavelet and cross-spectral methods, threshold and early-warning diagnostics, and explicit falsification criteria. It also separates the physical Earth model from ancient calendrical data so that any later comparison with the Master Time Architecture cannot be manufactured retrospectively. The goal is not to prove that every major event belongs to one hidden cycle, but to determine whether a stable relational architecture of interacting oscillations can explain why Earth repeatedly enters recognizable regimes without repeating them exactly.
Keywords: Earth system dynamics, oscillation, quasi-periodicity, coupled oscillators, paleoclimate, Milankovitch cycles, ENSO, polar motion, threshold dynamics, wavelet analysis, regime shifts, phase locking
1. From “Cycles” to an Architecture
The usual language of Earth science encourages compartmentalization. ENSO belongs to climate dynamics; precession belongs to celestial mechanics; the Chandler wobble belongs to geodesy; ice-sheet cycles belong to paleoclimatology; length-of-day variations belong to Earth orientation; earthquakes belong to geophysics. Yet the physical planet does not respect disciplinary boundaries. The atmosphere exchanges angular momentum with the solid Earth, ocean and ice redistribute mass, lunar tides alter rotation, orbital geometry changes insolation, and climate feedbacks change the distribution of water and ice that in turn measurably changes polar motion and day length. NASA-funded work has quantified modern climate-driven changes in polar motion and length of day, while geodetic services continuously measure the nonuniformity of Earth rotation.
The architecture proposed here therefore begins with coupling rather than with a catalogue. Earth is modeled as a system of interacting state variables, each with characteristic response times, memory, forcing, and feedback. The toy-top analogy is useful but incomplete. A rigid toy top gradually loses energy while retaining a fairly stable geometry. Earth is a top whose mass distribution, fluid circulation, surface loading, boundary conditions, and forcing all evolve while it spins.
Figure 1. Conceptual Oscillatory Earth Architecture. The arrows represent possible two-way coupling; they do not imply equal strength or instantaneous causation.
2. Periodic, Quasi-Periodic, Stochastic, and Threshold Behavior
A central guardrail is vocabulary. “Cycle” is often used too loosely. A strictly periodic process returns after a fixed interval T. A quasi-periodic process is organized around characteristic frequencies but allows phase drift or superposition of incommensurate frequencies. A stochastic recurrence can produce clusters or apparent spacing without a deterministic clock. A threshold system can remain in one regime despite ongoing forcing and then switch rapidly when a stability boundary is crossed. Earth exhibits all four kinds of behavior in different subsystems.
Strict periodicity: X(t + T) = X(t)
Drifting recurrence: Tₙ = T₀ + εₙ
Coupled state: X(t) = Σᵢ Aᵢ(t) sin[2πt / Tᵢ(t) + φᵢ(t)] + η(t)
The final term η(t) represents unresolved variability or stochastic forcing. The amplitudes Aᵢ, periods Tᵢ, and phases φᵢ may themselves vary. This formulation captures the user-level intuition behind the worn-wheel analogy: a system can preserve recognizable recurrence while changing enough that no two revolutions are identical.
3. A Ladder of Known Earth Timescales
The architecture must begin from well-established characteristic timescales rather than from desired matches. The following values are illustrative anchors, not a claim that each is a clean oscillator of equal physical status.
Process | Characteristic timescale | Status in this paper | Primary caution |
|---|
Annual seasonal forcing | 1 year | Core periodic | Amplitude and regional impact vary |
Chandler wobble | ~435 days | Core free rotational mode | Excitation and amplitude vary |
ENSO | Irregular ~2-7 years | Core coupled ocean-atmosphere mode | Not clock-periodic |
Solar activity cycle | ~11 years | Core external variability | Climate response is not a simple one-to-one mapping |
Core/length-of-day variability | Interannual to multidecadal; one reported 65-80 y mode | Candidate internal coupling band | Mechanisms and climate links require cautious interpretation |
Dansgaard-Oeschger recurrence | Millennial; ~1,470 y proposed in glacial records | Contested / test case | Regularity may be state dependent or statistically spurious |
Axial/climatic precession | ~23,000 years average | Core orbital forcing | Acts through seasonal/latitudinal insolation |
Obliquity | ~41,000 years | Core orbital forcing | Climate expression depends on feedbacks |
Eccentricity | ~100,000 years dominant band | Core orbital forcing | Weak direct annual-mean forcing; nonlinear climate response matters |
Figure 2. Selected characteristic timescales shown on a logarithmic axis. The ladder emphasizes nested bands rather than a single universal period.
NASA describes eccentricity, obliquity, and precession as the accepted long-timescale orbital framework for glacial-interglacial climate pacing. NOAA describes ENSO as an irregular two-to-seven-year oscillation. IERS and the U.S. Naval Observatory describe the Chandler wobble as a roughly 435-day component of polar motion. These provide a set of anchored scales against which more speculative recurrence claims can be tested rather than assumed.
4. The Same Forcing Can Produce Different Outcomes
A fundamental property of nonlinear systems is state dependence. The same perturbation can have a small effect when the system is far from a threshold and a large effect when the system is near one. This is why the architecture should never predict event magnitude from forcing amplitude alone.
Impact(t) = f[forcing(t), state(t), coupling(t), memory(t), resilience(t)]
The last glacial climate provides a useful example. Dansgaard-Oeschger events show abrupt warming transitions followed by slower relaxations. A proposed ~1,470-year recurrence has been modeled as an emergent response to shorter forcings interacting with nonlinear thermohaline dynamics, yet statistical work also shows that the event waiting times can be compatible with stochastic timing. Both results belong in the architecture. They demonstrate that an apparent long period may emerge without a corresponding external master clock, and that visual regularity must be tested against null models.
5. Beats, Harmonics, and Constructive Alignment
When several oscillatory processes operate simultaneously, their superposition can create beat frequencies and recurrent windows of constructive alignment. The physical implication is not that every alignment produces catastrophe. Rather, alignment can create intervals when a threshold is more easily crossed or when a weak forcing is amplified by background state.
Ψ(t) = Σᵢ wᵢXᵢ(t)
Transition condition: Ψ(t) > Θ(t)
The threshold Θ(t) is allowed to move because the planet itself evolves. Ice volume, greenhouse-gas concentration, continental geometry, vegetation, salinity, ocean gateways, and background temperature can all change the response surface. A recurrence architecture can therefore persist even when the exact event spacing and magnitude drift.
Figure 3. Illustrative constructive alignment. Threshold crossings occur irregularly even when the contributing oscillations themselves are regular or quasi-regular.
6. The Microscope and the Distant-Planet View
The project requires an explicit scale operator. A century of weather can look chaotic day by day and highly structured when aggregated seasonally. A glacial record can look irregular event by event but organized when viewed over tens of millennia. Conversely, coarse averaging can manufacture smoothness by erasing meaningful variability. The methodological task is therefore not to choose the “right” scale after seeing the pattern, but to examine a preregistered ladder of temporal resolutions and record which structures persist.
Xτ(t) = Cτ[X(t)]
Here Cτ is a coarse-graining operator over timescale τ. The analysis should use multiple window widths and, where possible, continuous wavelet transforms so that frequency bands can strengthen, weaken, or drift through time rather than being forced into a stationary Fourier picture.
Figure 4. Conceptual demonstration of scale-dependent regularity. Fine-scale variability may obscure a lower-frequency architecture that becomes visible only after controlled coarse-graining.
7. Rotation, Water, Ice, and the Moving Mass Problem
The spinning-top analogy becomes physically concrete through conservation of angular momentum and mass redistribution. NASA reports that atmosphere and ocean exchange angular momentum with the solid Earth and alter length of day on seasonal and interannual scales. Modern ice loss and groundwater redistribution also shift polar motion and lengthen the day. The Moon’s tidal torque drives a much longer secular slowing. Earth’s rotation is therefore not a perfect independent metronome; it is a measured output of a coupled mass-and-momentum system.
This point matters because it links phenomena that are usually discussed separately without claiming that one simple causal chain explains all of them. Water movement can change rotation; rotation shapes Coriolis forces; ocean and atmospheric circulation move water and momentum; ice and groundwater alter surface loading. These are real couplings. Their strengths, lags, and directions must be estimated empirically.
8. Earthquakes as a Boundary Case
Large earthquakes provide a useful methodological test because they dramatically redistribute mass and can measurably alter Earth’s figure axis or calculated day length, yet this does not imply a demonstrated global earthquake cycle synchronized to climate or orbital forcing. NASA has calculated tiny rotational effects from major earthquakes, but the ordinary atmosphere and oceans produce larger short-term rotation changes. Therefore “earthquake activity increases every X years” should enter the simulation only as a hypothesis to test against global seismic catalogues, not as an assumed component of the architecture.
A strong analysis would separate tectonic loading cycles, aftershock clustering, regional recurrence, tidal triggering hypotheses, and global event counts. If no robust cross-scale periodicity survives declustering and null-model testing, earthquakes should be excluded from the master oscillator set even though individual earthquakes participate in the planet’s mass redistribution.
9. Abrupt Events and Regime Shifts
Abrupt paleoclimate events are especially valuable because they reveal the difference between forcing and response. The 8.2 ka event is widely associated with freshwater input into the North Atlantic and a weakened overturning circulation. Dansgaard-Oeschger events are strongly state dependent and characteristic of glacial conditions. The physical architecture should therefore classify events by mechanism and background climate rather than placing all “resets” on one undifferentiated timeline.
A regime shift is represented here as movement between attractor-like states rather than as an instantaneous planetary reset. A system can trend for decades or centuries before crossing a threshold, then relax toward another state over a different timescale. This preserves the intuition of an upward or downward trajectory followed eventually by reversal while avoiding the false expectation of sharp, clock-timed discontinuities.
10. Early-Warning Signals Without Prophecy
If some transitions are genuine bifurcations, the model can search for statistical warning behavior such as rising variance, increasing autocorrelation, altered recovery time, flickering between states, and changes in cross-correlation among subsystems. These are research diagnostics, not prophecy. Early-warning signals can produce false positives, can depend on detrending choices, and may not appear before all kinds of abrupt transition. They should therefore be evaluated on historical and paleoclimate intervals where the outcome is already known before they are applied prospectively.
The same discipline applies to contemporary climate. Current anthropogenic warming cannot be attributed to Milankovitch cycles; NASA explicitly notes that the orbital cycles operate on far longer timescales and do not explain the rapid modern warming trend. The Oscillatory Earth Architecture must therefore include external and anthropogenic forcing where appropriate rather than using natural cycles as a universal explanation.
11. The Simulation-Ready State Vector
The first simulation should be deliberately simpler than a general circulation model. Its purpose is to test the architecture, not to reproduce every physical process. Define a state vector containing normalized observables or proxy indices:
S(t) = [R, P, O, E, A, M, I, H, V, G, C, ...]
where R denotes rotation/polar-motion variables, P orbital/precessional forcing, O ocean state, E ENSO, A Atlantic overturning, M monsoon state, I ice/cryosphere, H hydrology, V volcanism, G geomagnetic/core-linked proxies where justified, and C atmospheric composition or radiative forcing. The exact variable list should be frozen before hypothesis testing.
dSᵢ/dt = Fᵢ(Sᵢ) + Σⱼ CᵢⱼSⱼ + Uᵢ(t) + ηᵢ(t)
The matrix C encodes coupling. Uᵢ(t) contains externally specified forcing such as orbital insolation or volcanic impulses. ηᵢ(t) represents stochastic variability. Parameter drift can be added only where justified by long records. The simulation should be run both with and without nonlinear thresholds so that apparent recurrence cannot automatically be attributed to tipping behavior.
Figure 5. Proposed workflow. The physical Earth architecture is frozen and tested before any comparison with ancient chronologies.
12. Statistical Program
The analysis should combine complementary methods rather than rely on one spectral plot. A minimum program includes: (1) Lomb-Scargle or appropriate spectral estimation for uneven paleoclimate series; (2) continuous wavelet transforms for time-varying frequency bands; (3) cross-wavelet coherence and phase analysis for candidate coupling; (4) recurrence-interval and survival analysis for event timing; (5) surrogate-data and red-noise null models; (6) change-point detection; (7) state-space or hidden-Markov models for regime structure; and (8) out-of-sample simulation tests.
The critical principle is preregistration. Candidate frequency bands, tolerance windows, smoothing scales, event definitions, and multiple-comparison corrections should be specified before searching for matches. If a 1,470-year band is tested, for example, the allowed tolerance cannot be widened after inspecting the answer. If several related periods are searched simultaneously, the null model must reflect that search freedom.
13. Falsifiable Predictions
The framework makes several predictions that can fail. First, some frequency bands should persist across independent proxies and analytic methods, but their amplitude and phase should drift. Second, apparent long recurrence intervals should sometimes be reproducible from interactions among shorter modes without requiring a forcing at the long period itself. Third, threshold-sensitive abrupt events should cluster preferentially in particular background states rather than occurring uniformly through time. Fourth, coarse-grained representations should reveal stable low-frequency organization that survives reasonable changes of smoothing window. Fifth, many visually attractive “cycles” should disappear under red-noise, Poisson, or phase-randomized null models. A model that finds every proposed cycle is a failed model because it has no capacity to reject patterns.
14. Relationship to the Master Time Architecture
This paper is intentionally independent of the comparative ancient chronology project. The Master Time Architecture asks whether terrestrial cultures encoded overlapping numerical and calendrical structures because they observed the same planet. The present paper asks what physical oscillatory structure Earth actually possesses. These data streams must not be tuned to one another.
Physical Earth architecture ⟂ Ancient time architecture during model construction
Only after both architectures are frozen should a synthesis paper ask whether culturally encoded intervals overlap independently detected physical frequency bands more strongly than arithmetic convenience, cultural transmission, and chance predict. This separation is the principal defense against numerology.
