Coordinate-Addressed Algorithm Discovery
Secretary Suite Shards, Multidimensional Digital Fingerprints, and Cross-Domain Relational Reuse
A Secretary Suite Project | Cross-disciplinary research paper | September 26, 2026
John Swygert
Proposed for publication across the author’s three journals; journal-specific framing may be adapted without changing the technical claims.
Abstract
This paper proposes a coordinate-addressed architecture for storing reusable problem-solving structures once, identifying them through Secretary Suite Shards carrying a Multidimensional Digital Fingerprint (MDDF), and discovering previously unrecognized applications across domains. The central hypothesis is that relationally equivalent problems can share a canonical algorithmic definition while retaining distinct domain mappings, assumptions, boundary conditions, and execution contexts. An MDDF is proposed as a searchable, versioned signature of a shard’s structural and operational properties, not as proof of equivalence. The architecture separates candidate retrieval from rigorous compatibility testing and solution validation; it also records failed transfers. A reproducible evaluation protocol compares independent domain-specific solving against coordinate-addressed retrieval and adaptation, measuring solution quality, computational cost, storage, retrieval latency, and the rate of useful novel mappings. The proposal is an independently testable Secretary Suite computational research program and may also serve as an applied investigation of TSTOEAO’s relational-coordinate ideas. It does not require acceptance of TSTOEAO as a physical theory.
Keywords: Secretary Suite; Shards; MDDF; multidimensional digital fingerprint; relational invariance; algorithm retrieval; cross-domain transfer; canonical coordinates; knowledge compression; hypothesis generation.
1. The Problem: Repeated Structure, Fragmented Knowledge
Algorithms are commonly indexed by field, vocabulary, software package, or original use case. A new biological problem may therefore be approached only with biological methods even when its essential constraints resemble a solved routing, optimization, or control problem elsewhere. Repeated definitions also fragment updates: an improved procedure can be copied inconsistently across many repositories. This paper asks whether a shared relational coordinate system could improve both the economy of representation and the discovery of new applications.
The stronger claim is not that all problems reduce to one algorithm. It is that some problems in different domains preserve enough structure for a common method to apply, and that a system designed to find those cases could outperform one organized solely by disciplinary labels.
2. Secretary Suite Shards and the MDDF
In this proposal, a Secretary Suite Shard is an addressable unit of reusable computational or conceptual capability. A shard contains or references a canonical definition, executable or formal specification where available, applicability conditions, known domain mappings, provenance, version history, and a Multidimensional Digital Fingerprint (MDDF). This is specifically the Secretary Suite Shards architecture; it is not a claim about LOGOS literary shards.
The MDDF is the shard’s multidimensional retrieval and comparison signature. It should encode as many relevant dimensions as the problem requires, while explicitly representing missing or uncertain dimensions. It may include:
Relational topology: entities, edges, directionality, cardinality, hierarchy, and temporal ordering.
Mathematical behavior: conservation rules, monotonicity, symmetry, linearity, continuity, stochasticity, and optimization objective.
Interface signature: inputs, outputs, units, variable types, required observations, and permissible transformations.
Operational constraints: boundary conditions, resource limits, computational complexity, safety constraints, and known failure modes.
Evidence and provenance: derivation, benchmarks, successful and unsuccessful mappings, confidence intervals, source identifiers, and version.
An MDDF must not be treated as a magical universal hash: collisions, incomplete descriptions, and context-dependent behavior are expected. It is a discovery index that proposes candidates for subsequent proof, simulation, or empirical testing.
3. Canonical Coordinates and Domain Overlays
Let R denote a canonical relational structure and A(R) its stable coordinate in the Secretary Suite registry. Let D be a domain and M_D a mapping from the canonical structure to that domain’s entities, variables, units, and constraints. A domain realization is S_D = M_D(R). A single canonical definition may support many mappings M_D1, M_D2, …, without requiring separate authoritative definitions of R.
The address identifies a versioned definition, not an assumption that every realization is equivalent. Distinct domain mappings retain their own evidence, restrictions, and outcomes. A stable logical address can point to an immutable version identifier; newer versions must not silently alter earlier published results. Physical caching and replicated copies remain desirable when they improve reliability and speed. “Store once” therefore means one canonical authority, not one literal copy on one device.
