{ "schemaVersion": "1.0", "updated": "2026-09-06", "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": "rbm43-eight-point-leakage-obstruction-2026-09-06", "name": "RBM(4,3) finite-selector leakage obstruction", "members": [ "rbm43-eight-point-obstruction" ], "sharedBoundary": "Unrefereed fixed classical real binary RBM(4,3) obstruction; no exact hidden threshold, minimality, sharp error, unaffiliated validation, formal proof, priority or impact claim." }, { "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." }, { "id": "cross-field-identification-and-selector-provenance", "name": "Cross-field identification and selector provenance", "members": [ "unique-answer-not-identified" ], "sharedBoundary": "A common Selector Ledger can expose assumption-supported narrowing across fields without establishing that their observation maps share one exact symmetry, that the field mappings are independently validated, or that the reporting instrument improves practice." }, { "id": "certified-demographic-identifiability", "name": "Certified demographic identifiability auditing", "members": [ "sfs-identifiability-audit" ], "sharedBoundary": "Certified identified-set bounds and pre-registered audits expose what declared error models concede without establishing that any declared model is scientifically correct, that the underlying spectra are artefact-free, or that a setting-conditional verdict settles the biological dispute." }, { "id": "wales-policy-attribution-identification", "name": "Wales policy-attribution identification audit", "members": [ "wales-20mph-casualty-attribution" ], "sharedBoundary": "The constructive witness establishes non-identification only for the registered aggregate corpus, affected-road estimand and admitted rival class; it does not estimate the policy effect, settle policy merit or establish workflow impact." }, { "id": "polydegree-fourier-persistence-certificates", "name": "Polydegree smooth-point and Fourier-persistence certificates", "members": [ "full-e3-column-polydegree-conjecture" ], "sharedBoundary": "The all-degree conclusion depends jointly on the stated Jacobian smooth-point reduction, asymptotic Fourier limit, exact eventual envelope and finite Arb bridge. Producer-side replay and reuse of the earlier smooth-point package do not constitute independent theorem reconstruction, specialist review or evidence for the conjectural fixed-e programme." }, { "id": "polydegree-e4-fourier-formal-boundary-bundle", "name": "Effective e=4 Polydegree persistence and scoped companion assurance", "members": [ "full-e4-polydegree-column" ], "sharedBoundary": "The all-degree e=4 candidate depends on the published specialization criterion, the stated smooth-zero and Fourier-persistence bridges, a producer-side finite Arb ledger and an analytic tail. The scoped Lean companion and conditional boundary theorem do not independently confirm the Polydegree argument or establish Furter's R(3), JC2, HC4, priority or workflow impact." }, { "id": "aggregation-licence-and-target-sufficiency", "name": "Aggregation licences and target sufficiency", "members": [ "aggregation-without-sufficiency" ], "sharedBoundary": "A common fibre-factorisation diagnostic can expose missing decision-relevant information across fields without establishing that their scientific mechanisms are identical, that the admissible sets and targets are empirically valid, or that the proposed reporting licence improves research or policy decisions." }, { "id": "frankl-entropy-obstruction-and-repair", "name": "Frankl entropy obstruction and repaired reductions", "members": [ "frankl-concavity-obstruction" ], "sharedBoundary": "The source-specific counterdirection and repaired support reductions do not prove the global candidate inequality, establish a new Frankl bound, validate the uninspected CISS text, or convert producer-side exact and directed-rounding checks into independent mathematical review." }, { "id": "finite-polynomial-rigidity-certificates", "name": "Finite polynomial-rigidity certificates and executable frontier", "members": [ "furter-r3-through-299" ], "sharedBoundary": "Exact finite-field certificates plus properness establish only the stated finite R(3,n) instances. They do not supply an all-degree theorem, independent reconstruction, a proof of the unrestricted Strong Factorial Conjecture or the general Polydegree Conjecture, or evidence of research-workflow impact." }, { "id": "inverse-root-support-fusion-atlas", "name": "Inverse-root support, Fourier fusion and bounded coefficient atlases", "members": [ "cyclicity-support-fusion-atlas" ], "sharedBoundary": "The universal written support and fusion theorems and the exact degree-twenty atlas remain unrefereed producer-workflow claims. Finite atlas replay does not establish the all-degree coefficient conjecture, independent reconstruction, specialist review, priority or field impact." }, { "id": "finite-sample-affine-signal-to-decision", "name": "Finite-sample affine signal-to-decision workflows", "members": [ "finite-sample-affine-diversification" ], "sharedBoundary": "The exact fixed-stem signal band and affine decision rule are conditional on the declared homogeneous model and observation boundary. Producer replay and a finite CRABS benchmark do not establish biological validity, broad comparative utility, independent reconstruction, specialist review, priority or field impact." }, { "id": "inverse-root-support-fusion-all-degree-2026-08-21", "name": "All-degree inverse-root classification and rank-preserving extension oracles", "supersedes": "inverse-root-support-fusion-atlas", "effectiveDate": "2026-08-21", "members": [ "cyclicity-support-fusion-atlas" ], "sharedBoundary": "The all-degree low-rank coefficient classification and extension oracle are unrefereed producer-workflow claims relative to named primitive-monodromy and finite-projective-group classifications. Written