15. What the Architecture Does Not Claim
The Oscillatory Earth Architecture does not claim that Earth experiences a civilization-ending reset at a fixed interval. It does not claim that all climate events share one cause, that earthquakes are controlled by climate cycles, that every ancient age records a geophysical period, or that modern warming is an orbital-cycle phenomenon. It does not require perfect periodicity. Its narrower claim is that a rotating, coupled, nonlinear planet should contain persistent characteristic timescales whose interactions can create scale-dependent recurrence, changing regimes, and threshold behavior. That claim is both physically motivated and falsifiable.
Conclusion
Earth is not one clock. It is a hierarchy of clocks, oscillators, memories, forcings, and slowly changing boundaries coupled through a single physical body. Some components are nearly periodic; others are quasi-periodic, stochastic, state dependent, or threshold driven. The result should resemble neither perfect repetition nor pure randomness. It should resemble a dynamic wheel whose balance, loading, and material condition change while it turns: recognizable structure with drift.
The practical implication is methodological. The search for recurrence must move away from isolated date matching and toward a multiscale architecture built from independently measured processes. The correct question is not “What is Earth’s master period?” but “Which frequency bands persist, how do they couple, when do they align, how do their periods drift, and under what states do small changes produce large transitions?” Viewed under a microscope, individual events will remain irregular. Viewed from progressively greater temporal distance, the hypothesis predicts that some relational structure will persist. The proposed simulation program is designed to discover whether that structure is real - and, equally importantly, to expose where it is not.
References
NASA Science. “Milankovitch (Orbital) Cycles and Their Role in Earth’s Climate.” Updated 2024. https://science.nasa.gov/science-research/earth-science/milankovitch-orbital-cycles-and-their-role-in-earths-climate/
NASA Science. “Why Milankovitch (Orbital) Cycles Can’t Explain Earth’s Current Warming.” https://science.nasa.gov/science-research/earth-science/why-milankovitch-orbital-cycles-cant-explain-earths-current-warming/
NOAA Climate.gov. “El Niño & La Niña (El Niño-Southern Oscillation).” ENSO described as an irregular two-to-seven-year pattern. https://www.climate.gov/enso
International Earth Rotation and Reference Systems Service (IERS). Glossary: “Chandler wobble,” approximately 435 days. https://www.iers.org/iers/en/service/glossary/functions/glossary/C
U.S. Naval Observatory. “What Are Earth Orientation Parameters?” Annual and Chandler components of polar motion. https://maia.usno.navy.mil/information/what-is-eop
NASA Jet Propulsion Laboratory. “NASA-Funded Studies Explain How Climate Is Changing Earth’s Rotation.” July 19, 2024. https://www.jpl.nasa.gov/news/nasa-funded-studies-explain-how-climate-is-changing-earths-rotation/
NASA Jet Propulsion Laboratory. “NASA Explains Why June 30 Will Get Extra Second.” Atmosphere, ocean, groundwater, ice, tides, and ENSO contributions to length-of-day variability. https://www.jpl.nasa.gov/news/nasa-explains-why-june-30-will-get-extra-second/
NASA Jet Propulsion Laboratory. “All Days Are Not Created Equal.” Earth rotation variability, atmospheric angular momentum, and core-linked longer patterns. https://www.jpl.nasa.gov/news/all-days-are-not-created-equal/
NASA Jet Propulsion Laboratory. “Japan Quake May Have Shortened Earth Days, Moved Axis.” March 2011. https://www.jpl.nasa.gov/news/japan-quake-may-have-shortened-earth-days-moved-axis/
Braun, H., Christl, M., Rahmstorf, S., et al. “Possible solar origin of the 1,470-year glacial climate cycle demonstrated in a coupled model.” Nature 438, 208-211 (2005). https://doi.org/10.1038/nature04121
Boers, N. “Early-warning signals for Dansgaard-Oeschger events in a high-resolution ice core record.” Nature Communications 9 (2018). https://doi.org/10.1038/s41467-018-04881-7
Hays, J. D., Imbrie, J., & Shackleton, N. J. “Variations in the Earth’s Orbit: Pacemaker of the Ice Ages.” Science 194 (1976): 1121-1132.
Oscillatory Earth Architecture
Formal Simulation Specification v1.1
Variables, Coupling, Lags, Nonlinearities, Null Models, Preregistration, and Falsification
John Swygert
August 25, 2026
Purpose
This document operationalizes The Oscillatory Earth Architecture as an executable research design. It is not a new claim layer. Its function is to freeze model components before exploratory fitting, make all search freedom explicit, and define what evidence would count for or against persistent multiscale recurrence in the Earth system.
1. Governing Principle
Earth is treated as a rotating, deformable, dissipative, non-stationary system containing coupled subsystems with different characteristic timescales, memories, forcings, lags, and thresholds. The model does not assume one master period. It tests whether persistent frequency bands, drifting recurrences, beat phenomena, phase relationships, and state-dependent transitions emerge more strongly than expected under appropriate stochastic null models.
Earth signal = forcing + internal modes + coupling + memory + thresholds + stochastic variability
Four ontological categories must remain separate throughout the analysis:
Forcing: an externally or independently specified driver, such as orbital insolation or a volcanic impulse.
Mode: a dynamical subsystem or internally organized oscillatory behavior, such as ENSO or a rotational mode.
Response: an observed consequence, such as drought, ice-volume change, circulation reorganization, or polar-motion shift.
Recurrence band: a statistical feature of the record. A recurrence band is not automatically a forcing or a causal mechanism.
forcing != mode != response != recurrence band
2. Frozen State Vector
The first-generation model uses a deliberately compact state vector. Variables may be represented by observed series or standardized proxy indices. The exact inclusion list must be frozen before frequency matching or ancient-calendar comparison.
S(t) = [R, P, O, E, A, M, I, H, V, G, C]
Code | Subsystem | Primary observable class | Expected memory / lag | Status |
|---|
R | Rotation / polar motion | Length of day, polar motion, angular-momentum exchange | days to decades | Core |
P | Orbital / precessional forcing | Precession, obliquity, eccentricity, insolation geometry | 10^4-10^5 y | Core external |
O | Ocean state | Heat content, basin-scale circulation, SST structure | months to millennia | Core |
E | ENSO | Niño-region or multivariate ENSO indices | months to years | Core mode |
A | Atlantic overturning | AMOC proxies / circulation strength | years to millennia | Core/candidate by era |
M | Monsoon state | Regional monsoon proxy composites | years to millennia | Core/candidate by dataset |
I | Cryosphere | Ice volume, sea ice, ice-sheet proxies | years to 10^4 y | Core |
H | Hydrology | Groundwater, river/lake, moisture-balance proxies | months to millennia | Core/candidate |
V | Volcanism | Aerosol / sulfate / eruption forcing | impulse to years | External impulse |
G | Geomagnetic / core-linked proxies | Field intensity / justified core-linked observables | decades to millennia | Candidate |
C | Atmospheric composition / radiative forcing | CO2, CH4, aerosol/radiative forcing | years to 10^5 y | Core forcing/state |
Rule: candidate variables may be removed for weak evidence or inadequate record length. New variables may not be added after the preregistered analysis begins unless the run is explicitly labeled exploratory and excluded from confirmatory claims.
3. Lagged Coupled-State Model
The governing equation must permit delayed coupling. Earth-system transfers are not instantaneous: atmospheric torque can act rapidly, ocean adjustment can be slower, ice-sheet response slower still, and glacial-isostatic effects may persist for millennia.
dS_i/dt = F_i(S_i) + sum_j C_ij(t) * S_j(t - tau_ij) + U_i(t) + eta_i(t)
Definitions:
F_i(S_i): intrinsic subsystem dynamics, including damping, self-excitation, or state-dependent restoring terms.
C_ij(t): signed coupling strength from subsystem j to subsystem i. It may be constant in the baseline model and slowly varying only in prespecified sensitivity runs.
tau_ij: physical or empirically estimated lag from j to i.
U_i(t): exogenous forcing specified independently of model output.
eta_i(t): unresolved variability or stochastic forcing.
3.1 Coupling matrix C
C is directed and generally asymmetric. C_ij need not equal C_ji. A nonzero entry is permitted only when a physically plausible or empirically defensible pathway exists. Statistical coherence alone does not authorize a coupling edge.
C_ij != C_ji in general
3.2 Lag matrix tau
The lag matrix is independent of coupling strength. For each permitted edge, lag bounds must be specified from physics or prior empirical literature before optimization. The model may estimate a lag only within that frozen interval.
Coupling class | Illustrative direction | Permitted lag class | Guardrail |
|---|
Fast exchange | Atmosphere -> rotation | days to seasons | Do not infer causality from same-day correlation alone |
Intermediate adjustment | Ocean <-> atmosphere | months to decades | Allow phase drift and regional dependence |
Slow memory | Cryosphere -> ocean / rotation | years to millennia | Account for persistence and hysteresis |
Very slow boundary evolution | Ice/solid-Earth loading -> figure/state | centuries to millennia | Treat as evolving boundary, not a short oscillator |
Impulse forcing | Volcanism -> atmosphere/ocean | near-zero onset; multi-year decay | Model impulse and decay separately |
4. Allowed Dynamical Forms
Model complexity increases by tiers. A more complex tier is accepted only if it improves preregistered out-of-sample performance and survives null-model comparison.
Tier 0 - Linear / stochastic baseline
dS/dt = A S(t) + B U(t) + eta(t)
Purpose: establish how much apparent structure is recoverable without nonlinear thresholds or time-varying parameters.
Tier 1 - Lagged linear coupling
dS_i/dt = a_i S_i + sum_j C_ij S_j(t - tau_ij) + U_i + eta_i
Tier 2 - Weak nonlinearities
dS_i/dt = F_i(S_i) + sum_j C_ij S_j(t - tau_ij) + U_i + eta_i
Permitted F_i forms include prespecified saturation, damping, or low-order polynomial terms. High-order polynomial fitting is prohibited in confirmatory runs because it can absorb arbitrary structure.
Tier 3 - Threshold / regime dynamics
Psi(t) = sum_i w_i X_i(t)
transition if Psi(t) > Theta_forward(t)
return if Psi(t) < Theta_return(t)
Hysteresis is allowed: the forward and return thresholds need not be equal. This permits a system to cross into a new regime without retracing the identical path when forcing reverses.
Theta_forward != Theta_return
5. Beat Frequencies, Harmonics, and Emergent Long Periods
Long recurrence intervals may emerge from interactions among shorter modes. A long observed band is therefore not evidence by itself for a forcing at that same period.
f_beat = |f_1 - f_2|
T_beat = 1 / |f_1 - f_2|
Confirmatory tests must distinguish: (a) an independently present long-period forcing, (b) a beat or combination frequency generated by shorter modes, (c) a nonlinear threshold response that recurs near preferred states, and (d) stochastic clustering that only resembles a cycle.
6. Multiscale Observation and Coarse-Graining
The model explicitly tests the microscope-versus-distant-planet principle. A structure counts as persistent only if it survives reasonable changes in temporal resolution rather than appearing at one hand-picked smoothing window.
X_tau(t) = C_tau[X(t)]
Preregistered analysis windows should include a ladder appropriate to each dataset, for example: native resolution, 10x aggregation, 100x aggregation, and physically meaningful windows such as seasonal, decadal, centennial, millennial, and orbital-scale bands where record length permits.
6.1 Persistence criterion
A candidate band is "multiscale persistent" only if all of the following are satisfied:
It appears in at least two independent proxies or observational products for the relevant subsystem.
It survives at least three adjacent preregistered smoothing / scale choices.
Its central frequency remains within the preregistered tolerance band.
It survives the relevant red-noise and phase-randomized null tests after multiple-comparison correction.
It is not created solely by edge effects, interpolation, detrending choice, or a single outlier interval.
7. Frequency-Band Registry
The registry must be frozen before confirmatory search. The first specification uses broad bands rather than exact target dates. Values below are architecture anchors inherited from the paper, not claims that each band has equal physical status.
Band ID | Approximate scale | Example process | Status | Confirmatory treatment |
|---|
B1 | ~1 year | Seasonal forcing | Core periodic | Positive-control band |
B2 | ~435 days | Chandler wobble | Core mode | Positive-control band |
B3 | ~2-7 years | ENSO | Core irregular mode | Band, not fixed period |
B4 | ~11 years | Solar activity | Core external variability | Forcing band |
B5 | ~65-80 years | Core/LOD candidate mode | Candidate | Exploratory-confirmatory boundary |
B6 | ~1,470 years | D-O recurrence proposal | Contested test case | Must beat stochastic waiting-time nulls |
B7 | ~23 kyr | Precession | Core orbital forcing | Positive-control long band |
B8 | ~41 kyr | Obliquity | Core orbital forcing | Positive-control long band |
B9 | ~100 kyr | Eccentricity-dominant pacing | Core orbital forcing | Positive-control long band |
8. Data Architecture
The simulation should consume frozen observational or proxy products through a versioned registry. Each dataset receives metadata sufficient to reproduce every transform.
Required field | Description |
|---|
dataset_id | Permanent internal identifier |
subsystem_code | R, P, O, E, A, M, I, H, V, G, or C |
source / version | Archive, DOI or agency product and version |
time_basis | Calendar years, years BP, ka BP, etc. |
native_resolution | Original time spacing |
coverage | Start and end time |
proxy_or_observable | Direct observation or proxy class |
uncertainty | Dating, measurement, calibration uncertainty |
preprocessing | Detrending, interpolation, normalization rules |
frozen_hash | Checksum or equivalent integrity identifier |
confirmatory_status | Confirmatory, sensitivity, or exploratory |
No ancient calendrical or mythological interval is permitted in this registry during physical-model construction. The physical and cultural architectures remain orthogonal until both are frozen.