4. What Must Survive a Transfer?
A candidate transfer from domain D1 to D2 is permissible only when the properties required by the algorithm survive the mapping. Let I_req(R) be the set of required invariants for algorithm R and I_D the invariants demonstrably preserved in a proposed domain mapping. A necessary screening condition is I_req(R) ⊆ I_D. It is not by itself sufficient: units, causal assumptions, data quality, boundary conditions, and implementation constraints must also be checked.
A graph-flow routine, for example, may transfer from road logistics to nutrient transport only if the intended quantities, edge capacities, conservation assumptions, and objective function have meaningful counterparts. Similar diagrams do not establish identical physics. An apparent match that fails conservation or causality must be rejected or reformulated.
5. Discovery Beyond Known Applications
The central extension is open-ended discovery. The registry should not merely answer “Where has this algorithm already been used?” It should also ask “Which presently unlinked problems have an MDDF compatible with this algorithm’s required structure?” New problems can be converted into provisional fingerprints and matched against shards from every indexed field. A discovery engine ranks candidates for testing without claiming that a high similarity score proves validity.
Candidate generation can combine graph matching, typed constraint unification, semantic retrieval, dimensional analysis, formal verification where feasible, and controlled simulation. Crucially, the search can run in both directions: a new problem may query all shards, and a newly registered shard may be evaluated against an existing backlog of unresolved problems.
6. Reference Architecture
6.1 Registry and shard schema
Each shard should have: canonical coordinate; immutable version; human-readable name; formal or executable definition; MDDF; required invariants; supported mappings; test suites; provenance; licensing; and failure records. The registry stores relationships among shards, including composition, specialization, incompatibility, and derivation.
6.2 Problem ingestion
An incoming problem is represented as a typed relational model. The system separates observed facts from hypotheses, identifies uncertain variables, extracts boundary conditions, and creates a provisional problem MDDF. Human review is important where descriptions are incomplete or consequences are significant.
6.3 Candidate retrieval and verification
A broad retrieval stage proposes candidate shards by MDDF similarity. A stricter compatibility stage checks required invariants, assumptions, units, input availability, and forbidden transformations. Surviving candidates are adapted and evaluated against a domain-specific baseline. Results are registered with reproducible evidence, not simply appended as claimed successes.
6.4 Composition and multiple scenarios
Some problems require several shards. A planner may compose compatible shards into a directed workflow and evaluate several plausible models before choosing an intervention. Shared subproblems can be cached, but incompatible assumptions must be surfaced rather than silently merged.
7. Compression as a Discovery Mechanism
The first benefit is representational: one authoritative relational definition and many lightweight mappings can replace many separately maintained definitions. A second potential benefit is computational: verified derivations, test cases, and partial solutions may be reused when the required conditions match. The third, less obvious benefit is epistemic: shared representation makes applications from unrelated disciplines discoverable through the same structural index.
This resembles abstraction and deduplication but differs from mere file compression. The goal is to preserve the meaning and conditions needed to retrieve, adapt, and verify a solution. An excessively compressed MDDF that loses decisive boundary conditions can increase false matches and waste computation. The optimum is not the shortest possible fingerprint; it is the smallest representation that supports reliable discovery and verification.
8. Proposed Evaluation Program
8.1 Test collections
Construct benchmark families with known cross-domain structural relationships, including network flow, scheduling, feedback control, resource allocation, graph diffusion, and constrained optimization. For each family, include equivalent instances, near-misses that violate a key assumption, and genuinely unrelated distractors. Reserve entire domains as held-out tests so the system cannot succeed by memorizing familiar labels.
8.2 Comparison conditions
Baseline A: independent domain-specific retrieval and solving, without cross-domain registry access.
Baseline B: ordinary semantic search over all descriptions, without structured MDDF fields.
Experimental C: MDDF retrieval, invariant screening, domain adaptation, and evidence registration.
Ablation D: the experimental system with selected MDDF dimensions or failure records removed.
8.3 Measurements
Measure top-k candidate recall, false-positive transfer rate, correctness under held-out tests, time to validated solution, total computational cost, registry storage, cache efficiency, and maintenance effort after an algorithm update. Track novel validated cross-domain mappings separately from rediscovery of known mappings. Record human review time, because apparent automation gains may conceal substantial manual verification.
8.4 Falsification criteria
The central practical claim is weakened if MDDF-guided retrieval does not improve validated solution discovery over semantic search after accounting for verification cost, or if its false matches consistently outweigh its reuse gains. Compression claims fail where metadata and mapping overhead exceed saved maintenance or storage. Novel-discovery claims fail if apparent new mappings do not survive held-out domain tests. Negative results must be retained as first-class registry records.