proof, partial Lean controls, separate same-programme CAS implementations, finite regressions and internal model-assisted re-audits do not establish correctness of imported results, independent reconstruction, external specialist review, priority or field impact." }, { "id": "inverse-root-amplitude-laurent-moments-2026-08-21", "name": "Inverse-root amplitude, endpoint-moment and Laurent-channel calculus", "supersedes": "inverse-root-support-fusion-all-degree-2026-08-21", "effectiveDate": "2026-08-21", "members": [ "cyclicity-support-fusion-atlas" ], "sharedBoundary": "The combined fixed-seed, polynomial-amplitude, specified-zero-cycle and Laurent local-channel theorems are unrefereed producer-workflow claims. The all-degree fixed-seed and endpoint classifications remain relative to named imported monodromy, finite-projective-group, Ritt and polynomial-moment results. Exact replay, partial Lean controls, same-programme CAS implementations, finite regressions and internal model-assisted review do not establish correctness of the imported results, a finite all-Laurent atlas, independent reconstruction, external specialist review, priority or field impact." }, { "id": "three-item-jrp-certification-and-logistics-handoff", "name": "Exact three-item replenishment certification and logistics handoff", "members": [ "certified-three-item-jrp-gap" ], "sharedBoundary": "The exact rational witness, finite primitive-plus-boundary closure, producer-side verifier and staged logistics protocol support a scoped unrefereed candidate only. They do not establish the exact global constant, independent reconstruction, formal verification, external specialist or editorial peer review, operational validation, savings or field impact." }, { "id": "txgraffiti-order48-certificate-successor", "name": "Order-48 cubic counterexample and exhaustive independent-domination certificate", "members": [ "txgraffiti-order48-successor" ], "sharedBoundary": "The explicit graph, witnesses and proof-tree replay establish only the stated order-48 object theorem and counterexample-order upper bound. They do not establish global minimality, uniqueness, independent reconstruction, formal verification, specialist review, priority or workflow impact." }, { "id": "s6-conditional-geometry-and-adjudication", "name": "Conditional geometry and executable adjudication around a claimed complex S6", "members": [ "s6-extension-results-candidate" ], "sharedBoundary": "Exact arithmetic, symbolic replay and written arguments under explicit hypotheses do not establish the source manuscript's compact complex threefold, smoothness, S6 topology, independent reconstruction, external specialist review, priority or workflow impact." }, { "id": "lps-fixed-width-structural-and-padic-programme", "name": "Fixed-width LPS reductions, quartic gauge repair and p-adic signals", "members": [ "lps-structural-reductions" ], "sharedBoundary": "The determinant duality, fixed-width adjacent-flag reduction, localized quartic gauge bridge, bounded exact checks and p-adic certificates expose a smaller research target. They do not establish the missing uniform radical membership, any of the five target conjectures, independent reconstruction, formal verification, external specialist review, priority or workflow impact." }, { "id": "amplitude-modules-fused-support-bautin-2026-08-28", "name": "Amplitude modules, fused inverse support and an ordinary coefficient-Bautin cutoff", "members": [ "amplitude-modules-fused-support-bautin-bound" ], "sharedBoundary": "The written classifications, exact producer replay and model-mediated editorial repair support an anonymous unrefereed theorem candidate only. They do not establish independent reconstruction, formal verification, external specialist or editorial peer review, identity with alternative Bautin conventions, absolute priority, three historically posed open problems solved, a real planar limit-cycle bound or research impact." }, { "id": "o01d0-hermite-boundary-and-falsification-2026-08-28", "name": "O-01d0 polar-fibre, Hermite-boundary, and falsification reductions", "members": [ "o01d0-polar-fibre-structural-reductions" ], "sharedBoundary": "The fixed-index properness criterion, Hermite incidence and boundary lemmas, exact architecture failures, and bounded pair-content scans expose four executable gates. They do not establish uniform O-01d0, AF5 transversality, any linked conjecture, independent reconstruction, formal verification, external specialist review, priority, or workflow impact." }, { "id": "odd-order-popular-difference-counterexample-2026-08-29", "name": "Three-layer popular-difference counterexample and endpoint obstruction", "members": [ "odd-order-one-third-popular-differences" ], "sharedBoundary": "The exact C21 witness, elementary three-layer count, below-2/5 odd-cyclic obstruction, producer replay and targeted source audit support an anonymous unrefereed candidate. They do not establish sufficiency or sharpness at 2/5, witness minimality, exhaustive novelty, absolute priority, independent reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact." }, { "id": "four-state-monotone-row-diameter-counterexample-2026-08-29", "name": "Four-state monotone row-diameter counterexample and two-spin classification", "members": [ "extremes-do-not-always-maximise" ], "sharedBoundary": "The exact four-state witness, all-time two-spin classification, cardinality-minimality proof, bounded zero-field screen and producer replay support an anonymous unrefereed candidate. They do not settle the all-graph zero-field Ising question or AIM diagnostics 1.6(2-3), and do not establish exhaustive novelty, absolute priority, independent reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact." }, { "id": "negative-square-energy-ordered-valley-2026-08-30", "name": "Negative square-energy ordered valley and five-vertex classification", "members": [ "negative-square-energy-five-vertex-valley" ], "sharedBoundary": "The exact five-vertex prescribed-order valley, structural minimality through four vertices, exhaustive five-vertex census, favourable-order boundary witness and producer replay support an anonymous unrefereed candidate. They refute only universal prescribed-order peak-unimodality and do not settle either favourable-order existential formulation or establish exhaustive novelty, absolute priority, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact." }, { "id": "four-point-inductive-cubical-excision-counterexample-2026-08-30", "name": "Four-point directed inductive-cubical excision counterexample", "members": [ "four-point-inductive-cubical-excision" ], "sharedBoundary": "The explicit four-point interior cover, integral relative-chain calculation, matrix certificate, producer-side concordance checks and clean-environment replay support an anonymous unrefereed candidate only for normalized (J_+, inductive-product) cubical singular homology. They do not decide the J_1 or I inductive theories, symmetric graph closures, historical priority, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, or workflow impact." }, { "id": "four-element-rowmotion-obstruction-2026-08-30", "name": "Four-element birational and piecewise-linear rowmotion obstruction", "members": [ "four-element-rowmotion-periodicity" ], "sharedBoundary": "The two exact fixed-point derivative obstructions, exhaustive enumeration and period calculation for every finite poset through size three, five semantic corruptions and producer replay support an anonymous unrefereed theorem candidate. They do not classify d-complete posets, rooted trees or fences, make the four-element Hasse shape new, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact." }, { "id": "pure-tensor-analytic-rank-normalization-obstruction-2026-08-30", "name": "Pure-tensor analytic-rank normalization obstruction", "members": [ "pure-tensor-analytic-rank-counterexample" ], "sharedBoundary": "The exact pure-tensor and diagonal-bias formulas, all-power written proof, direct coefficient enumeration, seven semantic controls and producer replay support an anonymous unrefereed conditional counterexample to one literal unnormalised analytic-rank comparator. They do not reconstruct historical intention, refute normalized or powered-identity formulations, settle partition rank, establish novelty or priority, or provide unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact." }, { "id": "free-by-cyclic-bns-component-orbit-obstruction-2026-08-31", "name": "Free-by-cyclic BNS component-orbit obstruction", "members": [ "unbounded-bns-component-orbits" ], "sharedBoundary": "The written all-m proof, exact 2m+2 BNS component count conditional on Cashen-Levitt Corollary 2.10, componentwise kernel-rank minima, at-least-m+1 outer-orbit obstruction, eight claim-boundary controls and producer replay support an anonymous unrefereed theorem candidate. They do not compute the exact orbit count or Out(G_m), replace the imported BNS theorem, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact." }, { "id": "factorial-spike-componentwise-fi-noetherianity-separation-2026-08-31", "name": "Factorial-spike componentwise versus FI-Noetherianity separation", "members": [ "factorial-spikes-fi-noetherianity" ], "sharedBoundary": "The universal monomial proof, exact native-width factorisation criterion, strict FI-ideal witnesses, four hostile controls and producer replay support an anonymous unrefereed characteristic-free separation of componentwise Noetherianity from FI-Noetherianity. They do not make the sub-FI-algebra finitely generated, produce a non-free module or a module counterexample over the ambient polynomial FI-algebra, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact." }, { "id": "ternary-rhombus-stability-and-dimensional-boundaries-2026-08-31", "name": "Ternary rhombus stability and higher-dimensional boundary separation", "members": [ "degree-independent-rhombus-criterion" ], "sharedBoundary": "The written factor-3 ternary proof, explicit coordinate-face quadratic family, strict-exchange impossibility, prior-art-Fano-derived normalized obstruction, hostile controls and deterministic producer replay support an anonymous unrefereed partial theorem candidate. They do not classify the normalized m=4,5,6 cases, prove the factor 3 optimal, exclude every higher-dimensional quantitative criterion, establish historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, or workflow impact." }, { "id": "hc4-binary-decimic-normal-layer-structural-reductions-2026-09-01", "name": "HC4 binary-decimic normal-layer structural reductions", "members": [ "hc4-five-support-structural-reductions" ], "sharedBoundary": "The exact five-support certificates, all-31-generator tangent radical containment, three rational secant colon elements, fail-closed fourth-target recovery and prospectively frozen 16-column rational source-kernel theorem support an anonymous unrefereed computer-assisted structural-reductions candidate. They do not prove inhomogeneous fourth-target membership, colon equality, saturation, secant-orbit closure, full normal-layer or polynomial-level closure, HC4, JC2, unaffiliated reconstruction, formal verification, external specialist review, editorial peer review, absolute priority or workflow impact." }, { "id": "free-normal-cover-all-fuchsian-pinching-2026-09-01", "name": "Free normal cover and all-Fuchsian pinching construction", "members": [ "pinching-free-normal-cover" ], "sharedBoundary": "The fixed-kernel construction, explicit reduced-surface and all-Fuchsian group-space bridge, imported-theorem hypothesis maps, fixed-width collar estimate, hostile controls and producer replay support an anonymous unrefereed all-Fuchsian strengthening candidate. They do not establish a first solution under the broad group-deformation