9. Preprocessing Rules
Preserve native time axes and uncertainties before resampling.
Use interpolation only when methodologically justified; retain a non-interpolated analysis where possible.
Preregister detrending choices. Run at least one no-detrend sensitivity analysis where stationarity permits.
Standardization may be used for coupling comparison, but raw-unit analyses must be retained for physically interpretable quantities.
For event catalogs, perform declustering where appropriate and report both raw and declustered results.
Do not choose a filter after inspecting whether it reveals the desired frequency.
10. Statistical Analysis Pipeline
1. Freeze data: Lock dataset versions, time bases, preprocessing, and confirmatory status.
2. Positive controls: Recover known annual, Chandler, ENSO-band, and orbital signals where records permit.
3. Spectral estimation: Use Lomb-Scargle or appropriate estimators for irregular sampling; Fourier methods only when assumptions are satisfied.
4. Time-frequency analysis: Use continuous wavelets to measure frequency drift, intermittency, and state dependence.
5. Coupling analysis: Use cross-wavelet coherence, phase analysis, lagged correlation, transfer-entropy or related tools only as prespecified. Statistical association does not equal physical coupling.
6. Event timing: Use recurrence, survival, and point-process methods for abrupt-event catalogs.
7. Regime detection: Use change-point, state-space, or hidden-Markov models to identify attractor-like states.
8. Null comparison: Run all candidate findings through the null suite defined below.
9. Out-of-sample test: Fit on a training interval or subset of proxies and test on held-out intervals / independent records.
10. Freeze Earth architecture: Only after confirmatory testing may results enter a later cultural comparison.
11. Mandatory Null-Model Suite
Every claimed recurrence structure must defeat a null model appropriate to the data-generating problem. No single null is sufficient.
Null ID | Null model | What it preserves | What it tests against |
|---|
N1 | AR(1) red noise | short-memory autocorrelation | spurious low-frequency spectral peaks |
N2 | Fractional Gaussian / long-memory noise | long-range dependence | apparent persistence from scale-free noise |
N3 | Phase-randomized surrogate | power spectrum / amplitude structure | spurious phase alignment and timing coherence |
N4 | Block bootstrap | local dependence | overconfident significance from serial correlation |
N5 | Poisson / renewal process | event-rate structure | apparent event periodicity |
N6 | State-conditioned surrogate | background-state occupancy | false threshold clustering caused by unequal regime duration |
N7 | Cross-series permutation / surrogate coherence | marginal series properties | chance cross-system coherence |
A candidate signal that survives only a weak null but fails an appropriate red-noise, long-memory, phase-randomized, or event-process null is not accepted as structural evidence.
12. Multiple-Comparison and Search-Freedom Control
Freeze all target bands and tolerance widths before confirmatory analysis.
Record every tested band, lag interval, smoothing scale, proxy, region, and model tier.
Apply false-discovery-rate or family-wise correction appropriate to the preregistered family of tests.
Penalize ad hoc integer multiples, divisors, harmonic substitutions, and post-hoc phase shifts.
Any parameter or frequency added after seeing the data is exploratory and cannot be cited as confirmatory evidence in the same analysis.
12A. v1.1 Execution Hardening
The following rules are frozen before Simulation Phase 1. They do not change the conceptual architecture; they remove implementation ambiguity identified during independent review.
12A.1 Common objective and complexity penalty
All model tiers must be compared on the same held-out predictive objective. The primary objective is held-out negative log-likelihood when a probabilistic observation model is available; otherwise use preregistered normalized root-mean-square error (NRMSE). Complexity is reported with BIC as the primary parsimony penalty and AIC as a sensitivity check.
Primary tier score: Score_k = L_holdout,k + lambda * Complexity_k
A higher tier cannot be accepted solely because it fits training data better. It must improve the frozen held-out objective, survive the null suite, and retain physically admissible parameters.
12A.2 Wavelet cone-of-influence rule
Continuous-wavelet significance is confirmatory only outside the cone of influence (COI). A recurrence band fails confirmatory wavelet support if its significance depends primarily on power inside the COI, on padded boundaries, or on an uneven-resampling choice selected after inspection. COI-dependent features may be reported only as exploratory.
12A.3 Machine-readable directed-edge registry
Every permitted coupling edge must be frozen as a directed record before optimization:
Edge_(j->i) = <Source_j, Target_i, LagBounds[tau_min,tau_max], SignConstraint, PhysicalEvidenceClass>
PhysicalEvidenceClass is ordinal: A = directly measured transfer/pathway; B = strongly supported mechanistic literature; C = plausible candidate pathway with limited direct constraint. Class C edges are sensitivity-only unless independently replicated. Statistical coherence cannot create an edge that is absent from the frozen registry.
12A.4 Frozen execution order
Phase 1 execution order is mandatory: (1) freeze registries, preprocessing, objective, COI rule, null suite, and edge records; (2) preprocess; (3) recover positive controls; (4) estimate spectra/wavelets; (5) test only permitted couplings and lags; (6) fit Tiers 0-3; (7) evaluate held-out performance and null survival; (8) freeze the smallest reproducible Physical Earth Architecture. Ancient chronology remains inaccessible to model selection until this freeze is complete.
13. Pass / Fail Criteria
The architecture is not evaluated by whether every proposed cycle appears. It is evaluated by whether a restricted set of structures survives independent replication and strong nulls while many attractive false patterns are rejected.
Criterion | PASS condition | FAIL condition |
|---|
Positive-control recovery | Known anchored modes are recovered within expected uncertainty | Pipeline cannot recover established bands |
Cross-proxy persistence | Candidate band appears in >=2 independent records and survives multiscale criterion | Exists only in one proxy or one smoothing choice |
Null-model survival | Significance survives prespecified appropriate nulls and multiplicity correction | Signal collapses under red-noise, long-memory, phase-randomized, or event nulls |
Out-of-sample performance | Model predicts held-out state structure or recurrence statistics better than null/baseline | Fit exists only in training data |
Parsimony | More complex tiers materially improve predictive adequacy | Threshold/nonlinear terms only improve in-sample fit |
Selective rejection | Model rejects many visually attractive proposed cycles | Model "finds" nearly every target |
Causal discipline | Physical coupling claims have independent pathway evidence plus compatible lag/phase behavior | Claim rests only on spectral or correlational coherence |
14. Falsification Outcomes
Strong support: a limited set of frequency bands and state-dependent transitions replicate across proxies, scales, and held-out intervals and outperform the null suite.
Partial support: known modes replicate, but proposed long recurrence bands prove intermittent, state-specific, or weak. The architecture survives in reduced form.
Null result: most nontrivial recurrence disappears under proper null models. The architecture remains useful as a negative framework documenting where apparent cycles are not robust.
Model failure: the pipeline cannot recover positive controls or repeatedly discovers structure in null data. The simulation methodology must be revised before substantive interpretation.
15. Separation from the Master Time Architecture
Physical Earth Architecture perpendicular to Ancient Time Architecture during model construction
The ancient chronology dataset must not influence physical frequency selection, tolerance windows, lags, thresholds, proxy inclusion, or model tier. Likewise, the physical model must not be used to choose which ancient numbers are considered important. Only after both datasets and methods are frozen may a synthesis test residual overlap.
Residual overlap = observed cross-architecture match - expected match from arithmetic convenience, transmission, and chance
16. Deliverables from Simulation Phase 1
A versioned Earth-system dataset registry with frozen preprocessing rules.
A signed coupling matrix C with permitted edges and evidence class for each edge.
A lag matrix tau with prespecified admissible ranges.
A frequency-band registry with status: positive control, core, candidate, or contested.
A null-model library and reproducible surrogate generator.
A preregistration file containing every confirmatory test and tolerance.
A simulation notebook / codebase implementing Tier 0 through Tier 3 models.
A results report separating confirmatory, sensitivity, and exploratory findings.
A frozen Physical Earth Architecture object suitable for later synthesis with the Master Time Architecture.
17. Minimal Pseudocode
freeze(dataset_registry, band_registry, C_edges, tau_bounds, preprocessing, null_suite)
for dataset in registry:
preprocess(dataset)
recover_positive_controls(dataset)
estimate_spectrum_and_wavelets(dataset)
for candidate_coupling in C_edges:
estimate_lag_within_frozen_bounds(candidate_coupling)
test_phase_and_coherence(candidate_coupling)
compare_against_cross-series_surrogates()
for model_tier in [0, 1, 2, 3]:
fit(training_data)
test(held_out_data)
compare_against_null_suite()
accept_structure_only_if(
cross_proxy_persistence and
multiscale_persistence and
null_survival and
out_of_sample_gain and
physical_plausibility
)
freeze(Physical_Earth_Architecture)
# Only now permit comparison with ancient chronology data.
18. Interpretation Rule
The simulation is not designed to prove that Earth repeats. It is designed to quantify how a non-stationary planet can preserve relational regularity while individual events drift in timing, magnitude, and mechanism. The preferred outcome is not the largest number of cycles discovered, but the smallest reproducible architecture that explains more structure than appropriate null models without sacrificing falsifiability.
Best model = maximum reproducible structure with minimum post-hoc freedom
Source Relationship
This specification operationalizes the framework defined in The Oscillatory Earth Architecture (August 25, 2026), especially its distinctions among periodic, quasi-periodic, stochastic and threshold behavior; its scale operator; its moving-mass coupling logic; its state-vector model; its statistical program; and its requirement that the physical architecture be frozen before comparison with ancient chronologies.
EARTH-SYSTEM SIMULATION REGISTRY
& PREREGISTRATION
Phase 1 — Input Architecture Freeze Record v1.0
Companion implementation document to The Oscillatory Earth Architecture and Formal Simulation Specification v1.1
25 August 2026
Purpose and Freeze Status
This document is the human-readable governing record for Simulation Phase 1. It converts the formal specification into a concrete input architecture: dataset registry, directed coupling and lag registry, frequency-band registry, preprocessing rules, null-model registry, objective functions, and preregistered pass/fail logic. It is intentionally constructed without consulting ancient calendrical intervals. The Master Time Architecture remains sealed from physical model selection until the Physical Earth Architecture is frozen.
Freeze status: CONDITIONAL FREEZE. The variables, candidate source families, coupling-edge schema, band classes, preprocessing rules, null suite, and decision rules below are frozen for the first implementation. Individual data files are not declared analysis-ready until checksum, metadata, chronology, licensing/access, missingness, and resolution audits are completed. A failed audit may remove a candidate dataset; it may not silently replace it with a more favorable series. Any replacement requires a versioned amendment before confirmatory analysis.
1. Governing Principles
Physical forcing ≠ dynamical mode ≠ observed response ≠ recurrence band.
Earth is modeled as a coupled, deformable, dissipative, non-stationary system; exact periodicity is not presumed.
Directed coupling requires an independently defensible physical pathway. Statistical coherence alone cannot create an edge.
All lag bounds, target bands, smoothing/coarse-graining scales, nulls, objective functions, and multiplicity rules are frozen before confirmatory inspection.
Candidate structures must survive independent proxies, neighboring temporal scales, appropriate nulls, and held-out tests.
The preferred result is the smallest reproducible architecture, including a sparse or null architecture if that is what the evidence supports.
Ancient chronology data, 432-family intervals, Yugas, baktuns, king-list durations, and other cultural intervals are prohibited inputs during this phase.
2. Frozen State Vector
First-generation state vector:
S(t) = [R, P, O, E, A, M, I, H, V, G, C]
Code | Subsystem | Primary observable class | Memory / scale | Status |
|---|
R | Rotation / polar motion | LOD, UT1-UTC, polar motion | days–decades | CORE |
P | Orbital / precessional forcing | eccentricity, obliquity, climatic precession, insolation | 10^4–10^5 y | CORE EXTERNAL |
O | Ocean state | SST, heat content, basin circulation proxies | months–millennia | CORE |
E | ENSO | Niño 3.4 / RONI / MEI-family indices | months–years | CORE MODE |
A | Atlantic overturning | AMOC observations/reconstructions/proxies | years–millennia | CORE/CANDIDATE by era |
M | Monsoon state | regional monsoon composites / speleothem δ18O | years–10^5 y | CORE/CANDIDATE |
I | Cryosphere | ice volume, ice-sheet/sea-ice proxies | years–10^5 y | CORE |
H | Hydrology | PDSI, lake/river/moisture-balance proxies | months–millennia | CORE/CANDIDATE |
V | Volcanism | sulfate/AOD/eruption forcing | impulse–years | EXTERNAL IMPULSE |
G | Geomagnetic/core-linked | field intensity / justified core-linked observables | decades–millennia | CANDIDATE |
C | Atmospheric composition/radiative state | CO2, CH4, aerosol/radiative forcing | years–10^5 y | CORE FORCING/STATE |
3. Earth-System Dataset Registry
Registry entries are source candidates selected before spectral inspection. Priority is given to authoritative institutional archives and published reconstructions with explicit metadata. NCEI's World Data Service for Paleoclimatology provides more than 10,000 archived datasets spanning ice cores, tree rings, corals, sediments, speleothems and reconstructions; it is the principal paleoclimate discovery archive for Phase 1.
