{ "schemaVersion": "1.0", "updated": "2026-08-10", "status": "working-taxonomy", "claimCeiling": "Registry inclusion means that a release illustrates a reusable method. It does not establish the release's correctness, novelty, independent reproduction or real-world impact.", "aims": [ "science", "policy", "productivity" ], "methods": [ { "id": "certificate-first", "name": "Certificate-first, proof-carrying research", "definition": "Separate expensive discovery from cheaper checking by emitting a compact witness, proof object, bound or certificate with a fail-closed verifier.", "mechanism": "Enables parallel candidate generation, reproducible rejection and bounded review without requiring every checker to repeat the discovery process.", "applicability": [ "finite combinatorial search", "exact optimisation", "computer-assisted proof", "bounded symbolic computation" ], "failureModes": [ "the substantive claim is translated incorrectly into the encoded proposition", "generator and verifier share a defect", "finite evidence is promoted to a universal theorem", "certificate checking is described as independent reproduction" ], "aims": [ "science", "productivity" ], "representativeReleases": [ "z20-equals-6", "erdos-848-all-n", "txgraffiti-c3-resolution", "certified-two-item-jrp" ] }, { "id": "structural-compression", "name": "Structural compression", "definition": "Replace a high-dimensional search, state space or family of calculations with a lower-dimensional coordinate, invariant, kernel, normal form or representation.", "mechanism": "Reduces search and verification cost by exposing the load-bearing structure instead of enumerating the original object space.", "applicability": [ "algebraic and geometric classification", "spectral or rank problems", "exact optimisation", "constraint encodings" ], "failureModes": [ "the reduction faithfully solves the wrong formal object", "a conditional analytic or semantic bridge is omitted", "the reduced coordinate excludes relevant cases", "bounded computation is mistaken for structural closure" ], "aims": [ "science", "policy", "productivity" ], "representativeReleases": [ "smooth-point-certificates-polydegree-containments", "exact-smith-invariants-affine-determinant-lines", "cyclicity-root-span-low-rank", "bilateral-deficiency-regular-dim" ] }, { "id": "regime-stitching", "name": "Exact regime stitching", "definition": "Partition a large or infinite domain into explicitly covered regimes and use the most suitable exact method in each, with checked seams and endpoints.", "mechanism": "Avoids forcing one monolithic method across scales while retaining a complete coverage argument.", "applicability": [ "all-parameter theorems", "phase diagrams", "tail bounds", "parametric optimisation" ], "failureModes": [ "an endpoint or transition region is uncovered", "normalisations differ across regimes", "an external tail theorem is misapplied", "the coverage checker shares the construction error" ], "aims": [ "science", "productivity" ], "representativeReleases": [ "erdos-848-all-n", "certified-two-item-jrp", "exact-low-length-recht-re-inequalities", "hahn-ewens-mixing-theorem" ] }, { "id": "adversarial-controls", "name": "Adversarial scientific controls", "definition": "Deliberately corrupt signs, witnesses, manifests, assumptions or encodings and require the relevant validator to reject them.", "mechanism": "Detects ceremonial replay, fail-open checks and fragile evidence pipelines before downstream work accumulates around them.", "applicability": [ "scientific software", "certificate checkers", "data and manifest pipelines", "machine-readable research packages" ], "failureModes": [ "only anticipated error classes are tested", "producer-designed mutations share the producer specification", "multiple internal routes are called independent", "a green control suite is promoted to theorem verification" ], "aims": [ "science", "policy", "productivity" ], "representativeReleases": [ "exact-smith-invariants-affine-determinant-lines", "smooth-point-certificates-polydegree-containments", "bordered-jacobian-foundations", "affine-diversification-fibres" ] }, { "id": "research-lineage-reuse", "name": "Explicit research-lineage reuse", "definition": "Publish parent-child dependencies and reusable components so an adjacent result can inherit a bounded object without reconstructing the entire programme.", "mechanism": "Lowers reconstruction cost and makes cumulative method development inspectable.", "applicability": [ "companion theorems", "method extensions", "shared certificate architectures", "multi-release research programmes" ], "failureModes": [ "a child is misdescribed as independent confirmation", "a common parent defect propagates across a lineage", "dependencies are described only in prose", "publication fragments work without standalone utility" ], "aims": [ "science", "policy", "productivity" ], "representativeReleases": [ "z20-equals-6", "vr2-k4-equals-20", "bordered-jacobian-foundations", "exact-smith-invariants-affine-determinant-lines" ] }, { "id": "productive-failure", "name": "Productive failure and stop receipts", "definition": "Retain failed routes and