reading, monotonicity, an exact exponent formula, global deformation-space identification, historical priority, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review or workflow impact." }, { "id": "fisk-toeplitz-deletion-interlacing-finite-certificate-2026-09-01", "name": "Finite Fisk Toeplitz-minor deletion-interlacing certificate", "members": [ "fisk-toeplitz-deletion-interlacing-through-five" ], "sharedBoundary": "The written Bezout-interlacing proof, complete 61,192-term degree-five certificate, lower-degree exact recomputation, semantic mutations and producer replay support an anonymous unrefereed finite theorem candidate through five positive alphabet entries. They do not establish degree six beyond the first three minors, zero-boundary cases, Fisk's all-degree conjecture, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact." }, { "id": "ap4-ramsey-diameter-36-finite-certificate-2026-09-03", "name": "Finite four-term-AP Ramsey diameter certificate", "members": [ "ap4-ramsey-diameter-36" ], "sharedBoundary": "The written source-to-CNF bridge, exact 26-point lower refutation, separately certified Graham 27-point upper witness, semantic reconstruction, small oracle and hostile controls support an anonymous unrefereed finite theorem candidate for v_{2,4}([37]) = 27. They do not establish W*(4) = 27, control primitive diameter above 36, answer the AIM asymptotic questions, supply unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact." }, { "id": "sharp-four-factor-schubert-surface-obstruction-2026-09-04", "name": "Sharp coordinate Schubert surface deformation obstruction", "members": [ "sharp-four-factor-cohen-macaulay-obstruction" ], "sharedBoundary": "The Stanley–Reisner connectivity criterion, multidegree-to-rank-two-matroid obstruction, complete-multipartite realization, scheme-theoretic degeneration bridge, sharp path and exact finite replay support an anonymous unrefereed classification candidate for coordinate Schubert surface unions in (P1)^n. They do not classify higher-dimensional Schubert unions or arbitrary flag varieties, supply unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact." }, { "id": "fixed-d-fi-d-toeplitz-kernel-obstruction-2026-09-04", "name": "Fixed-d FI_d Toeplitz kernel obstruction", "members": [ "fixed-d-toeplitz-obstruction" ], "sharedBoundary": "The explicit countable two-colour construction, bidiagonal Toeplitz blocks, symmetric-group coinvariant calculation, Yoneda kernel obstruction, hostile mutations and producer replay support an anonymous unrefereed theorem candidate showing that finitely presented FI_d-modules are not abelian for each fixed finite d at least two over characteristic-zero fields. They do not settle positive characteristic, d=1, related noetherianity categories, unaffiliated reconstruction, formal verification, authenticated external specialist review, editorial peer review, exhaustive novelty, absolute priority or workflow impact." }, { "id": "rbm31-channel-convex-cover-radius-2026-09-05", "name": "Reverse-channel and exact convex-cover KL radius certificate", "members": [ "rbm31-exact-kl-radius" ], "sharedBoundary": "Anonymous AI-assisted unrefereed computer-assisted theorem candidate for the exact three-bit two-product-mixture KL radius, with a constructive rational interface and a non-sharp conditioning corollary. Not unaffiliated verification, formal proof, authenticated specialist review, journal peer review, exhaustive novelty, priority, a four-star rating or demonstrated impact." }, { "id": "quartic-coefficient-power-boundary-2026-09-05", "name": "Quartic coefficient-power boundary classification", "members": [ "sharp-quartic-hadamard-powers" ], "sharedBoundary": "Unrefereed quartic theorem candidate with exact auxiliary checks; no external validation, formal proof, full AIM solution, all-degree classification, historical priority, four-star grade or impact established." }, { "id": "nonbacktracking-jordan-valuation-realization", "name": "Non-backtracking Jordan valuation and graph realization", "members": [ "linear-nonbacktracking-jordan-growth" ], "sharedBoundary": "Written arbitrary-parameter valuation and graph embedding, with finite producer controls; no independent validation, exact extremum, optimal constants, priority or impact established." }, { "id": "potts-finite-word-censoring-obstruction-2026-09-06", "name": "Exact finite-word ferromagnetic Potts censoring obstruction", "members": [ "potts-censoring-counterexample" ], "sharedBoundary": "Unrefereed exact finite-horizon q=3 counterexample candidate. No mixing-time, random-scan, every-q, minimality, practical speed-up, exhaustive novelty, priority, unaffiliated validation, formal proof or impact claim." }, { "id": "dyck-two-cut-entropy-2026-09-06", "name": "Two-cut entropy for the original Dyck rejection walk", "members": [ "dyck-transpositions-n-log-n" ], "sharedBoundary": "Unrefereed analytic proof candidate for the original length-2n ordered independent-coordinate Dyck rejection walk. No cutoff, sharp upper constant, numerical burn-in guarantee, computational-runtime bound, sampler optimality, external peer review, formal verification or priority clearance." }, { "id": "hilb8-local-reducedness-2026-09-07", "name": "Hilbert-scheme local reducedness and mixed-prime finite-module comparison", "members": [ "hilbert-eight-points-reducedness" ], "sharedBoundary": "Source-specific unrefereed characteristic-zero proof candidate; finite arithmetic and internal replay do not establish external validation or transfer to other Hilbert schemes." } ], "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", "cyclicity-support-fusion-atlas", "amplitude-modules-fused-support-bautin-bound" ], "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." }, { "id": "affine-diversification-programme", "name": "Affine diversification partial-identification