ID | S | Dataset / product | Authority | Coverage | Resolution | Observable | Role | Freeze note |
|---|
R-01 | R | IERS Earth Orientation Parameters: finals.all / Bulletin B / long-term EOP | IERS | 1973–present for finals.all; longer EOP products available | daily/monthly | LOD, UT1-UTC, polar motion | POSITIVE CONTROL / CORE | Use IAU2000 series; archive exact file/version. |
P-01 | P | La2010 / Laskar long-term orbital solution | A&A / CDS VizieR | 0 to deep past; La2010 spans to -250 Myr | 1 kyr in distributed tables | eccentricity + orbital elements; derived precession/obliquity as specified | POSITIVE CONTROL / CORE | Use a frozen solution/version; do not switch orbital solutions after results. |
E-01 | E | Niño 3.4 SST index (ERSST family) | NOAA CPC / PSL | 1950–present | monthly | Niño 3.4 SST anomaly | POSITIVE CONTROL / CORE | Historical index; freeze ERSST version and climatology. |
E-02 | E | RONI / official ENSO monitoring series | NOAA CPC | modern monitoring era | 3-month seasons | relative Niño 3.4 anomaly | SENSITIVITY | Do not splice with ONI without explicit transform. |
O-01 | O | NOAA PSL monthly ocean/climate index collection | NOAA PSL | varies; many series 19th/20th c.–present | monthly | SST/ocean indices | CORE SUPPORT | Select named series before analysis; no post-hoc index shopping. |
A-01 | A | AMOC reconstruction 10,000–2,000 BP | NOAA/WDS NCEI; Swingedouw & Jomelli | 10 ka–2 ka BP | proxy/reconstruction dependent | AMOC reconstruction | CORE PALEO | DOI 10.25921/vdw7-w626; chronology uncertainty retained. |
A-02 | A | Observation-based AMOC reconstruction / modern observational products | published observational reconstruction | ~century / instrumental | annual or finer | AMOC strength | CORE MODERN | Must be kept distinct from paleo A-01; no forced stitching. |
M-01 | M | China 640,000-year speleothem oxygen-isotope composite | NOAA/WDS NCEI; Cheng et al. | ~641 ka BP–modern | ~200 y composite working resolution reported | δ18O / Asian monsoon | CORE PALEO | Long, precisely dated test record; retain dating uncertainty. |
I-01 | I | EPICA Dome C / Antarctic long ice-core climate records | NOAA/WDS NCEI | up to ~800 ka | variable | ice-core climate/chemistry proxies | CORE PALEO | Use explicit variable and age scale; no mixing age models silently. |
H-01 | H | North American Drought Atlas PDSI reconstruction | NOAA/WDS NCEI; Cook et al. | ~1 CE–2003 CE | annual | PDSI | POSITIVE CONTROL / CORE REGIONAL | Regional, not global hydrology; spatial multiplicity handled explicitly. |
H-02 | H/O/C | Last Millennium Reanalysis v2 + LMR proxy database | NOAA/WDS NCEI | Common Era; proxy DB extends farther for some records | annual / proxy-dependent | temperature, PDSI, climate fields, multiproxy | CORE CROSS-CHECK | Use reconstruction and raw proxy DB as separate products; avoid circular validation. |
V-01 | V | Global/Hemispheric 1200-year volcanic forcing reconstruction | NOAA/WDS NCEI; Crowley & Unterman | ~800–2000 CE | annual/subannual source chronology | sulfate-derived AOD forcing | CORE IMPULSE | Eruption timing uncertainty recorded. |
V-02 | V | 1500-year stratospheric volcanic sulfate forcing | NOAA/WDS NCEI; Gao et al. | 501–2000 CE | annual | sulfate / forcing index | INDEPENDENT SENSITIVITY | Use as alternate reconstruction, not merged automatically. |
C-01 | C | EPICA Dome C / Vostok composite CO2 | NOAA/WDS NCEI | to ~800 ka BP | irregular | CO2 ppm | CORE PALEO | DOI 10.25921/xgzs-gd10; later revised Antarctic composite can be sensitivity. |
C-02 | C | EPICA Dome C methane | NOAA/WDS NCEI | to ~800 ka BP | avg ~380 y in extended record | CH4 ppb | CORE PALEO | DOI 10.25921/gfsj-jc86. |
G-01 | G | Geomagnetic/core-linked series | TO BE FROZEN AFTER SOURCE AUDIT | TBD | TBD | field intensity / core-linked observable | CANDIDATE ONLY | No confirmatory use until one or more high-quality records pass source/chronology audit. |
3.1 Dataset admission audit
Exact dataset title, version, DOI or institutional product identifier, access date, and immutable/local checksum recorded.
Chronology/age model identified; age uncertainty retained as data, not discarded.
Native temporal resolution and gaps quantified before interpolation.
Proxy interpretation documented separately from measured variable.
Calibration target and reconstruction method documented to prevent circular validation.
Spatial representativeness labeled: local, regional, basin, hemispheric, or global.
Known revisions or alternate products listed as sensitivity candidates before confirmatory analysis.
Dataset cannot be replaced after spectral inspection because another series produces a cleaner peak.
4. Directed Coupling and Lag Registry
Frozen edge schema:
Edge(j→i) = <Source, Target, LagBounds[τmin,τmax], SignConstraint, PhysicalEvidenceClass>
Evidence class A = directly measured transfer/pathway; B = strong mechanistic literature; C = plausible candidate with limited direct constraint. Class C is sensitivity-only unless independently replicated.
Edge | Physical pathway | Lag bounds | Sign | Evidence | Guardrail |
|---|
C→O | radiative forcing → ocean thermal state | years–centuries | state-dependent | A/B | Heat uptake; sign depends on forcing definition. |
C→I | radiative forcing → cryosphere | years–millennia | warming forcing generally reduces ice | A/B | Nonlinear thresholds/hysteresis allowed only Tier 3. |
O→C | ocean state → atmospheric carbon exchange | months–millennia | state-dependent | A/B | Carbon feedback; do not assume symmetry with C→O. |
O→E | ocean background state → ENSO mode | months–years | state-dependent | B | Mode modulation, not a fixed sign scalar in all regimes. |
E→O | ENSO → ocean heat redistribution | months–years | state-dependent | A/B | Regional sign varies; use defined target observable. |
E→H | ENSO → hydrology | months–seasons | regional/state-dependent | A/B | Regional edges only; no global drought scalar presumed. |
O↔M | ocean state ↔ monsoon | months–decades | state-dependent | B | Represent as two separately registered directed edges. |
P→M | orbital insolation → monsoon | 10^3–10^4 y response envelope | phase/latitude dependent | A/B | Use insolation geometry, not raw period matching. |
P→I | orbital insolation → cryosphere | 10^3–10^4+ y | state-dependent | A/B | Ice response lag constrained by proxy/model literature. |
I→O | cryosphere/freshwater → ocean circulation | years–millennia | state-dependent | A/B | Freshwater and density pathways; threshold behavior possible. |
O→I | ocean heat transport → cryosphere | years–centuries | state-dependent | A/B | Keep separate from I→O. |
I→R | ice/mass redistribution → rotation/polar motion | seasonal–millennia | geometry dependent | A/B | Mass loading/unloading pathway. |
O→R | ocean angular momentum/mass → rotation | days–years | geometry dependent | A | Fast exchange positive-control class. |
M/H→R | atmospheric/hydrologic mass redistribution → rotation | days–years | geometry dependent | A/B | Implement only with measurable mass/angular-momentum proxy. |
V→C | volcanic aerosols → radiative state | near-zero onset; ~1–5 y decay | negative shortwave forcing convention | A | Impulse/decay model. |
V→O | volcanic forcing → ocean response | months–decades | state-dependent | B | Must be mediated/defined consistently with C. |
V→I | volcanic forcing → cryosphere response | years–decades | state-dependent | B/C | Sensitivity unless robust pathway/record supports. |
A→O | AMOC state → North Atlantic/ocean heat distribution | years–decades | state-dependent | A/B | Avoid double-counting if O observable already encodes AMOC. |
O→A | density/ocean state → AMOC | years–centuries | state-dependent | A/B | Separate direction and lag. |
M→C | monsoon/wetland state → CH4 component | years–centuries | state-dependent | B | Relevant primarily to methane sensitivity runs. |
G→R | core-linked/geomagnetic observable → rotation | decades–multidecades | unknown/state-dependent | C | Candidate only; cannot support climate causation by itself. |
5. Frequency-Band Registry
Band windows are targets for recovery or testing, not declarations of deterministic clocks. Exact tolerances will be expressed in frequency space and must account for record length and dating uncertainty. Long-period bands are tested only where the record contains enough independent cycles to support inference.
ID | Band | Window | Class | Targets | Rule |
|---|
B01 | Annual/seasonal | ~1 y | POSITIVE CONTROL | Instrumental records | Pipeline sanity check; not substantive discovery. |
B02 | Chandler wobble | ~14 months | POSITIVE CONTROL | R | Recover in polar-motion data. |
B03 | ENSO | ~2–7 y | POSITIVE CONTROL / CORE | E,O | Broad, drifting band; no single fixed period. |
B04 | Decadal–multidecadal ocean variability | ~10–100 y | CANDIDATE FAMILY | O,A | Do not collapse heterogeneous modes into one clock. |
B05 | Orbital precession | ~19–23 kyr | POSITIVE CONTROL / CORE FORCING | P; response in M/I/C | Forcing band; response phase may drift. |
B06 | Obliquity | ~41 kyr | POSITIVE CONTROL / CORE FORCING | P; response in I/C | Known orbital component. |
B07 | Eccentricity | ~100 kyr family | POSITIVE CONTROL / CORE FORCING | P; response in I/C | Climate response is not proof of direct amplitude mechanism. |
B08 | Long eccentricity modulation | ~405 kyr | CORE/CANDIDATE depending interval | P | Use only with sufficiently long records. |
B09 | Millennial D–O recurrence neighborhood | ~1–2 kyr; ~1.47 kyr often proposed | CONTESTED | ice-core / North Atlantic proxies | Must beat stochastic waiting-time and state-conditioned nulls. |
B10 | Holocene centennial–millennial bands | UNFROZEN NUMERIC SUBBANDS until proxy audit | M,A,H,C | EXPLORATORY/CANDIDATE | No ancient-calendar intervals may set these windows. |
6. Preprocessing Freeze
Item | Frozen rule |
|---|
Time axis | Preserve native chronology. Convert to a common analysis axis only with explicit transformation; retain age uncertainty. |
Missing data | No interpolation across gaps larger than a preregistered multiple of native median spacing. Gap thresholds recorded per dataset. |
Resampling | Use the coarsest resolution required for a given cross-series comparison; never upsample a coarse proxy to create information. |
Normalization | Z-score or robust scaling only after preserving native units in archived copy; method frozen per analysis family. |
Detrending | No single universal detrend. Compare no-detrend and prespecified physically justified detrend as separate analyses; report sensitivity. |
Smoothing/coarse-graining | Use a preregistered ladder appropriate to each record; adjacent-scale persistence required. No window chosen after seeing peaks. |
Wavelets | Confirmatory significance only outside the cone of influence; COI-dependent features are exploratory. |
Filtering | Zero-phase or explicitly phase-aware filters only; filter order/cutoff frozen. Filtering cannot define the same band later claimed as discovered. |
Age uncertainty | For paleo records, propagate chronology uncertainty by ensemble/jitter methods where metadata permit; a peak that vanishes under plausible age uncertainty fails. |
Spatial aggregation | Regional composites must state weights and coverage; no global label for a regional proxy. |
Standardization | All transformed series retain provenance to raw/native record and transformation script/version. |
7. Analysis and Objective Functions
Tier comparison uses the same held-out objective across models.
Primary probabilistic objective: held-out negative log-likelihood when an explicit observation-error model is available.
Fallback objective: normalized root-mean-square error (NRMSE) on held-out standardized anomalies.
Primary parsimony penalty: Bayesian Information Criterion (BIC); AIC is a sensitivity report, not the primary selection rule.
Higher tiers must improve held-out performance, survive the null suite, and retain physically admissible parameters.
Spectral tools: Lomb–Scargle for uneven sampling where appropriate; multitaper/FFT for appropriate regular series; continuous wavelets for non-stationary bands.
Cross-series tools: cross-wavelet/coherence and lagged association only for pre-authorized physical edges.
Change-point/hidden-state methods may test regime behavior; they do not by themselves establish periodic forcing.
Transfer entropy or directed-information measures are exploratory unless prespecified for an authorized edge and supported by compatible physical lag/pathway evidence.
8. Null-Model Registry
ID | Null | Failure mode addressed | Implementation rule |
|---|
N1 | AR(1) red noise | Short-memory persistence can create apparent low-frequency power. | Fit parameters from each series; generate surrogate ensemble. |
N2 | Fractional Gaussian / long-memory noise | Long-range dependence can mimic multiscale cycles. | Use only where long-memory estimation is stable; sensitivity across estimators. |
N3 | Phase-randomized surrogates | Preserve spectrum/amplitude structure while destroying phase relationships. | Primary coherence/phase-lock null. |
N4 | Block bootstrap | Preserve local autocorrelation while disrupting long-range alignment. | Block length frozen from autocorrelation structure, not target period. |
N5 | Poisson / renewal event process | Event clustering may resemble periodic recurrence. | For event chronologies such as abrupt transitions/eruptions where appropriate. |
N6 | State-conditioned event surrogate | Waiting times can depend on climate state without a clock. | Mandatory for contested millennial recurrence claims. |
N7 | Cross-series permutation / time-shift surrogate | Independent persistent series can align by chance. | Preserve each series' internal structure while breaking cross-series alignment. |
N8 | Age-model ensemble null | Chronology uncertainty can create/destroy apparent phase. | Jitter/resample within published age uncertainty where available. |
9. Multiscale Persistence and Acceptance Criteria
A candidate recurrence structure is confirmatory only if all applicable conditions are met:
Appears in at least two genuinely independent records or independent measurement families.
Persists across at least three adjacent preregistered temporal resolutions/coarse-graining scales where those scales are scientifically meaningful.
Peak/band location remains within preregistered tolerance after age-uncertainty and preprocessing sensitivity tests.