blockers, publish independently useful modules, and state precisely why the parent target remains open or the programme stopped.", "mechanism": "Converts sunk work into reusable negative knowledge and can prevent repeated dead ends or unjustified continuation.", "applicability": [ "open conjecture attacks", "feasibility pilots", "non-identification", "failed optimisation routes" ], "failureModes": [ "selective disclosure hides unflattering failures", "a trivial failure is published without decision value", "a bounded calculation is inflated into the missing theorem", "the unresolved parent target is obscured" ], "aims": [ "science", "policy", "productivity" ], "representativeReleases": [ "irreducible-pushforwards-quartic-transitions", "random-reshuffling-baseline-policy", "stocks-are-not-flows", "smooth-point-certificates-polydegree-containments" ] }, { "id": "identification-gate", "name": "Identification before estimation", "definition": "Specify the estimand, observation map, accounting identities and rival mechanisms, then test whether the available evidence can distinguish the target before estimating it.", "mechanism": "Prevents false precision and redirects effort toward discriminating measurements or bounded conclusions.", "applicability": [ "causal attribution", "mechanism claims", "aggregate observational data", "policy evidence assessment" ], "failureModes": [ "the rival class is too narrow", "the observation map is semantically wrong", "conditional non-identification is advertised as universal", "non-identification is interpreted as a zero effect" ], "aims": [ "policy", "science" ], "representativeReleases": [ "stocks-are-not-flows", "affine-diversification-fibres" ], "programmePaths": [ "/observatory/" ] }, { "id": "partial-identification", "name": "Partial identification and robust decisions", "definition": "Characterise the admissible set and its sharp extrema, report incompatibility where appropriate, and identify decisions robust across the supported set.", "mechanism": "Replaces unsupported point estimates and finite random clouds with bounded decision-relevant uncertainty.", "applicability": [ "incomplete measurement", "multiple compatible latent histories", "model ambiguity", "value-of-information analysis" ], "failureModes": [ "input uncertainty is frozen without disclosure", "plausible states are excluded", "sampled extrema are called sharp", "utilities, rights or information costs are omitted" ], "aims": [ "policy", "science", "productivity" ], "representativeReleases": [ "affine-diversification-fibres", "stocks-are-not-flows", "certified-commitment-horizons" ], "programmePaths": [ "/observatory/" ] }, { "id": "counterexample-proxy-first", "name": "Counterexample- and proxy-first analysis", "definition": "Try to refute the proposed conjecture, proxy or search region before optimising or generalising it, and compare surrogates with the terminal outcome that matters.", "mechanism": "Prunes invalid programmes early and exposes metric reversals, obstructions and approximation gaps.", "applicability": [ "algorithm selection", "theoretical proxies", "structural conjectures", "heuristic optimisation" ], "failureModes": [ "the target outcome is undefined", "a narrow counterexample is overgeneralised", "distributional relevance is untested", "the invalidated proxy remains the decision criterion" ], "aims": [ "science", "policy", "productivity" ], "representativeReleases": [ "txgraffiti-c3-resolution", "exact-low-length-recht-re-inequalities", "random-reshuffling-baseline-policy", "reducible-incidence-divisors" ] }, { "id": "certified-decision-margin", "name": "Certified decision margins", "definition": "Compute how far inputs may move before a decision changes, or certify a result relative to a declared baseline with an explicit fallback when the sign is unresolved.", "mechanism": "Concentrates recomputation and human attention near decision boundaries while preserving a safe incumbent elsewhere.", "applicability": [ "forecast-sensitive planning", "resource-constrained optimisation", "selective automated action", "bounded-regret decisions" ], "failureModes": [ "the baseline is mismatched", "switching or measurement costs are omitted", "the model is transferred beyond its declared scope", "nominal stability is confused with field robustness" ], "aims": [ "policy", "productivity" ], "representativeReleases": [ "certified-commitment-horizons", "certified-two-item-jrp", "random-reshuffling-baseline-policy", "affine-diversification-fibres" ] }, { "id": "assurance-vector", "name": "Assurance as a vector", "definition": "Keep semantic mapping, certificate checking, producer replay, independent rerun, independent reimplementation, formal verification, specialist review, peer review and impact as separate claims.", "mechanism": "Prevents evidence from one dimension borrowing credibility from another and directs scarce review to the unresolved gate.", "applicability": [ "AI-assisted research", "computer-assisted proof", "open evidence packages", "policy and productivity evaluation" ], "failureModes": [ "one omnibus badge replaces scoped states", "correlated agents are counted