programme", "rootReleaseSlug": "affine-diversification-fibres", "members": [ "affine-diversification-fibres", "finite-sample-affine-diversification" ], "basis": "The finite-sample successor explicitly extends the predecessor's affine cumulative-loss fibre, fixed-signal sharp bounds and endpoint-sampling diagnostic by adding signal uncertainty, three-valued decisions and a frozen CRABS comparison.", "sharedBoundary": "The successor reuses the predecessor's mathematical and software framework and therefore does not independently confirm it. A shared error in the affine coordinate, probability bridge or encoding can propagate across the lineage." }, { "id": "joint-replenishment-exact-certification-programme", "name": "Exact joint-replenishment certification programme", "rootReleaseSlug": "certified-two-item-jrp", "members": [ "certified-two-item-jrp", "certified-three-item-jrp-gap" ], "basis": "The three-item successor explicitly extends the parent's common-origin model, independent-cap reduction boundary, exact two-item interval and certificate-first conventions with a distinct primitive-triple tail architecture and logistics evaluation handoff.", "sharedBoundary": "The successor reuses parent assumptions, code patterns and producer coordination. This lineage is dependency evidence, not independent confirmation, and a shared semantic, algebraic or implementation defect may propagate across both releases." }, { "id": "txgraffiti-counterexample-order-programme", "name": "TxGraffiti cubic-counterexample order programme", "rootReleaseSlug": "txgraffiti-c3-resolution", "members": [ "txgraffiti-c3-resolution", "txgraffiti-order48-successor" ], "basis": "The order-48 successor explicitly identifies the public 50-vertex release as its parent, supplies a different smaller graph and resolves the parent's open below-50 search direction by construction without retracting the parent or inheriting its separate restricted-class theorems.", "sharedBoundary": "The successor reuses problem framing, provenance and certificate architecture from the parent. This lineage is dependency evidence, not independent confirmation, and a shared source-to-semantics or implementation defect may propagate across both releases." } ], "releaseAssignments": { "rbm43-eight-point-obstruction": [ "certificate-first", "structural-compression", "adversarial-controls", "counterexample-proxy-first", "assurance-vector", "agent-readable-research-object" ], "linear-nonbacktracking-jordan-growth": [ "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "aggregation-without-sufficiency": [ "structural-compression", "adversarial-controls", "identification-gate", "partial-identification", "counterexample-proxy-first", "assurance-vector", "agent-readable-research-object" ], "frankl-concavity-obstruction": [ "certificate-first", "structural-compression", "adversarial-controls", "productive-failure", "assurance-vector", "agent-readable-research-object" ], "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" ], "full-e3-column-polydegree-conjecture": [ "certificate-first", "structural-compression", "regime-stitching", "adversarial-controls", "research-lineage-reuse", "assurance-vector", "agent-readable-research-object" ], "full-e4-polydegree-column": [ "certificate-first", "structural-compression", "regime-stitching", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "furter-r3-through-299": [ "certificate-first", "structural-compression", "regime-stitching", "adversarial-controls", "counterexample-proxy-first", "assurance-vector", "agent-readable-research-object" ], "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" ], "unique-answer-not-identified": [ "identification-gate", "partial-identification", "assurance-vector", "agent-readable-research-object" ], "wales-20mph-casualty-attribution": [ "adversarial-controls", "productive-failure", "identification-gate", "counterexample-proxy-first", "assurance-vector", "agent-readable-research-object" ], "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" ], "sfs-identifiability-audit": [ "certificate-first", "identification-gate", "partial-identification", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "cyclicity-support-fusion-atlas": [ "certificate-first", "structural-compression", "adversarial-controls", "research-lineage-reuse", "productive-failure", "assurance-vector", "agent-readable-research-object" ], "finite-sample-affine-diversification": [ "structural-compression", "adversarial-controls", "research-lineage-reuse", "productive-failure", "identification-gate", "partial-identification", "certified-decision-margin", "assurance-vector", "agent-readable-research-object" ], "certified-three-item-jrp-gap": [ "certificate-first", "structural-compression", "regime-stitching", "adversarial-controls", "research-lineage-reuse", "certified-decision-margin", "staged-adoption-evaluation", "assurance-vector", "agent-readable-research-object" ], "txgraffiti-order48-successor": [ "certificate-first", "adversarial-controls", "research-lineage-reuse", "counterexample-proxy-first", "assurance-vector", "agent-readable-research-object" ], "s6-extension-results-candidate": [ "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "lps-structural-reductions": [ "certificate-first", "structural-compression", "adversarial-controls", "productive-failure", "assurance-vector", "agent-readable-research-object" ], "amplitude-modules-fused-support-bautin-bound": [ "structural-compression", "adversarial-controls", "research-lineage-reuse", "productive-failure", "assurance-vector", "agent-readable-research-object" ], "o01d0-polar-fibre-structural-reductions": [ "certificate-first", "structural-compression", "regime-stitching", "adversarial-controls", "research-lineage-reuse", "productive-failure", "assurance-vector", "agent-readable-research-object" ], "odd-order-one-third-popular-differences": [ "counterexample-proxy-first", "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "extremes-do-not-always-maximise": [ "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "negative-square-energy-five-vertex-valley": [ "counterexample-proxy-first", "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "four-point-inductive-cubical-excision": [ "counterexample-proxy-first", "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "four-element-rowmotion-periodicity": [ "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "pure-tensor-analytic-rank-counterexample": [ "counterexample-proxy-first", "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "unbounded-bns-component-orbits": [ "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "factorial-spikes-fi-noetherianity": [ "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "degree-independent-rhombus-criterion": [ "certificate-first", "structural-compression", "counterexample-proxy-first", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "hc4-five-support-structural-reductions": [ "certificate-first", "structural-compression", "adversarial-controls", "productive-failure", "assurance-vector", "agent-readable-research-object" ], "pinching-free-normal-cover": [ "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "fisk-toeplitz-deletion-interlacing-through-five": [ "certificate-first", "structural-compression", "adversarial-controls", "counterexample-proxy-first", "productive-failure", "assurance-vector", "agent-readable-research-object" ], "ap4-ramsey-diameter-36": [ "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "sharp-four-factor-cohen-macaulay-obstruction": [ "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "fixed-d-toeplitz-obstruction": [ "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "rbm31-exact-kl-radius": [ "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "sharp-quartic-hadamard-powers": [ "structural-compression", "regime-stitching", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "potts-censoring-counterexample": [ "certificate-first", "structural-compression", "adversarial-controls", "counterexample-proxy-first", "assurance-vector", "agent-readable-research-object" ], "dyck-transpositions-n-log-n": [ "structural-compression", "regime-stitching", "productive-failure", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "hilbert-eight-points-reducedness": [ "certificate-first", "structural-compression", "adversarial-controls", "productive-failure", "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." }, { "date": "2026-08-11", "summary": "Registered identification, partial-identification, assurance-vector and agent-readable-research-object assignments for the prospective unique-answer-not-identified synthesis and appended a bounded singleton method cluster without rewriting an existing cluster or creating a research lineage or impact claim." }, { "date": "2026-08-11", "summary": "Registered sfs-identifiability-audit in a new appended certified-demographic-identifiability cluster (published clusters are immutable in place) with certificate-first, identification-gate, partial-identification, adversarial-controls, assurance-vector and agent-readable-research-object assignments." }, { "date": "2026-08-11", "summary": "Registered adversarial-controls, productive-failure, identification-gate, counterexample-proxy-first, assurance-vector and agent-readable-research-object assignments for the prospective Wales 20 mph casualty-attribution audit and appended a bounded singleton method cluster without rewriting an existing cluster or creating a research lineage or impact claim." }, { "date": "2026-08-12", "summary": "Registered the prospective full-e3-column-polydegree-conjecture release in a new bounded smooth-point and Fourier-persistence certificate cluster, recorded its certificate, compression, regime-stitching, adversarial-control, reuse, assurance and agent-readable assignments, and left the previously published binary-form cluster and research lineages unchanged." }, { "date": "2026-08-13", "summary": "Registered aggregation-without-sufficiency in a new bounded singleton aggregation-licence cluster with structural-compression, adversarial-control, identification, partial-identification, counterexample, assurance and agent-readable assignments; retained existing published clusters and research lineages unchanged and made no impact claim." }, { "date": "2026-08-14", "summary": "Registered frankl-concavity-obstruction in a new bounded singleton entropy-obstruction cluster with certificate-first, structural-compression, adversarial-control, productive-failure, assurance-vector and agent-readable assignments; retained existing clusters and research lineages unchanged and made no theorem, priority or impact promotion." }, { "date": "2026-08-14", "summary": "Registered furter-r3-through-299 in a new bounded finite polynomial-rigidity cluster with certificate, compression, regime-stitching, adversarial-control, counterexample, assurance and agent-readable assignments; retained published clusters and lineages unchanged and did not promote finite coverage to universal R(3) or an impact claim." }, { "date": "2026-08-20", "summary": "Registered cyclicity-support-fusion-atlas in a new bounded inverse-root support and Fourier-fusion cluster, appended it to the cyclicity-programme lineage using reciprocal parent links, assigned certificate, compression, adversarial-control, lineage-reuse, productive-failure, assurance and agent-readable methods, and preserved the finite degree-twenty versus open all-degree boundary without an impact claim." }, { "date": "2026-08-21", "summary": "Registered finite-sample-affine-diversification in a new bounded signal-to-decision cluster, created the two-release affine-diversification-programme lineage using the successor's explicit legacy-parent link, assigned compression, adversarial-control, lineage-reuse, productive-failure, identification, partial-identification, certified-decision, assurance