9. Illustrative Applications
9.1 Forest decline and causal reconstruction
A temporal causal-reconstruction shard might distinguish predisposition, initiation, transmission, amplification, and terminal mortality. A candidate mapping to clinical diagnosis could reveal similar causal questions, while domain-specific biology, measurements, and interventions remain distinct. The registry should encode the analogy as a hypothesis until the necessary causal structure has been tested.
9.2 Logistics and biological distribution
A constrained network-flow shard may be applicable to both delivery routing and selected models of biological transport. The shared abstraction is not proof that real biological systems optimize the same objective; conservation and capacity assumptions require explicit validation.
9.3 Software fault localization and ecological failure
Dependency graphs and fault-propagation procedures could suggest questions for investigating cascading ecological damage. The comparison becomes useful when it identifies discriminating tests, not merely when both systems can be drawn as networks.
10. Relationship to TSTOEAO
The Secretary Suite implementation offers an operational test bed for coordinate-addressed relational reuse, domain overlays, and invariant-preserving transport. In the terminology of the author’s broader TSTOEAO research program, the registry provides candidate coordinates for reusable structures, while mappings instantiate those structures in distinct domains. These computational constructs are proposed analogues and engineering commitments; they do not establish a physical universal coordinate system or validate any untested physical interpretation.
This separation is productive. The computational architecture can be implemented, benchmarked, criticized, and improved independently. Positive results would support the usefulness of the retrieval-and-transfer methodology, not automatically the truth of a theory of everything.
11. Attribution, Provenance, and Stewardship
Because shared shards can propagate widely, attribution must be part of the architecture rather than an optional afterthought. Every canonical shard should carry original authorship, source identifiers, licenses, version lineage, and citations for incorporated work. Each domain mapping should record who proposed it, who validated it, what changed, and which source evidence supports it. An MDDF identifies structure; it is not by itself a copyright watermark or proof of authorship.
A downstream generated artifact should retain a machine-readable provenance manifest referencing the canonical shard coordinates and the mappings actually used. The system should also distinguish independent rediscovery from documented derivation. This makes the proposed compression model compatible with meaningful credit rather than allowing a shared library to erase contributors.
12. Implementation Roadmap
Phase I — Define a minimal shard schema and MDDF vocabulary. Implement a small registry with immutable versioning and ten to twenty well-characterized algorithms.
Phase II — Create paired cross-domain benchmarks and adversarial near-miss cases. Implement structural candidate retrieval and explicit invariant checks.
Phase III — Add mapping tools, executable validation, failure records, and provenance manifests. Compare against semantic search and independent solving.
Phase IV — Introduce shard composition, asynchronous discovery across an unresolved-problem backlog, and human-in-the-loop review. Publish benchmark datasets, protocols, and both positive and negative results.
13. Limitations and Open Questions
No single fingerprint is guaranteed to capture every useful feature of an algorithm. Equivalent formulations may look different, and similar formulations may have incompatible causal meanings. Canonicalization can itself be computationally expensive. Registry governance raises questions about version disputes, competing definitions, security, licensing, and the right to contest an asserted mapping. Discovery engines may favor well-documented fields and underrepresent disciplines whose knowledge is difficult to formalize. Finally, physical memory savings may be small relative to the value of faster access and verified reuse; all three benefits should be measured separately.
Conclusion
A reusable problem-solving structure may have far more applications than its original developers recognized. Secretary Suite Shards equipped with a Multidimensional Digital Fingerprint offer a proposed mechanism for finding those applications: define a structure at a stable coordinate, characterize its required invariants, retrieve it by structural similarity, map it into new domains, and validate every transfer. The architecture links economical representation with a broader discovery process while preserving domain-specific constraints, provenance, and negative results. Its significance is an experimentally answerable question: can a shared, coordinate-addressed library of relational structures help people and machines solve unfamiliar problems more accurately or efficiently than discipline-bound methods? The next step is to build and benchmark it.
Publication and Research Note
This manuscript presents an original proposed architecture and research protocol, not completed experimental findings. Illustrative mappings are hypotheses. A versioned public release should include the MDDF schema, example shards, benchmark definitions, and a provenance manifest. For publication in multiple journals, preserve a canonical version and clearly identify journal-specific adaptations to avoid ambiguity about priority and citation.