Significance survives the strongest appropriate nulls and multiplicity correction for the full preregistered search family.
Does not rely primarily on wavelet power inside the cone of influence.
For coupling claims, the edge was pre-authorized by physical evidence and the observed lag falls within its frozen lag bounds.
Adds held-out predictive or state-classification value beyond the simpler tier/baseline.
Does not require post-hoc integer multiples, divisors, phase shifts, or selective exclusion of inconvenient intervals.
10. Multiple Testing and Search-Freedom Ledger
Every tested dataset, band, proxy, region, smoothing scale, lag interval, model tier, null family, and sensitivity variant must be logged. False-discovery-rate or family-wise correction is applied to the preregistered family of tests. Any new band, edge, proxy, threshold, or transformation proposed after inspection is labeled EXPLORATORY and cannot be used as confirmatory evidence in the same run.
11. Positive Controls and Stop Rules
ID | Control | What it validates | Stop rule |
|---|
PC1 | Annual/seasonal structure where present | Basic pipeline and time-axis integrity | Stop if absent without known physical/data reason. |
PC2 | Chandler wobble in IERS polar motion | Rotation spectral recovery | Stop R analysis if not recovered within expected uncertainty. |
PC3 | ENSO broad 2–7 y variability in Niño 3.4 / ENSO indices | Non-stationary band recovery | Stop modern climate mode analysis if pipeline forces a single fixed period or misses broad band. |
PC4 | Orbital precession/obliquity/eccentricity in orbital solution | Long-period spectral recovery | Stop paleo-frequency pipeline if known orbital components are not recovered. |
PC5 | Known volcanic impulses in forcing reconstruction | Impulse timing/decay handling | Stop V coupling analysis if event chronology is materially shifted by preprocessing. |
12. Model Tiers and Gating
Tier | Form | Core representation | Gate |
|---|
Tier 0 | Linear/stochastic baseline | dS/dt = A S + B U + η | Mandatory baseline. |
Tier 1 | Lagged linear coupling | directed Cij with frozen τij | Accepted only with held-out gain and null survival. |
Tier 2 | Weak nonlinearities | prespecified damping/saturation/low-order terms | No high-order polynomial fishing. |
Tier 3 | Threshold/hysteresis | Ψ(t)>Θforward; return below Θreturn | Requires clear held-out gain and robust regime evidence; Θforward may differ from Θreturn. |
13. Preregistered Outcomes
Outcome | Definition |
|---|
STRONG SUPPORT | A limited set of bands/couplings/state transitions replicate across independent records/scales, beat appropriate nulls, and improve held-out prediction. |
PARTIAL SUPPORT | Positive controls and some core structures replicate, but proposed long bands are intermittent, state-specific, or weak; architecture is reduced. |
NULL RESULT | Most nontrivial recurrence disappears under proper nulls/age uncertainty/multiplicity. Report the negative architecture without replacement fishing. |
MODEL FAILURE | Pipeline misses positive controls or repeatedly discovers structure in null data. Revise methodology before substantive interpretation. |
14. Phase 1 Execution Sequence
1. Archive exact source files and metadata; compute checksums; complete admission audit.
2. Freeze dataset registry version and exclusions before spectral inspection.
3. Freeze directed edge registry, evidence class, sign constraints, and lag bounds.
4. Freeze band registry, scale ladder, preprocessing, objective, COI rule, null suite, and multiplicity family.
5. Run positive controls. If a stop rule triggers, halt and repair the pipeline without inspecting target results.
6. Run within-series spectra/wavelets and multiscale persistence tests.
7. Run only pre-authorized cross-series coupling/lag tests.
8. Fit Tiers 0→3 on training intervals; evaluate held-out intervals and null ensembles.
9. Accept only structures meeting all applicable criteria.
10. Freeze Physical Earth Architecture v1.0.
11. Only after Step 10 may the separately frozen Master Time Architecture be unlocked for synthesis.
15. Machine-Readable Companion Files to Generate
File | Required contents |
|---|
datasets.csv | dataset_id, state_code, title, authority, DOI/product_id, version, coverage_start, coverage_end, resolution, chronology, uncertainty, role, checksum, status |
edges.csv | edge_id, source, target, tau_min, tau_max, lag_unit, sign_constraint, evidence_class, mechanism, references, status |
bands.csv | band_id, label, f_min/f_max or T_min/T_max, class, target_states, tolerance_rule, status |
preprocessing.yaml | per-dataset transforms, resampling, detrending, gap rules, scale ladder, wavelet/COI rules |
nulls.yaml | null family, parameter-estimation rule, ensemble size, random-seed policy, applicability |
preregistration.yaml | objectives, held-out splits, multiplicity family, pass/fail rules, stop rules, version hashes |
run_ledger.csv | every executed confirmatory/sensitivity/exploratory test and its versioned inputs |
16. Locked Separation from the Master Time Architecture
PHYSICAL EARTH ARCHITECTURE ⟂ ANCIENT TIME ARCHITECTURE DURING MODEL CONSTRUCTION
No ancient calendar, cosmological age, Sumerian reign duration, biblical lifespan, Yuga interval, Maya Long Count unit, 432-family value, or other cultural chronology may influence dataset selection, band windows, lag bounds, thresholds, smoothing scales, proxy inclusion, or model tier. The later synthesis will test residual overlap only after both architectures are independently frozen.
Residual overlap = observed cross-architecture match − expected match from arithmetic convenience + transmission + chance
17. Source Register for Phase 1
IERS Earth Orientation Center / Rapid Service products: Earth Orientation Parameters including polar motion, UT1-UTC and length of day; finals.all provides high-quality EOP since 2 January 1973.
NOAA Climate Prediction Center / Physical Sciences Laboratory: Niño 3.4, ONI/RONI and related ENSO time series; historical and current products must be versioned separately.
NOAA National Centers for Environmental Information, World Data Service for Paleoclimatology: principal archive for paleoclimate proxy and reconstruction datasets.
Laskar et al. orbital solutions (La93/La2010) distributed through A&A/CDS/VizieR; La2010 supplies long-term orbital elements, while established Milankovitch bands provide positive controls.
Swingedouw & Jomelli AMOC reconstruction, 10,000–2,000 BP, NOAA/WDS NCEI, DOI 10.25921/vdw7-w626.
Cheng et al. China 640,000-year speleothem oxygen-isotope composite, NOAA/WDS NCEI; long Asian monsoon record.
Cook et al. North American Drought Atlas PDSI reconstructions, NOAA/WDS NCEI, DOI 10.25921/grrg-z534.
Last Millennium Reanalysis v2 and LMR multi-proxy database, NOAA/WDS NCEI, DOI 10.25921/gn22-5866 and 10.25921/x5zr-8498.
Crowley & Unterman 1200-year volcanic forcing reconstruction, NOAA/WDS NCEI, DOI 10.25921/zztg-6f51; Gao et al. 1500-year sulfate reconstruction as sensitivity.
EPICA Dome C / Antarctic ice-core CO2 and CH4 records, NOAA/WDS NCEI, including DOI 10.25921/xgzs-gd10 and 10.25921/gfsj-jc86.
18. Freeze Declaration
This Phase 1 document freezes the research architecture, not unverified bytes. Confirmatory analysis may begin only after the source-file audit populates the machine-readable companion registries and records their hashes. Removal of a failed dataset is allowed and must be logged. Addition or substitution after target inspection is prohibited without a new preregistration version. The governing objective remains: maximum reproducible structure with minimum post-hoc freedom.
PHASE 1 INPUT ARCHITECTURE — CONDITIONAL FREEZE v1.0
Oscillatory Earth — Phase 1 Implementation Package v1.0
Oscillatory_Earth_Phase1_Implementation_Package_v1.0.zip
Oscillatory_Earth_Phase1_Implementation/README.md
# Oscillatory Earth — Phase 1 Implementation Package
This package operationalizes the Phase 1 Registry & Preregistration freeze.
Files:
- datasets.csv — source/data registry
- edges.csv — directed physical coupling and lag registry
- bands.csv — preregistered frequency/period band registry
- preprocessing.yaml — frozen preprocessing rules
- nulls.yaml — null-model library configuration
- preregistration.yaml — gates, objectives, and acceptance rules
- run_ledger.csv — append-only execution ledger template
- audit_phase1.py — schema, checksum, and freeze-gate validator
Important:
1. `PENDING_BYTES` is not analysis-ready.
2. A dataset becomes `ANALYSIS_READY` only after its exact bytes are archived and the SHA-256 field is populated.
3. A candidate may be removed if it fails audit. Replacement requires a versioned preregistration amendment before confirmatory analysis.
4. Ancient chronology data are prohibited from this package until the Physical Earth Architecture has been independently frozen.
Usage:
python audit_phase1.py --package .
python audit_phase1.py --package . --data-root /path/to/archived/data
With `--data-root`, the validator looks for each dataset under:
<data-root>/<dataset_id>/
If a file named `primary_file` is added to datasets.csv in a later schema version, that exact file can be checked directly. In v1.0 the validator hashes every regular file in the dataset folder and compares the combined manifest hash to `sha256` when status is ANALYSIS_READY.
Oscillatory_Earth_Phase1_Implementation/audit_phase1.py
#!/usr/bin/env python3
import argparse, csv, hashlib, json, sys
from pathlib import Path
try:
import yaml
except ImportError:
print("ERROR: PyYAML is required.", file=sys.stderr)
sys.exit(2)
REQUIRED = {
"datasets.csv": ["dataset_id","state_code","title","authority","product_id","doi","coverage","resolution","observable","role","status","sha256","freeze_note"],
"edges.csv": ["edge_id","source","target","tau_min","tau_max","lag_unit","sign_constraint","evidence_class","mechanism","references","status"],
"bands.csv": ["band_id","label","period_min","period_max","period_unit","class","target_states","tolerance_rule","freeze_note"],
"run_ledger.csv": ["run_id","timestamp_utc","analysis_class","dataset_ids","edge_ids","band_ids","model_tier","null_ids","code_version","input_hash_manifest","status","notes"],
}
STATE_CODES = set("R P O E A M I H V G C".split())
DATA_STATUS = {"PENDING_BYTES","SOURCE_AUDIT_REQUIRED","ANALYSIS_READY","REMOVED_FAILED_AUDIT"}
EDGE_STATUS = {"FROZEN","CANDIDATE","REMOVED"}
EVIDENCE = {"A","B","C","A_B"}
BAND_CLASSES = {
"POSITIVE_CONTROL","POSITIVE_CONTROL_CORE","POSITIVE_CONTROL_CORE_FORCING",
"CANDIDATE_FAMILY","CORE_CANDIDATE","CONTESTED"
}
def load_csv(path):
with path.open(newline="", encoding="utf-8") as f:
return list(csv.DictReader(f))
def sha256_file(path):
h=hashlib.sha256()
with path.open("rb") as f:
for chunk in iter(lambda:f.read(1024*1024), b""):
h.update(chunk)
return h.hexdigest()
def dataset_folder_manifest_hash(folder):
files=sorted([p for p in folder.rglob("*") if p.is_file()])
h=hashlib.sha256()
manifest=[]
for p in files:
fh=sha256_file(p)
rel=str(p.relative_to(folder))
manifest.append({"path":rel,"sha256":fh,"size":p.stat().st_size})
h.update(rel.encode("utf-8")); h.update(b"\0"); h.update(fh.encode("ascii")); h.update(b"\n")
return h.hexdigest(), manifest
def check_headers(path, expected, errors):
with path.open(newline="",encoding="utf-8") as f:
reader=csv.reader(f)
header=next(reader,[])
if header != expected:
errors.append(f"{path.name}: header mismatch. Expected {expected}; got {header}")
def duplicate_check(rows, key, name, errors):
seen=set()
for i,r in enumerate(rows, start=2):
v=r.get(key,"").strip()
if not v: errors.append(f"{name}:{i}: blank {key}")
elif v in seen: errors.append(f"{name}:{i}: duplicate {key}={v}")
seen.add(v)
def main():
ap=argparse.ArgumentParser()
ap.add_argument("--package",default=".")