and agent-readable methods, and retained the fixed-stem model, failed H4 and no-impact boundaries." }, { "date": "2026-08-21", "summary": "Appended a dated all-degree successor cluster for cyclicity-support-fusion-atlas without rewriting the immutable v0.5 bounded-atlas cluster, and recorded the named-import, unrefereed, same-programme-control, external-review, priority and no-impact boundaries." }, { "date": "2026-08-21", "summary": "Appended a dated combined amplitude, endpoint-moment and Laurent-channel successor cluster for cyclicity-support-fusion-atlas without rewriting the v0.5 or v0.6 cluster records; retained the named-import, unrefereed, no-finite-all-Laurent, external-assurance, priority and no-impact boundaries." }, { "date": "2026-08-22", "summary": "Registered certified-three-item-jrp-gap in a new bounded three-item replenishment-certification cluster, created the two-release joint-replenishment exact-certification lineage from the successor's explicit parent link, assigned certificate, compression, regime-stitching, adversarial-control, lineage-reuse, certified-decision, staged-adoption, assurance and agent-readable methods, and retained the unrefereed, partial-assurance and no-impact boundaries." }, { "date": "2026-08-23", "summary": "Registered full-e4-polydegree-column in a new bounded e=4 Fourier, formal-companion and boundary-transfer cluster with certificate, compression, regime-stitching, adversarial-control, assurance-vector and agent-readable assignments; retained the earlier e=3 cluster unchanged and made no R(3), JC2, HC4, priority or workflow-impact promotion." }, { "date": "2026-08-24", "summary": "Registered txgraffiti-order48-successor in a new bounded order-48 certificate cluster, created the two-release TxGraffiti counterexample-order lineage from the successor's explicit legacy-parent link, assigned certificate, adversarial-control, lineage-reuse, counterexample, assurance and agent-readable methods, and retained the global-minimality, uniqueness, external-assurance, priority and no-impact boundaries." }, { "date": "2026-08-24", "summary": "Registered s6-extension-results-candidate in a new bounded conditional-geometry and executable-adjudication cluster with certificate, structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved the unverified source-construction, conditional-proof, external-assurance, priority and no-impact boundaries." }, { "date": "2026-08-25", "summary": "Registered lps-structural-reductions in a new fixed-width structural and p-adic signal cluster with certificate, structural-compression, adversarial-control, productive-failure, assurance-vector and agent-readable assignments; created no evidential lineage from topical neighbours and preserved the open radical-membership, target-conjecture, external-assurance, priority and no-impact boundaries." }, { "date": "2026-08-28", "summary": "Registered amplitude-modules-fused-support-bautin-bound in a new bounded amplitude-module, fused-support and ordinary coefficient-Bautin cluster; appended it to the cyclicity-programme lineage through its explicit Atlas parent link; assigned compression, adversarial-control, lineage-reuse, productive-failure, assurance and agent-readable methods; and preserved the anonymous unrefereed-candidate, convention, independent-assurance, historical-open-problem, real-limit-cycle, priority and no-impact boundaries." }, { "date": "2026-08-28", "summary": "Registered o01d0-polar-fibre-structural-reductions in a new Hermite-boundary and falsification cluster, retained its explicit LPS parent as a direct dependency without retrospectively rewriting the published parent into a formal lineage, assigned certificate, compression, regime-stitching, adversarial-control, lineage-reuse, productive-failure, assurance, and agent-readable methods, and preserved O-01d0, the four remaining gates, external assurance, priority, and impact as open." }, { "date": "2026-08-29", "summary": "Registered odd-order-one-third-popular-differences in a bounded three-layer popular-difference counterexample cluster with counterexample-first, certificate, structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved the open 2/5 endpoint, witness-minimality, external-assurance, novelty, priority and no-impact boundaries." }, { "date": "2026-08-29", "summary": "Registered extremes-do-not-always-maximise in a bounded four-state monotone row-diameter counterexample cluster with certificate, structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved the all-graph zero-field question, AIM diagnostics 1.6(2-3), external-assurance, novelty, priority and no-impact boundaries." }, { "date": "2026-08-30", "summary": "Registered negative-square-energy-five-vertex-valley in a bounded ordered-valley and five-vertex-classification cluster with counterexample-first, certificate, structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved both favourable-order existential formulations, external assurance, novelty, priority and no-impact boundaries." }, { "date": "2026-08-30", "summary": "Registered four-point-inductive-cubical-excision in a bounded directed inductive-cubical excision counterexample cluster with counterexample-first, certificate, structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved the other interval and product theories, symmetric graph restrictions, external assurance, novelty, priority and no-impact boundaries." }, { "date": "2026-08-30", "summary": "Registered four-element-rowmotion-periodicity in a bounded four-element birational and piecewise-linear rowmotion obstruction cluster with certificate, structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved the classification, object-ancestry, external-assurance, novelty, priority and no-impact boundaries." }, { "date": "2026-08-30", "summary": "Registered