as independent", "producer replay is described as acceptance", "protocol conformance is treated as impact" ], "aims": [ "science", "policy", "productivity" ], "representativeReleases": [ "z20-equals-6", "exact-smith-invariants-affine-determinant-lines", "stocks-are-not-flows", "random-reshuffling-baseline-policy" ], "programmePaths": [ "/observatory/assurance/", "/productivity/" ] }, { "id": "agent-readable-research-object", "name": "Agent-readable research objects", "definition": "Publish claims, dependencies, evidence, objections, open problems and replay routes in durable machine-readable forms alongside human explanations.", "mechanism": "Reduces rediscovery and reconstruction cost when another person or agent audits, extends or challenges the work.", "applicability": [ "open scholarly communication", "distributed review", "research handoff", "automated evidence triage" ], "failureModes": [ "machine-readable errors propagate faster", "metadata integrity is confused with scientific truth", "schemas omit the semantic boundary", "communication assets are counted as evidence" ], "aims": [ "science", "policy", "productivity" ], "representativeReleases": [ "z20-equals-6", "erdos-848-all-n", "exact-smith-invariants-affine-determinant-lines", "random-reshuffling-baseline-policy" ] }, { "id": "staged-adoption-evaluation", "name": "Staged adoption and impact evaluation", "definition": "Keep method conformance separate from benefit and progress through usability, feasibility, controlled comparison and organisational follow-up with explicit stop rules.", "mechanism": "Prevents model-only or structural checks from becoming workplace-impact claims and preserves evidence about burden, errors, rework and adoption.", "applicability": [ "agent workflow adoption", "organisational pilots", "human-computer work evaluation", "method transfer" ], "failureModes": [ "an underpowered pilot is promoted", "missing outcomes are deleted", "field association is called causal", "average gain conceals harm or support cost" ], "aims": [ "productivity", "policy" ], "representativeReleases": [ "random-reshuffling-baseline-policy", "certified-two-item-jrp", "certified-commitment-horizons" ], "programmePaths": [ "/productivity/", "/protocols/start/" ] } ], "methodClusters": [ { "id": "binary-form-jacobian-and-obstruction", "name": "Binary-form Jacobian, determinant and obstruction toolkit", "members": [ "degree-difference-affine-slices", "bordered-jacobian-foundations", "exact-smith-invariants-affine-determinant-lines", "smooth-point-certificates-polydegree-containments", "reducible-incidence-divisors", "exotic-affine-three-spheres" ], "sharedBoundary": "Related internal releases can reuse identities and methods but do not independently validate their shared mathematical or semantic premises." }, { "id": "cyclicity-and-spectral-compression", "name": "Cyclicity and spectral compression", "members": [ "cyclicity-loci-exponential-periods", "cyclicity-root-span-low-rank", "hahn-ewens-mixing-theorem" ], "sharedBoundary": "Exact algebraic or representation-theoretic compression does not discharge every analytic bridge or establish application-level impact." }, { "id": "exact-combinatorial-certificates", "name": "Exact combinatorial certificate architecture", "members": [ "z20-equals-6", "vr2-k4-equals-20", "txgraffiti-c3-resolution", "bilateral-deficiency-regular-dim", "erdos-848-all-n" ], "sharedBoundary": "Certificate replay establishes encoded bounded claims; source-to-encoding correctness and independent reconstruction remain separate." }, { "id": "identification-and-robust-operations", "name": "Identification and robust operations", "members": [ "stocks-are-not-flows", "affine-diversification-fibres", "certified-commitment-horizons", "certified-two-item-jrp" ], "sharedBoundary": "Identified sets, exact bounds and decision margins are conditional on the declared observation map and model; real-world decision effects are unmeasured." }, { "id": "sampling-and-optimisation-diagnostics", "name": "Sampling and optimisation diagnostics", "members": [ "random-reshuffling-baseline-policy", "exact-low-length-recht-re-inequalities" ], "sharedBoundary": "Exact quadratic or finite-factor counterexamples do not establish frequency or magnitude in model-scale nonlinear workloads." }, { "id": "grand-problem-salvage", "name": "Grand-problem salvage", "members": [ "irreducible-pushforwards-quartic-transitions" ], "sharedBoundary": "The extracted modules may be useful while the parent conjecture remains explicitly unresolved." } ], "lineages": [ { "id": "binary-form-programme", "name": "Binary-form factorisation programme", "rootReleaseSlug": "degree-difference-affine-slices", "members": [ "degree-difference-affine-slices", "exotic-affine-three-spheres", "reducible-incidence-divisors", "bordered-jacobian-foundations", "exact-smith-invariants-affine-determinant-lines" ], "basis": "Each member explicitly identifies another member as foundational, parent, child, companion or continuation work in the published release metadata.", "sharedBoundary": "Dependency and reuse within this programme are not independent confirmation; a shared