ap.add_argument("--data-root",default=None)
ap.add_argument("--report",default="audit_report.json")
args=ap.parse_args()
pkg=Path(args.package)
errors=[]; warnings=[]; checks=[]
for fn,headers in REQUIRED.items():
p=pkg/fn
if not p.exists():
errors.append(f"Missing {fn}")
else:
check_headers(p,headers,errors)
for fn in ["preprocessing.yaml","nulls.yaml","preregistration.yaml"]:
p=pkg/fn
if not p.exists():
errors.append(f"Missing {fn}")
else:
try:
obj=yaml.safe_load(p.read_text(encoding="utf-8"))
if not isinstance(obj,dict): errors.append(f"{fn}: root must be mapping")
except Exception as e:
errors.append(f"{fn}: YAML parse failure: {e}")
if errors:
report={"status":"FAIL","errors":errors,"warnings":warnings,"checks":checks}
(pkg/args.report).write_text(json.dumps(report,indent=2),encoding="utf-8")
print(json.dumps(report,indent=2)); return 1
ds=load_csv(pkg/"datasets.csv")
ed=load_csv(pkg/"edges.csv")
bd=load_csv(pkg/"bands.csv")
duplicate_check(ds,"dataset_id","datasets.csv",errors)
duplicate_check(ed,"edge_id","edges.csv",errors)
duplicate_check(bd,"band_id","bands.csv",errors)
for i,r in enumerate(ds,2):
if r["state_code"] not in STATE_CODES:
errors.append(f"datasets.csv:{i}: invalid state_code {r['state_code']}")
if r["status"] not in DATA_STATUS:
errors.append(f"datasets.csv:{i}: invalid status {r['status']}")
if r["status"]=="ANALYSIS_READY" and not r["sha256"].strip():
errors.append(f"datasets.csv:{i}: ANALYSIS_READY requires sha256")
if r["status"]!="ANALYSIS_READY" and r["sha256"].strip():
warnings.append(f"datasets.csv:{i}: sha256 present while status={r['status']}")
for i,r in enumerate(ed,2):
if r["source"] not in STATE_CODES or r["target"] not in STATE_CODES:
errors.append(f"edges.csv:{i}: invalid source/target")
try:
lo=float(r["tau_min"]); hi=float(r["tau_max"])
if lo < 0 or hi < lo: errors.append(f"edges.csv:{i}: invalid lag bounds")
except ValueError:
errors.append(f"edges.csv:{i}: lag bounds not numeric")
if r["evidence_class"] not in EVIDENCE:
errors.append(f"edges.csv:{i}: invalid evidence_class {r['evidence_class']}")
if r["status"] not in EDGE_STATUS:
errors.append(f"edges.csv:{i}: invalid status {r['status']}")
for i,r in enumerate(bd,2):
try:
lo=float(r["period_min"]); hi=float(r["period_max"])
if lo <= 0 or hi <= lo: errors.append(f"bands.csv:{i}: invalid period bounds")
except ValueError:
errors.append(f"bands.csv:{i}: period bounds not numeric")
if r["class"] not in BAND_CLASSES:
errors.append(f"bands.csv:{i}: invalid class {r['class']}")
# Cross-file state references
ds_states={r["state_code"] for r in ds}
for r in ed:
if r["source"] not in ds_states:
warnings.append(f"edge {r['edge_id']}: source state {r['source']} has no dataset registry row")
if r["target"] not in ds_states:
warnings.append(f"edge {r['edge_id']}: target state {r['target']} has no dataset registry row")
# Data-root checksum gate
manifest={}
if args.data_root:
dr=Path(args.data_root)
for r in ds:
did=r["dataset_id"]; status=r["status"]
folder=dr/did
if status=="ANALYSIS_READY":
if not folder.exists():
errors.append(f"{did}: ANALYSIS_READY but folder missing: {folder}")
continue
mh, files=dataset_folder_manifest_hash(folder)
manifest[did]={"manifest_sha256":mh,"files":files}
if mh.lower()!=r["sha256"].strip().lower():
errors.append(f"{did}: checksum mismatch; registry={r['sha256']} computed={mh}")
else:
checks.append(f"{did}: checksum PASS")
elif folder.exists():
warnings.append(f"{did}: bytes exist but status={status}; complete audit before promotion.")
# Freeze gates from prereg
pre=yaml.safe_load((pkg/"preregistration.yaml").read_text(encoding="utf-8"))
if "separation_rule" not in pre:
errors.append("preregistration.yaml: missing separation_rule")
if pre.get("optimization",{}).get("model_selection_criterion")!="BIC":
warnings.append("preregistration.yaml: primary model selection criterion differs from frozen BIC")
status="PASS" if not errors else "FAIL"
report={
"status":status,
"errors":errors,
"warnings":warnings,
"checks":checks,
"counts":{"datasets":len(ds),"edges":len(ed),"bands":len(bd)},
"analysis_ready_datasets":sum(r["status"]=="ANALYSIS_READY" for r in ds),
"manifest":manifest
}
(pkg/args.report).write_text(json.dumps(report,indent=2),encoding="utf-8")
print(json.dumps(report,indent=2))
return 0 if status=="PASS" else 1
if __name__=="__main__":
raise SystemExit(main())
Oscillatory_Earth_Phase1_Implementation/audit_report.json
{
"status": "PASS",
"errors": [],
"warnings": [],
"checks": [],
"counts": {
"datasets": 15,
"edges": 12,
"bands": 9
},
"analysis_ready_datasets": 0,
"manifest": {}
}
Oscillatory_Earth_Phase1_Implementation/bands.csv
band_id,label,period_min,period_max,period_unit,class,target_states,tolerance_rule,freeze_note
B01,Annual/seasonal,0.95,1.05,years,POSITIVE_CONTROL,R;O;E;H,instrumental where physically present,Pipeline sanity check; not substantive discovery.
B02,Chandler wobble,1.1,1.3,years,POSITIVE_CONTROL,R,recover near ~435 days,Positive control in polar motion.
B03,ENSO,2.0,7.0,years,POSITIVE_CONTROL_CORE,E;O,broad drifting band,No single fixed period permitted.
B04,Decadal–multidecadal ocean variability,10,100,years,CANDIDATE_FAMILY,O;A,family only,Do not collapse heterogeneous modes into one clock.
B05,Orbital precession,19000,23000,years,POSITIVE_CONTROL_CORE_FORCING,P;M;I;C,known forcing band,Response phase may drift.
B06,Obliquity,39000,43000,years,POSITIVE_CONTROL_CORE_FORCING,P;I;C,known forcing band,Known orbital component.
B07,Eccentricity family,80000,125000,years,POSITIVE_CONTROL_CORE_FORCING,P;I;C,broad family,Climate response does not imply direct forcing amplitude equivalence.
B08,Long eccentricity modulation,380000,430000,years,CORE_CANDIDATE,P,only sufficiently long records,Long-record test only.
B09,Millennial D-O neighborhood,1000,2000,years,CONTESTED,I;A,must beat event/state-conditioned nulls,"~1.47 kyr is a test target, not a presumed clock."
Oscillatory_Earth_Phase1_Implementation/datasets.csv
dataset_id,state_code,title,authority,product_id,doi,coverage,resolution,observable,role,status,sha256,freeze_note
R-01,R,IERS Earth Orientation Parameters: finals.all / Bulletin B / long-term EOP,IERS,IERS EOP product,,1973-present for finals.all,daily/monthly,LOD; UT1-UTC; polar motion,POSITIVE_CONTROL_CORE,PENDING_BYTES,,Use IAU2000 series; archive exact file/version; longer EOP products may be separate records.
P-01,P,La2010 long-term orbital solution,Laskar et al. / A&A / CDS,La2010,,0 to deep past; distributed long-term solution,~1 kyr distributed tables,eccentricity; orbital elements; derived climatic precession/obliquity,POSITIVE_CONTROL_CORE,PENDING_BYTES,,Freeze exact solution/version; no post-hoc switch to alternate orbital solution.
E-01,E,Niño 3.4 SST index,NOAA CPC / PSL,ERSST-family Niño 3.4,,1950-present,monthly,Niño 3.4 SST anomaly,POSITIVE_CONTROL_CORE,PENDING_BYTES,,Freeze ERSST version and climatology before analysis.
E-02,E,Relative Oceanic Niño Index (RONI) / official ENSO monitoring,NOAA CPC,RONI,,modern monitoring era,3-month seasons,relative Niño 3.4 anomaly,SENSITIVITY,PENDING_BYTES,,Do not splice with ONI/Niño3.4 without preregistered transform.
O-01,O,Monthly ocean/climate index collection,NOAA PSL,PSL climate indices,,varies,monthly,SST/ocean indices,CORE_SUPPORT,PENDING_BYTES,,Named series must be selected before spectral inspection; no post-hoc index shopping.
A-01,A,"AMOC reconstruction 10,000–2,000 BP",NOAA/WDS NCEI; Swingedouw & Jomelli,10.25921/vdw7-w626,10.25921/vdw7-w626,10 ka–2 ka BP,proxy-dependent,AMOC reconstruction,CORE_PALEO,PENDING_BYTES,,Chronology uncertainty retained.
M-01,M,"China 640,000-year speleothem oxygen-isotope composite",NOAA/WDS NCEI; Cheng et al.,Cheng 640 ka composite,,~641 ka BP–modern,~centennial,δ18O / Asian monsoon,CORE_PALEO,PENDING_BYTES,,Retain dating uncertainty and original age model.
I-01,I,EPICA Dome C long ice-core climate records,NOAA/WDS NCEI,EPICA Dome C,,up to ~800 ka,variable,ice-core climate/chemistry proxies,CORE_PALEO,PENDING_BYTES,,Variable and age scale must be explicit; no silent age-model mixing.
H-01,H,North American Drought Atlas PDSI reconstruction,NOAA/WDS NCEI; Cook et al.,10.25921/grrg-z534,10.25921/grrg-z534,~1 CE–2003 CE,annual,PDSI,POSITIVE_CONTROL_CORE_REGIONAL,PENDING_BYTES,,"Regional, not global hydrology; spatial multiplicity handled explicitly."
H-02,H,Last Millennium Reanalysis v2 and proxy database,NOAA/WDS NCEI,LMR v2 / proxy DB,10.25921/gn22-5866;10.25921/x5zr-8498,Common Era / proxy-dependent,annual / proxy-dependent,temperature; PDSI; multiproxy fields,CORE_CROSSCHECK,PENDING_BYTES,,Reconstruction and proxy DB remain separate products to avoid circular validation.
V-01,V,Global/Hemispheric 1200-year volcanic forcing reconstruction,NOAA/WDS NCEI; Crowley & Unterman,10.25921/zztg-6f51,10.25921/zztg-6f51,~800–2000 CE,annual/subannual chronology,sulfate-derived AOD forcing,CORE_IMPULSE,PENDING_BYTES,,Eruption timing uncertainty recorded.
V-02,V,1500-year stratospheric volcanic sulfate forcing,NOAA/WDS NCEI; Gao et al.,Gao 1500-year sulfate,,501–2000 CE,annual,sulfate / forcing index,INDEPENDENT_SENSITIVITY,PENDING_BYTES,,Alternate reconstruction; never merged automatically with V-01.
C-01,C,EPICA Dome C / Vostok composite CO2,NOAA/WDS NCEI,10.25921/xgzs-gd10,10.25921/xgzs-gd10,to ~800 ka BP,irregular,CO2 ppm,CORE_PALEO,PENDING_BYTES,,Revised Antarctic composites are sensitivity products only if preregistered.
C-02,C,EPICA Dome C methane,NOAA/WDS NCEI,10.25921/gfsj-jc86,10.25921/gfsj-jc86,to ~800 ka BP,~centennial to multi-centennial,CH4 ppb,CORE_PALEO,PENDING_BYTES,,Preserve original age scale and uncertainty metadata.
G-01,G,Geomagnetic/core-linked series,TO BE FROZEN AFTER SOURCE AUDIT,TBD,,TBD,TBD,field intensity / core-linked observable,CANDIDATE_ONLY,SOURCE_AUDIT_REQUIRED,,No confirmatory use until high-quality record passes source and chronology audit.
Oscillatory_Earth_Phase1_Implementation/edges.csv
edge_id,source,target,tau_min,tau_max,lag_unit,sign_constraint,evidence_class,mechanism,references,status
E01,C,O,1,100,years,state_dependent,A_B,Radiative forcing to ocean heat uptake,IPCC/NCEI physical literature,FROZEN
E02,C,I,1,1000,years,negative_under_warming_forcing,A_B,Radiative warming reduces cryospheric mass/extent,ice-core/cryosphere literature,FROZEN
E03,O,C,0.083,1000,years,state_dependent,A_B,Ocean carbon uptake/outgassing and solubility feedback,carbon-cycle literature,FROZEN
E04,O,E,0.083,2,years,state_dependent,B,Background ocean state modulates ENSO dynamics,NOAA/ENSO literature,FROZEN
E05,E,O,0.083,2,years,state_dependent,A_B,ENSO redistributes ocean heat,NOAA/PSL,FROZEN
E06,E,H,0.083,0.5,years,regional_state_dependent,A_B,ENSO teleconnections to hydrology,NOAA/NADA,FROZEN
E07,P,M,1000,10000,years,phase_dependent,A_B,Orbital insolation forcing of monsoon intensity,La2010/Cheng,FROZEN
E08,P,I,1000,10000,years,state_dependent,A_B,Orbital insolation pacing of ice sheets,Milankovitch literature,FROZEN
E09,I,R,0.25,1000,years,geometry_dependent,A_B,Cryospheric mass redistribution to polar motion/LOD,IERS/JPL,FROZEN
E10,O,R,0.003,1,years,geometry_dependent,A,Ocean angular momentum exchange with solid Earth,IERS/JPL,FROZEN
E11,V,C,0,5,years,negative_shortwave_forcing_convention,A,Volcanic sulfate/AOD radiative forcing,Crowley/Unterman,FROZEN
E12,G,R,10,100,years,state_dependent,C,Core-mantle / core-linked coupling to LOD,EOP/core literature,CANDIDATE
Oscillatory_Earth_Phase1_Implementation/nulls.yaml
version: '1.0'
random_seed_policy:
type: fixed_registry
master_seed: 42060
null_models:
N1_AR1:
description: AR(1) red-noise surrogates
fit_method: MLE_or_Yule_Walker_prespecified_by_series
ensemble_size: 2000
N2_LongMemory:
description: Fractional Gaussian/long-memory noise
ensemble_size: 2000
guardrail: Use only if long-memory estimation is stable.