pure-tensor-analytic-rank-counterexample in a bounded analytic-rank normalization-obstruction cluster with counterexample-first, certificate, structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved historical intention, normalized analytic rank, partition rank, external assurance, novelty, priority and impact as unresolved or unestablished." }, { "date": "2026-08-31", "summary": "Registered unbounded-bns-component-orbits in a bounded free-by-cyclic BNS component-orbit obstruction cluster with certificate-first, structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved the exact-orbit, full-Out-group, imported-theorem, external-assurance, novelty, priority and no-impact boundaries." }, { "date": "2026-08-31", "summary": "Registered factorial-spikes-fi-noetherianity in a bounded factorial-spike componentwise versus FI-Noetherianity separation cluster with certificate-first, structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved the FI-finite-generation, module-scope, source, external-assurance, novelty, priority and no-impact boundaries." }, { "date": "2026-08-31", "summary": "Registered degree-independent-rhombus-criterion in a bounded ternary-stability and dimensional-boundary cluster with certificate-first, structural-compression, counterexample-first, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved the normalized m=4,5,6, optimal-constant, external-assurance, novelty, priority and no-impact boundaries." }, { "date": "2026-09-01", "summary": "Registered hc4-five-support-structural-reductions in a bounded binary-decimic normal-layer cluster with certificate-first, structural-compression, adversarial-control, productive-failure, assurance-vector and agent-readable assignments; created no evidential lineage from topical polynomial-map releases and preserved fourth-target membership, secant closure, HC4, JC2, external assurance, novelty, priority and impact as open or unestablished." }, { "date": "2026-09-01", "summary": "Registered pinching-free-normal-cover in a bounded free-normal-cover and all-Fuchsian pinching cluster with structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved the broad-reading Astala-Zinsmeister precedent, reduced-space interpretation, imported-theorem, monotonicity, exact-formula, external-assurance, novelty, priority and no-impact boundaries." }, { "date": "2026-09-01", "summary": "Registered fisk-toeplitz-deletion-interlacing-through-five in a bounded finite deletion-interlacing certificate cluster with certificate-first, structural-compression, adversarial-control, counterexample-first, productive-failure, assurance-vector and agent-readable assignments; created no internal research lineage and preserved the degree-six, zero-boundary, all-degree, external-assurance, novelty, priority and no-impact boundaries." }, { "date": "2026-09-03", "summary": "Registered ap4-ramsey-diameter-36 in a bounded finite four-term-AP Ramsey certificate cluster with certificate-first, structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved W*(4), primitive diameter above 36, the AIM asymptotic questions, external assurance, novelty, priority and impact as open or unestablished." }, { "date": "2026-09-04", "summary": "Registered sharp-four-factor-cohen-macaulay-obstruction in a bounded coordinate Schubert surface classification cluster with certificate-first, structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved higher-dimensional unions, arbitrary flag varieties, external assurance, novelty, priority and impact as open or unestablished." }, { "date": "2026-09-04", "summary": "Registered fixed-d-toeplitz-obstruction in a bounded fixed-d FI_d Toeplitz kernel-obstruction cluster with structural-compression, adversarial-control, assurance-vector and agent-readable assignments; created no internal research lineage and preserved positive characteristic, d=1, adjacent noetherianity categories, external assurance, novelty, priority and impact as open or unestablished." }, { "date": "2026-09-05", "summary": "Registered the exact three-bit KL-radius candidate, constructive witness interface and non-sharp conditioning consequence; preserved prior constant/transfer attribution and all unaffiliated-assurance, priority, four-star and no-impact boundaries." }, { "date": "2026-09-05", "summary": "Registered the quartic boundary, scale-escape and reciprocal classification methods; scoped auxiliary replay is not a whole-proof certificate, all-degree result or impact claim." }, { "date": "2026-09-05", "summary": "Registered linear Jordan-growth valuation, uniform encoding and simple-graph realization; no internal lineage, external assurance, priority or impact promotion." }, { "date": "2026-09-06", "summary": "Registered the exact finite-word Potts censoring counterexample methods; no internal lineage, external assurance, priority or impact promotion." }, { "date": "2026-09-06", "summary": "Registered the RBM(4,3) eight-point leakage obstruction with certificate-first, structural-compression, adversarial-control, counterexample-first, assurance-vector and agent-readable assignments. Added a bounded singleton method cluster, not an evidential lineage. Preserved the unrefereed claim ceiling, open four-hidden sufficiency and minimal-support questions, and the absence of unaffiliated validation, historical priority and impact evidence." }, { "date": "2026-09-06", "summary": "Registered Dyck two-cut entropy candidate methods without external assurance, priority or impact promotion." }, { "date": "2026-09-07", "summary": "Registered the Hilbert eight-point characteristic-zero reducedness candidate in a source-specific local-reducedness and mixed-prime finite-module cluster, with certificate-first, structural-compression, adversarial-control, productive-failure, assurance-vector and agent-readable assignments. No internal lineage, external assurance, novelty, priority or impact promotion." } ] }