semantic or mathematical defect can propagate across the lineage." }, { "id": "cyclicity-programme", "name": "Fixed-seed cyclicity programme", "rootReleaseSlug": "cyclicity-loci-exponential-periods", "members": [ "cyclicity-loci-exponential-periods", "cyclicity-root-span-low-rank" ], "basis": "The root-span release explicitly cites the cyclicity-loci release as its predecessor and extends the same fixed-seed cyclicity programme.", "sharedBoundary": "The child release reuses the fixed-seed framework and therefore does not independently confirm the parent release or its analytic bridge." } ], "releaseAssignments": { "affine-diversification-fibres": [ "structural-compression", "adversarial-controls", "identification-gate", "partial-identification", "certified-decision-margin", "agent-readable-research-object" ], "bilateral-deficiency-regular-dim": [ "certificate-first", "structural-compression", "adversarial-controls", "research-lineage-reuse" ], "bordered-jacobian-foundations": [ "structural-compression", "adversarial-controls", "research-lineage-reuse", "assurance-vector" ], "certified-commitment-horizons": [ "certificate-first", "structural-compression", "partial-identification", "certified-decision-margin", "staged-adoption-evaluation" ], "certified-two-item-jrp": [ "certificate-first", "structural-compression", "regime-stitching", "certified-decision-margin", "staged-adoption-evaluation" ], "cyclicity-loci-exponential-periods": [ "certificate-first", "structural-compression", "adversarial-controls", "counterexample-proxy-first" ], "cyclicity-root-span-low-rank": [ "structural-compression", "adversarial-controls", "research-lineage-reuse", "productive-failure" ], "degree-difference-affine-slices": [ "structural-compression", "adversarial-controls", "research-lineage-reuse" ], "erdos-848-all-n": [ "certificate-first", "regime-stitching", "adversarial-controls", "agent-readable-research-object" ], "exact-low-length-recht-re-inequalities": [ "certificate-first", "regime-stitching", "adversarial-controls", "counterexample-proxy-first" ], "exact-smith-invariants-affine-determinant-lines": [ "certificate-first", "structural-compression", "adversarial-controls", "research-lineage-reuse", "assurance-vector", "agent-readable-research-object" ], "exotic-affine-three-spheres": [ "structural-compression", "adversarial-controls", "counterexample-proxy-first", "research-lineage-reuse" ], "hahn-ewens-mixing-theorem": [ "structural-compression", "regime-stitching", "adversarial-controls" ], "irreducible-pushforwards-quartic-transitions": [ "structural-compression", "productive-failure", "agent-readable-research-object" ], "random-reshuffling-baseline-policy": [ "certificate-first", "productive-failure", "counterexample-proxy-first", "certified-decision-margin", "assurance-vector", "agent-readable-research-object", "staged-adoption-evaluation" ], "reducible-incidence-divisors": [ "structural-compression", "counterexample-proxy-first", "research-lineage-reuse" ], "smooth-point-certificates-polydegree-containments": [ "certificate-first", "structural-compression", "regime-stitching", "adversarial-controls", "research-lineage-reuse", "productive-failure" ], "stocks-are-not-flows": [ "identification-gate", "partial-identification", "productive-failure", "assurance-vector", "agent-readable-research-object" ], "txgraffiti-c3-resolution": [ "certificate-first", "adversarial-controls", "research-lineage-reuse", "counterexample-proxy-first" ], "vr2-k4-equals-20": [ "certificate-first", "research-lineage-reuse", "assurance-vector" ], "z20-equals-6": [ "certificate-first", "adversarial-controls", "research-lineage-reuse", "assurance-vector", "agent-readable-research-object" ] }, "updatePolicy": { "mode": "append-only-semantic-history", "rules": [ "Do not rewrite a published method, method cluster, lineage identity, name, basis, root or shared boundary, or release assignment in place; retain the prior entry and use a new identifier or dated successor for a semantic replacement.", "Append a lineage member only at the tail after its release declares the reciprocal lineage identifier and an evidential parent link to an earlier member, unless it is the explicitly registered root; never delete, replace or reorder a published member.", "Append a dated changeLog entry for every semantic addition, correction, deprecation or reassignment.", "Keep broad method clustering separate from evidence-backed research lineage, and do not infer lineage from topical similarity alone.", "Registry inclusion or revision does not promote correctness, novelty, independent reproduction or real-world impact." ] }, "changeLog": [ { "date": "2026-08-10", "summary": "Established the initial working taxonomy, distinguished broad method clusters from the two release programmes with explicit lineage evidence, and aligned representative releases with their release assignments." }, { "date": "2026-08-10", "summary": "Named an immutable root for each lineage and adopted append-only tail membership with reciprocal per-release lineage and parent evidence; a singleton lineage records only a prospective programme root, not demonstrated reuse." } ] }