N3_PhaseRandomized:
description: Phase-randomized / AAFT surrogates for coherence
algorithm: AAFT_or_IAAFT_prespecified
ensemble_size: 2000
N4_BlockBootstrap:
description: Local autocorrelation-preserving bootstrap
ensemble_size: 2000
block_rule: derived_from_autocorrelation_not_target_period
N5_EventProcess:
description: Poisson/renewal event timing null
ensemble_size: 5000
N6_StateConditioned:
description: State-conditioned renewal/non-homogeneous event process
ensemble_size: 5000
mandatory_for: contested_millennial_event_recurrence
N7_CrossSeriesPermutation:
description: Time-shift/permutation preserving internal structure
ensemble_size: 5000
N8_AgeModel:
description: Chronology jitter within published age uncertainties
ensemble_size: 1000
distribution: dataset_specific_from_metadata
Oscillatory_Earth_Phase1_Implementation/preprocessing.yaml
version: '1.0'
rules:
time_axis: Preserve native chronology; common axis requires explicit transformation
and retained age uncertainty.
missing_data:
rule: No interpolation across gaps larger than preregistered threshold relative
to native median spacing.
threshold_policy: per_dataset_frozen_before_analysis
resampling: Use coarsest resolution required for cross-series comparison; never
upsample to create information.
normalization:
primary: zscore
sensitivity: robust_scale
archive_native_units: true
detrending:
confirmatory:
- none
- physically_justified_prespecified
posthoc_detrending_forbidden: true
coarse_graining:
ladder:
- native
- x2
- x5
- x10
- x20
- x50
- x100
persistence: 3_adjacent_scales_when_scientifically_meaningful
wavelet:
cone_of_influence: strict_exclusion_confirmatory
coi_features: exploratory_only
filtering: Zero-phase or explicitly phase-aware only; order/cutoff frozen. Filter
cannot define the claimed discovery band.
age_uncertainty: Propagate via ensemble/jitter when published uncertainty permits.
spatial_aggregation: Region/weights/coverage explicit; regional proxy cannot be
relabeled global.
Oscillatory_Earth_Phase1_Implementation/preregistration.yaml
version: '1.0'
governing_specification: Oscillatory Earth Formal Simulation Specification v1.1
phase: Phase 1
separation_rule: Ancient chronology remains inaccessible to physical model selection
until Physical Earth Architecture is frozen.
pipeline_gates:
positive_controls:
PC1_Seasonal:
target: B01
status: MANDATORY_PASS_WHERE_PHYSICALLY_PRESENT
PC2_Chandler:
target: B02
status: MANDATORY_PASS
PC3_ENSO:
target: B03
status: MANDATORY_PASS
PC4_Orbital:
target:
- B05
- B06
- B07
status: MANDATORY_PASS
PC5_Volcanic:
target: known_impulses
status: MANDATORY_PASS_FOR_V_ANALYSIS
optimization:
primary_loss: held_out_negative_log_likelihood
fallback_loss: normalized_root_mean_square_error
model_selection_criterion: BIC
sensitivity_criterion: AIC
acceptance:
cross_proxy_persistence: at_least_2_independent_records_or_measurement_families
multiscale_persistence: at_least_3_adjacent_preregistered_scales_when_applicable
null_survival: true
multiplicity_correction: true
held_out_gain_required_for_model_complexity: true
physical_pathway_required_for_coupling: true
coi_rule: strict_exclusion_confirmatory
posthoc_integer_multiple_or_phase_tuning: forbidden_confirmatory
outcomes:
- STRONG_SUPPORT
- PARTIAL_SUPPORT
- NULL_RESULT
- MODEL_FAILURE
Oscillatory_Earth_Phase1_Implementation/run_ledger.csv
run_id,timestamp_utc,analysis_class,dataset_ids,edge_ids,band_ids,model_tier,null_ids,code_version,input_hash_manifest,status,notes
Oscillatory Earth — Phase 1
Data Acquisition & Provenance Record
Acquisition Batch 1 — 25 August 2026
Status
This record accompanies the Phase 1 Frozen Data Archive. It distinguishes source verification from byte-level freezing. One authoritative numerical series (NOAA Niño 3.4) is archived locally as a text snapshot. The authoritative IERS EOP, La2010 orbital, and Crowley–Unterman volcanic endpoints have been verified, but full byte-for-byte capture remains pending because this execution runtime could not export those complete remote objects directly. They are therefore not promoted to ANALYSIS_READY and cannot be used for confirmatory positive-control execution yet.
Acquisition Register
ID | Dataset | Authority | Coverage | Resolution | Archive status | Positive control |
E-01 | Niño 3.4 SST Index | NOAA PSL/CPC | 1948–2026 snapshot | Monthly | AUTHORITATIVE TEXT SNAPSHOT CAPTURED | PC3 |
R-01 | Standard Rapid EOP / finals2000A.all | IERS | 1973–present + prediction | Daily | SOURCE VERIFIED; BYTE CAPTURE PENDING | PC2 |
P-01 | La2010 orbital solution | Laskar et al.; CDS/VizieR | Long-term; 1 kyr table | 1 kyr in catalogue table | SOURCE VERIFIED; BYTE CAPTURE PENDING | PC4 |
V-01 | 1200-year volcanic forcing | NOAA/WDS NCEI; Crowley & Unterman | 800–2000 CE | Annual | SOURCE VERIFIED; FULL BYTE CAPTURE PENDING | PC5 |
E-01 — NOAA Niño 3.4
The NOAA PSL source describes Niño 3.4 as the area-averaged SST anomaly for 5°N–5°S, 170°W–120°W. The source is monthly and identifies the series as ERSST-based. The archive contains a local text snapshot through July 2026, with later 2026 months marked missing by the source.
Archived file: E-01/nina34_anom_authoritative_text_snapshot.data
Source: https://psl.noaa.gov/data/correlation/nina34.anom.data
Use: eligible for ingestion-format and PC3 pipeline preparation; final byte provenance should still be compared against a direct raw download when available.
R-01 — IERS Earth Orientation Parameters
IERS identifies finals2000A.all as Standard Rapid EOP Data since 2 January 1973. The product includes x/y pole, UT1–UTC, LOD, dX and dY, with daily observations and a prediction horizon. The source endpoint and product metadata are recorded in the archive, but raw bytes are not yet locally frozen.
Source: https://datacenter.iers.org/data/9/finals2000A.all
Status rule: PC2 (Chandler wobble) remains locked until byte capture and checksum validation are complete.
P-01 — La2010 Orbital Solution
The CDS/VizieR catalogue J/A+A/532/A89 is the La2010 orbital solution for long-term Earth motion. The catalogue exposes orbital elements for multiple La2010 solutions, including a 1-kyr sampled table. Catalogue provenance and DOI are frozen; complete table bytes are still pending local acquisition.
Catalogue DOI: 10.26093/cds/vizier.35320089
Status rule: PC4 remains locked until the selected La2010 table/version is archived and hashed.
V-01 — Crowley & Unterman Volcanic Forcing
NOAA/WDS NCEI archives the Crowley & Unterman 1200-year volcanic forcing reconstruction (800–2000 CE), including annual global AOD at 550 nm and effective aerosol radius. The authoritative raw endpoint and dataset DOI are frozen. The archive contains a metadata/selected-row excerpt only; that excerpt is explicitly barred from analysis as a substitute for the full series.
Dataset DOI: 10.25921/zztg-6f51
Raw source: https://www.ncei.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/crowley2013/crowley2013aod-reff.txt
Status rule: PC5 remains locked until the complete file is captured and checksum-verified.
Checksum Policy
SHA-256 values in SHA256SUMS.txt and manifest.csv certify the exact local files in this acquisition archive. They do not claim identity with a remote raw object unless the status explicitly says byte-level source capture. A future acquisition batch may supersede a pointer or excerpt only through a versioned manifest update.
Next Gate
The next gate is not spectral interpretation. It is completion of byte acquisition for R-01, P-01, and V-01, followed by a checksum audit. Only then can PC2, PC4, and PC5 be executed. PC3 preparation may begin with E-01, but the physical architecture remains unfrozen until the full positive-control set is admitted.
References / Authoritative Endpoints
IERS Rapid Service Prediction Centre, Standard Rapid EOP Data (finals2000A.all), product metadata dated August 2026.
NOAA Physical Sciences Laboratory / Climate Prediction Center, Niño 3.4 monthly SST anomaly time series.
Laskar, J., Fienga, A., Gastineau, M., et al. (2011), La2010 orbital solution; CDS/VizieR J/A+A/532/A89; DOI 10.26093/cds/vizier.35320089.
Crowley, T.J. & Unterman, M.B. (2013), Global and Hemispheric 1200 Year Volcanic Climate Forcing Estimates; NOAA/WDS NCEI; DOI 10.25921/zztg-6f51.
Oscillatory Earth — Phase 1 Frozen Data Archive — Batch 1
Oscillatory_Earth_Phase1_Frozen_Data_Archive_Batch1.zip
Oscillatory_Earth_Phase1_Frozen_Data_Archive/SHA256SUMS.txt
8d003dd7996067e91cd9dd71bafb3095c76d1ef435503273389a709117dde627 R-01/SOURCE_PROVENANCE.json
631413eefe471c968b31e031e399ce5a3bf5bc882aeab1fa138856310f0c8979 P-01/SOURCE_PROVENANCE.json
9f55f38674d647c0514136158d6efa77a86379b1f12ee0044a4a8a3741417fed E-01/SOURCE_PROVENANCE.json
c70b42818af2f4676cc034cf0e984a50c784e60c1a8cd233d844e2a4aa367b37 E-01/nina34_anom_authoritative_text_snapshot.data
b075f63643e2e1d1cccc037f8fd0f6daffdd3bc7096a141f9a4f80e58fe6ac2f V-01/SOURCE_PROVENANCE.json
ebd90e7ace28a1a75deefd5b380ea37c7056541aec4e9907148b2776546b1b18 V-01/crowley2013_metadata_and_selected_rows_EXCERPT_ONLY.txt
Oscillatory_Earth_Phase1_Frozen_Data_Archive/README.txt
OSCILLATORY EARTH — PHASE 1 FROZEN DATA ARCHIVE
Acquisition Batch 1
This archive deliberately distinguishes three states:
1. AUTHORITATIVE_TEXT_SNAPSHOT_CAPTURED — a local snapshot of authoritative source content is present.
2. SOURCE_VERIFIED_BYTE_CAPTURE_PENDING — authoritative source and metadata are verified, but raw bytes are not yet frozen locally.
3. EXCERPT_ONLY — a provenance/inspection excerpt that MUST NOT be analyzed as the full dataset.
Current Batch 1:
- E-01 NOAA Niño 3.4: authoritative text snapshot captured locally.
- R-01 IERS EOP: source verified; byte capture pending.
- P-01 La2010 orbital solution: source/catalogue verified; byte capture pending.
- V-01 Crowley & Unterman volcanic forcing: source verified; full byte capture pending; metadata/selected-row excerpt included.
IMPORTANT:
This ZIP is an acquisition archive, not yet the complete ANALYSIS_READY archive. Do not run PC2, PC4, or PC5 from pointer/excerpt files.
Only E-01 has a local numerical source snapshot suitable for preliminary ingestion checks.
Oscillatory_Earth_Phase1_Frozen_Data_Archive/manifest.csv
dataset_id,archive_path,size_bytes,sha256
R-01,R-01/SOURCE_PROVENANCE.json,572,8d003dd7996067e91cd9dd71bafb3095c76d1ef435503273389a709117dde627
P-01,P-01/SOURCE_PROVENANCE.json,468,631413eefe471c968b31e031e399ce5a3bf5bc882aeab1fa138856310f0c8979
E-01,E-01/SOURCE_PROVENANCE.json,518,9f55f38674d647c0514136158d6efa77a86379b1f12ee0044a4a8a3741417fed
E-01,E-01/nina34_anom_authoritative_text_snapshot.data,8358,c70b42818af2f4676cc034cf0e984a50c784e60c1a8cd233d844e2a4aa367b37
V-01,V-01/SOURCE_PROVENANCE.json,572,b075f63643e2e1d1cccc037f8fd0f6daffdd3bc7096a141f9a4f80e58fe6ac2f
V-01,V-01/crowley2013_metadata_and_selected_rows_EXCERPT_ONLY.txt,935,ebd90e7ace28a1a75deefd5b380ea37c7056541aec4e9907148b2776546b1b18
Oscillatory_Earth_Phase1_Frozen_Data_Archive/P-01/SOURCE_PROVENANCE.json
{
"dataset": "La2010 orbital solution for long-term Earth motion",
"authority": "Laskar et al.; CDS/VizieR",
"source_url": "https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/532/A89",
"doi": "10.26093/cds/vizier.35320089",
"coverage": "long-term orbital solution; table includes 1 kyr sampling",
"status": "SOURCE_VERIFIED_BYTE_CAPTURE_PENDING",
"reason": "Catalogue and data table verified; FTP/catalogue byte download was not available to the runtime."
}
Oscillatory_Earth_Phase1_Frozen_Data_Archive/V-01/crowley2013_metadata_and_selected_rows_EXCERPT_ONLY.txt
# SOURCE METADATA EXCERPT — NOT THE COMPLETE DATA FILE
# Source: NOAA/WDS NCEI Crowley & Unterman (2013)
# URL: https://www.ncei.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/crowley2013/crowley2013aod-reff.txt
# Dataset DOI: 10.25921/zztg-6f51
# Study: Global and Hemispheric 1200 Year Volcanic Climate Forcing Estimates
# Variables: age_AD, AOD at 550 nm, effective aerosol radius (Reff, um)
# Coverage: 800–2000 CE
# Chronology stated by source: accurate to within ~1 yr for 1104–2000 and ~2 yr for 800–1103.
# This file is intentionally an excerpt/provenance record only and MUST NOT be analyzed as the full V-01 series.
age_AD AOD Reff
800 0.007 0.2
801 0.002 0.2
802 0.005 0.2
803 0.011 0.22
804 0.003 0.2
814 0.043 0.35
842 0.092 0.45
854 0.075 0.42
897 0.108 0.48
971 0.116 0.49
1193 0.085 0.44
1228 0.130 0.51
1229 0.249 0.63
1257 0.078 0.43
1258 0.571 0.83
1259 0.332 0.69
1456 0.272 0.65
1457 0.193 0.58
Oscillatory_Earth_Phase1_Frozen_Data_Archive/V-01/SOURCE_PROVENANCE.json
{
"dataset": "Global and Hemispheric 1200 Year Volcanic Climate Forcing Estimates",
"authority": "NOAA/WDS NCEI; Crowley & Unterman (2013)",
"source_url": "https://www.ncei.noaa.gov/pub/data/paleo/climate_forcing/volcanic_aerosols/crowley2013/crowley2013aod-reff.txt",
"doi": "10.25921/zztg-6f51",
"coverage": "800-2000 CE",
"resolution": "annual",
"status": "SOURCE_VERIFIED_BYTE_CAPTURE_PENDING",
"reason": "Raw authoritative text endpoint verified and readable, but the runtime cannot export the complete remote object byte-for-byte in one operation."
}
Oscillatory_Earth_Phase1_Frozen_Data_Archive/R-01/SOURCE_PROVENANCE.json
{
"dataset": "IERS Standard Rapid EOP Data / finals2000A.all",
"authority": "IERS Rapid Service Prediction Centre",
"source_url": "https://datacenter.iers.org/data/9/finals2000A.all",
"metadata_url": "https://datacenter.iers.org/versionMetadata.php?filename=latestVersionMeta/9_FINALS.ALL_IAU2000_V2013_019.txt",
"coverage": "1973-01-02 onward plus prediction horizon",
"resolution": "daily",
"status": "SOURCE_VERIFIED_BYTE_CAPTURE_PENDING",
"reason": "Authoritative endpoint verified, but this runtime could not complete a byte-for-byte HTTP download."
}
Oscillatory_Earth_Phase1_Frozen_Data_Archive/E-01/nina34_anom_authoritative_text_snapshot.data
1948 2026
1948 -0.43 -0.11 0.12 -0.00 0.43 -0.06 0.00 -0.22 -0.47 -0.95 -1.01 0.12
1949 -0.38 0.07 -0.85 -0.22 0.03 -1.14 -0.48 -0.50 -0.97 -0.81 -1.64 -1.35
1950 -1.41 -1.47 -1.07 -1.25 -1.35 -1.03 -0.80 -0.92 -1.27 -0.91 -1.29 -1.05
1951 -1.12 -0.60 -0.28 -0.13 -0.03 0.10 0.25 0.40 0.32 0.57 0.44 0.38
1952 0.19 0.09 -0.30 0.29 -0.26 -0.79 -0.72 -0.49 -0.40 -0.20 -0.44 -0.60
1953 0.27 0.18 -0.00 0.37 0.35 0.53 0.24 0.05 0.51 -0.08 0.44 -0.14
1954 0.09 0.24 -0.25 -0.62 -0.49 -0.63 -0.79 -1.16 -1.34 -0.70 -0.80 -0.95
1955 -0.66 -0.74 -0.85 -0.89 -1.28 -0.80 -1.27 -0.92 -1.43 -1.94 -1.90 -1.72
1956 -1.44 -0.79 -0.68 -0.72 -0.63 -0.66 -0.78 -0.92 -0.95 -0.82 -0.85 -0.56
1957 -0.40 -0.16 0.00 0.36 0.54 0.17 0.35 0.81 0.33 0.63 0.79 0.96
1958 1.37 1.35 0.91 0.44 0.35 0.28 0.10 0.15 -0.16 -0.09 0.14 0.06
1959 0.55 0.36 0.16 0.20 0.15 -0.29 -0.50 -0.47 -0.49 -0.25 -0.25 -0.24
1960 -0.40 -0.37 -0.21 -0.16 -0.25 -0.43 -0.41 -0.32 -0.30 -0.43 -0.49 -0.34
1961 -0.30 -0.20 -0.41 -0.37 -0.27 -0.03 -0.41 -0.64 -0.82 -0.82 -0.43 -0.57
1962 -0.68 -0.53 -0.49 -0.45 -0.71 -0.48 -0.42 -0.46 -0.77 -0.67 -0.64 -0.72
1963 -0.76 -0.51 -0.29 -0.17 -0.31 -0.41 0.52 0.42 0.44 0.57 0.47 0.57
1964 0.48 0.28 -0.33 -0.53 -0.88 -1.01 -0.92 -1.14 -1.40 -1.15 -1.37 -1.21
1965 -0.83 -0.47 -0.42 -0.30 -0.08 0.37 0.51 0.68 0.61 1.07 1.02 1.04
1966 0.78 0.44 0.66 0.28 -0.40 0.10 0.18 -0.29 -0.34 -0.39 -0.27 -0.53
1967 -0.81 -0.75 -0.58 -0.64 -0.31 -0.10 -0.31 -0.55 -0.79 -0.61 -0.51 -0.52
1968 -0.73 -0.70 -0.78 -0.52 -0.68 0.09 0.06 0.01 -0.24 0.12 0.53 0.45
1969 0.96 0.99 0.50 0.38 0.46 0.20 -0.11 0.17 0.33 0.46 0.46 0.66
1970 0.20 -0.05 0.04 0.17 -0.12 -0.42 -0.65 -0.88 -1.04 -0.89 -0.96 -1.18
1971 -1.71 -1.46 -1.30 -0.94 -0.92 -1.04 -0.90 -0.93 -1.05 -1.05 -0.92 -0.86
1972 -0.68 -0.20 -0.16 0.20 0.23 0.41 0.64 0.73 0.76 1.12 1.30 1.26
1973 1.09 0.91 0.39 -0.39 -0.64 -0.92 -1.13 -1.24 -1.43 -1.60 -2.05 -2.18
1974 -2.04 -1.60 -1.38 -1.11 -1.08 -0.61 -0.96 -0.57 -0.67 -1.08 -1.11 -0.97
1975 -0.58 -0.57 -0.87 -0.75 -0.98 -1.33 -1.21 -1.47 -1.69 -1.72 -1.51 -1.97
1976 -1.74 -1.04 -0.83 -0.59 -0.61 -0.30 -0.10 -0.01 0.16 0.52 0.66 0.36
1977 0.57 0.25 0.18 -0.23 -0.16 0.23 0.37 -0.01 0.26 0.59 0.61 0.61
1978 0.52 0.31 0.02 -0.49 -0.35 -0.47 -0.33 -0.77 -0.45 -0.44 -0.20 0.09
1979 0.05 0.05 0.07 0.05 -0.06 -0.05 -0.13 -0.20 0.17 0.04 0.33 0.48
1980 0.44 0.35 0.18 0.13 0.23 0.30 0.10 -0.35 -0.36 -0.20 0.08 0.10
1981 -0.45 -0.42 -0.11 -0.57 -0.29 -0.33 -0.55 -0.39 -0.22 -0.16 -0.42 -0.12
1982 0.07 -0.13 0.03 0.26 0.53 0.80 0.34 0.44 1.04 1.48 1.40 1.61
1983 1.68 1.48 1.15 0.66 0.68 0.41 -0.13 -0.23 -0.51 -1.08 -1.04 -0.77
1984 -0.79 -0.47 -0.60 -0.66 -0.69 -0.82 -0.54 -0.46 -0.41 -0.74 -0.97 -1.21
1985 -0.80 -0.83 -0.88 -1.01 -0.88 -0.85 -0.49 -0.46 -0.47 -0.40 -0.29 -0.25
1986 -0.50 -0.32 -0.30 -0.29 -0.22 -0.06 0.13 0.33 0.51 0.52 1.01 0.94
1987 0.84 0.90 0.87 0.59 0.63 0.84 0.98 1.05 1.18 1.15 1.08 0.89
1988 0.74 0.15 0.10 -0.45 -1.09 -1.35 -1.28 -1.10 -1.02 -1.72 -1.89 -1.75
1989 -1.81 -1.36 -1.11 -1.04 -0.72 -0.57 -0.52 -0.73 -0.38 -0.35 -0.45 0.07
1990 -0.01 0.35 0.12 0.27 0.15 0.02 0.27 0.22 0.22 0.31 0.22 0.37
1991 0.58 0.41 0.24 0.45 0.45 0.59 0.70 0.73 0.42 0.89 1.06 1.27
1992 1.34 1.32 1.19 1.17 0.97 0.57 0.37 0.09 -0.03 -0.17 -0.06 -0.00
1993 0.35 0.43 0.36 0.63 0.86 0.39 0.20 0.26 0.33 0.22 0.29 0.34
1994 0.22 -0.09 0.13 0.21 0.25 0.32 0.38 0.51 0.38 0.78 0.97 1.08
1995 0.84 0.80 0.52 0.32 0.12 0.02 -0.03 -0.49 -0.63 -0.75 -0.88 -0.77
1996 -0.68 -0.65 -0.50 -0.31 -0.25 -0.26 -0.31 -0.20 -0.33 -0.27 -0.19 -0.39
1997 -0.25 -0.08 0.05 0.44 0.72 0.91 1.21 1.40 1.63 1.69 1.85 1.78
1998 1.81 1.53 1.06 0.55 0.59 -0.44 -0.53 -0.74 -0.97 -1.16 -1.08 -1.45
1999 -1.68 -1.28 -0.90 -0.71 -0.78 -0.76 -0.89 -1.02 -0.87 -0.95 -1.33 -1.43
2000 -1.41 -1.26 -1.07 -0.81 -0.84 -0.55 -0.54 -0.35 -0.33 -0.56 -0.61 -0.89
2001 -0.74 -0.70 -0.39 -0.26 -0.14 0.00 0.13 0.07 -0.04 0.13 -0.11 -0.27
2002 0.01 0.15 0.22 0.28 0.40 0.65 0.66 0.67 0.81 0.93 1.20 1.25
2003 0.58 0.68 0.54 0.22 -0.26 0.12 0.26 0.30 0.21 0.49 0.44 0.43
2004 0.43 0.36 0.07 0.24 0.19 0.27 0.57 0.65 0.67 0.74 0.83 0.82
2005 0.77 0.48 0.55 0.40 0.33 0.27 -0.02 0.07 0.05 0.10 -0.26 -0.65
2006 -0.69 -0.63 -0.62 -0.14 0.02 0.19 0.26 0.51 0.66 0.76 0.99 1.08
2007 0.69 0.27 0.06 -0.01 -0.23 -0.02 -0.24 -0.53 -0.90 -1.07 -1.36 -1.42
2008 -1.60 -1.64 -1.14 -0.89 -0.75 -0.55 -0.17 -0.15 -0.29 -0.27 -0.39 -0.74
2009 -0.86 -0.65 -0.58 -0.15 0.22 0.54 0.60 0.61 0.63 0.97 1.38 1.59
2010 1.33 1.20 0.93 0.59 0.00 -0.38 -0.80 -1.08 -1.34 -1.49 -1.39 -1.43
2011 -1.40 -1.07 -0.79 -0.65 -0.46 -0.21 -0.18 -0.56 -0.69 -0.90 -0.92 -0.99
2012 -0.91 -0.64 -0.53 -0.29 -0.21 0.05 0.23 0.45 0.29 0.26 0.33 -0.01
2013 -0.30 -0.37 -0.23 -0.09 -0.25 -0.28 -0.23 -0.34 -0.10 -0.15 0.12 -0.16
2014 -0.25 -0.23 0.12 0.44 0.53 0.41 0.13 0.15 0.31 0.45 0.84 0.78
2015 0.63 0.67 0.74 1.07 1.10 1.23 1.35 1.49 1.67 1.91 2.21 2.13
2016 2.13 1.87 1.50 1.08 0.63 0.37 0.01 -0.10 -0.21 -0.39 -0.37 -0.17
2017 -0.23 0.22 0.18 0.35 0.40 0.45 0.38 0.05 -0.20 -0.12 -0.44 -0.65
2018 -0.64 -0.48 -0.49 -0.11 0.18 0.31 0.39 0.35 0.50 1.01 1.15 1.10
2019 0.88 0.87 0.92 0.82 0.83 0.80 0.65 0.35 0.18 0.78 0.82 0.73
2020 0.84 0.67 0.65 0.66 0.05 -0.05 0.08 -0.29 -0.66 -0.90 -0.89 -1.02
2021 -1.12 -1.00 -0.64 -0.47 -0.25 -0.03 -0.18 -0.36 -0.49 -0.74 -0.69 -0.89
2022 -0.56 -0.55 -0.67 -0.74 -0.78 -0.52 -0.50 -0.80 -0.93 -0.83 -0.74 -0.63
2023 -0.57 -0.47 -0.08 0.25 0.49 0.86 0.97 1.20 1.41 1.51 1.86 1.76
2024 1.64 1.39 1.04 0.98 0.50 0.37 0.40 0.19 -0.10 -0.01 -0.03 -0.52
2025 -0.64 -0.42 0.04 -0.05 0.07 0.15 0.14 -0.15 -0.32 -0.42 -0.54 -0.39
2026 -0.40 -0.02 0.22 0.74 1.09 1.58 1.73 -99.99 -99.99 -99.99 -99.99 -99.99
-99.99
NINA34
5N-5S 170W-120W
ERSST V6
Anomaly from 1981-2010
https://psl.noaa.gov/data/timeseries/month/DS/NINO34/
units=degC
https://psl.noaa.gov/data/timeseries/month/DS/NINO34/
units=degC
Oscillatory_Earth_Phase1_Frozen_Data_Archive/E-01/SOURCE_PROVENANCE.json
{
"dataset": "Ni\u00f1o 3.4 SST Index",
"authority": "NOAA PSL / CPC",
"source_url": "https://psl.noaa.gov/data/correlation/nina34.anom.data",
"coverage": "1948-2026 in source snapshot",
"resolution": "monthly",
"units": "degC anomaly",
"status": "AUTHORITATIVE_TEXT_SNAPSHOT_CAPTURED",
"local_file": "E-01/nina34_anom_authoritative_text_snapshot.data",
"note": "Snapshot content captured from the authoritative NOAA PSL text endpoint via web retrieval; checksum applies to this archived snapshot."
}
