{ "schemaVersion": "1.6", "slug": "fisk-toeplitz-deletion-interlacing-through-five", "title": "Exact deletion interlacing for Fisk's Toeplitz-minor transform through five variables", "shortTitle": "Fisk deletion interlacing through five", "url": "https://evidencepress.org/releases/fisk-toeplitz-deletion-interlacing-through-five/", "oneLine": "Exact positive-coefficient Bezout certificates prove real negative roots and strict arbitrary-deletion interlacing for Fisk's 3x3 Toeplitz-minor transform through five positive alphabet entries; the all-degree and zero-boundary problems remain open.", "abstract": "This anonymous, AI-assisted, unrefereed computer-assisted finite theorem candidate addresses AIM-ANALYSIS-0142. For a positive alphabet rho of size n, let F_rho(t) be the sum of the rectangular Schur polynomials s_(3^k)(rho) times t^k. The candidate proves that F_rho has n simple negative roots for 0 <= n <= 5 and that, for 2 <= n <= 5, deleting any chosen alphabet entry gives strict interlacing, with the larger polynomial supplying the two outer roots. The proof reduces arbitrary deletion by symmetry, constructs a signed Bezout matrix, and proves all leading principal minors positive by exact positive monomial expansions. The degree-five certificate contains 61,192 terms across five minors and is regenerated byte-for-byte by public CI. The package also preserves failed structural routes, corrected exact searches, hostile certificate mutations, a supplied Major Revision review, a producer-coordinated five-role review and one bounded exact-byte confirmation. Fisk's all-degree conjecture, zero-boundary cases, degree six beyond the first three minors, independent reconstruction, formal verification, external specialist review, novelty and priority remain open or unassessed.", "datePublished": "2026-09-01", "dateModified": "2026-09-01", "version": "0.3.0-candidate", "doi": "10.5281/zenodo.22233444", "doiUrl": "https://doi.org/10.5281/zenodo.22233444", "conceptDoi": null, "pdfUrl": "https://github.com/ipitchford/fisk-toeplitz-deletion-interlacing-through-five/releases/download/v0.3.0-candidate/paper.pdf", "altPdfUrl": "https://zenodo.org/records/22233444/files/paper.pdf?download=1", "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/22233444", "repoUrl": "https://github.com/ipitchford/fisk-toeplitz-deletion-interlacing-through-five", "releaseUrl": "https://github.com/ipitchford/fisk-toeplitz-deletion-interlacing-through-five/releases/tag/v0.3.0-candidate", "markdownUrl": "https://evidencepress.org/releases/fisk-toeplitz-deletion-interlacing-through-five/index.md", "bibtexUrl": "https://evidencepress.org/releases/fisk-toeplitz-deletion-interlacing-through-five/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/fisk-toeplitz-deletion-interlacing-through-five.mp3?v=b9b839427d", "imageUrl": "https://evidencepress.org/assets/og/fisk-toeplitz-deletion-interlacing-through-five.png?v=b94647505d", "coverArtUrl": "https://evidencepress.org/assets/art/fisk-toeplitz-deletion-interlacing-through-five.svg?v=939c402d49", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/fisk-toeplitz-deletion-interlacing-through-five.mp3", "name": "Audio briefing — Fisk deletion interlacing through five", "description": "Plain-English OpenAI API synthetic-voice account of the finite theorem, exact Bezout certificates and open all-degree boundary; a communication aid, not additional evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/fisk-toeplitz-deletion-interlacing-through-five.txt" }, { "type": "video", "url": "https://youtu.be/0I546lO8OHk", "name": "Exact Deletion Interlacing for Fisk's Toeplitz-Minor Transform", "description": "Evidence Press video overview of this release. This is a communication aid; it does not extend the release's claims or assurance status and is not additional research evidence." } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Anonymous, AI-assisted, unrefereed computer-assisted finite theorem candidate at internal PASS_WITH_NOTES with no residual or new P0/P1 findings in the final exact-byte confirmation. The finite theorem is a written Bezout-interlacing argument supported by complete positive coefficient streams through five positive alphabet entries. Symmetry covers deletion of any chosen entry. The exhaustive small grid and seeded degree-16-through-40 search are non-load-bearing reconnaissance, not evidence for the universal claim. Degree six has only its first three leading minors certified. Inputs with a zero entry, degree drops, collision limits needed for the unrestricted parent formulation, Fisk's all-degree conjecture, independent reconstruction, proof-assistant formalization, external specialist review, journal peer review, exhaustive novelty assessment and priority adjudication remain open or unassessed." }, "assurance": [ { "dimension": "availability", "label": "Availability and archiving", "question": "Is the evidence package publicly retrievable from an archive under a persistent identifier?", "state": "passed", "evidenceUrl": "https://zenodo.org/records/22233444", "note": "The tagged GitHub prerelease and published Zenodo record expose the same archive, PDF and checksum sidecar; independently downloaded SHA-256 values match the frozen local assets." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "A clean public runner verifies release metadata, regenerates every degree-five certificate stream, byte-compares deterministic outputs, recomputes lower degrees and rejects two semantic mutations.", "evidenceUrl": "https://github.com/ipitchford/fisk-toeplitz-deletion-interlacing-through-five/actions/runs/33522388763" }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "No authenticated unaffiliated party has rerun the complete immutable package and published a separate environment and result receipt." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "The verifier and structural checks remain producer-coordinated; no independently authored implementation has reconstructed the theorem." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No proof assistant formalizes the Schur-to-Bezout construction, sign convention, positivity bridge or interlacing theorem application." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "The supplied review, five-role reports and bounded confirmation are internal workflow records, not authenticated unaffiliated specialist review." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "No journal or comparable external venue has conducted editorial peer review to a decision." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "partial", "evidenceUrl": "https://github.com/ipitchford/fisk-toeplitz-deletion-interlacing-through-five/blob/v0.3.0-candidate/ENVIRONMENT.txt", "note": "Producing versions and replay commands are public and a clean hosted runner passes, but no authenticated unaffiliated environment reconstruction is reported." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI systems under human direction", "OpenAI Codex", "Python 3.14.6", "SymPy 1.14.0", "Singular 4.4.1", "SageMath 10.9" ], "humanRole": "Research direction, problem selection, review provision, claim-boundary decisions, publication authorization and institutional responsibility by the human creator; repository maintenance and Evidence Press publication are not scholarly authorship, and scholarly attribution remains Anonymous.", "disclosure": "AI systems contributed proof search, exact computation, code, literature and GitHub search, drafting, action of the supplied review, internal role-separated review, replay and release engineering within one producer-coordinated workflow. Exact replay, implementation-diverse checks, internal reviews, matching public hashes and publication are not unaffiliated reconstruction, authenticated specialist review or editorial peer review." }, "attributionBoundary": null, "problem": { "name": "Fisk's 3x3 Toeplitz-minor real-rootedness conjecture (AIM-ANALYSIS-0142)", "url": "https://arxiv.org/abs/0808.1850" }, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "certificate-backed-computation", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Authored prospectively against the DOI-bearing v0.3.0-candidate, exact GitHub release, green public replay, published Zenodo record, supplied-review response, five-role internal editorial record and bounded exact-byte confirmation on 1 September 2026. Canonical Evidence Press deployment and terminal publication metrics are recorded separately and do not promote the mathematical assurance ceiling.", "grandfatheredAtSchemaVersion": null, "keywords": [ "Fisk conjecture", "Toeplitz minors", "Schur polynomials", "Bezout matrix", "real-rooted polynomial", "interlacing", "computer-assisted proof", "unrefereed candidate" ], "keyResults": [ "For every positive alphabet rho of size 0 through 5, the polynomial F_rho(t) = sum s_(3^k)(rho)t^k has exactly n simple negative roots.", "For every positive alphabet of size 2 through 5, deleting any chosen entry gives strict root interlacing, with the larger polynomial supplying both outer roots.", "All five degree-five leading Bezout minors have positive monomial coefficients; their exact certificate streams contain 15, 771, 8,790, 29,460 and 22,156 terms.", "Fresh public replay regenerates the degree-five certificates byte-for-byte and rejects both non-positive and positive-but-semantically-wrong certificate mutations.", "Degree six is checked only through the first three leading minors, and Fisk's all-degree conjecture and zero-boundary cases remain open." ], "reviews": [], "evidencePackage": "A five-page theorem manuscript and accessible Markdown; exact direct degree-two-through-four Bezout calculations; five compressed term-level degree-five certificate streams containing 61,192 positive terms; generated Singular sources and raw logs; coefficient, modular point and standard-library semantic checks; normal and optimized replay receipts; a safe-extraction and exact-inventory archive replay; negative and positive-but-wrong hostile mutations; corrected exact grid and seeded search receipts retained only as supporting reconnaissance; failed structural routes and a degree-six first-three-minor boundary; a supplied Major Revision review; a producer-coordinated five-role internal review, response matrix and bounded exact-byte confirmation; green public GitHub replay; and byte-identical GitHub and Zenodo archive, PDF and checksum assets. These establish public availability, package integrity, producer replay and the stated finite certificate—not the all-degree or zero-boundary conjecture, independent reconstruction, formal verification, external specialist review, peer review, novelty or priority.", "openProblems": [ "Prove positivity of every deletion Bezout minor for arbitrary positive alphabet size, or find an exact positive rational counterexample.", "Complete the degree-six leading-minor calculation beyond the first three orders and explain any resulting positive or negative structure.", "Extend the finite positive-alphabet theorem to the zero boundary with a rigorous account of degree drops, multiple roots and collision limits.", "Find a characteristic-polynomial, matching-polynomial, network or total-positivity representation that supplies an all-degree real-zero theorem.", "Obtain an unaffiliated reconstruction, a separately authored verifier, proof-assistant formalization and external specialist assessment of correctness and closest prior art." ], "mathObjects": [ { "id": "finite-real-rootedness-through-five", "kind": "statement", "status": "claimed-result", "label": "Finite real-rootedness through five", "plainText": "For a positive alphabet rho of size n at most five, F_rho has n simple negative roots.", "latex": "F_{\\rho}(t)=\\sum_{k=0}^{n}s_{(3^k)}(\\rho)t^k", "scope": "Strictly positive real alphabet entries, repetitions allowed, and 0 <= n <= 5." }, { "id": "arbitrary-deletion-interlacing-through-five", "kind": "statement", "status": "claimed-result", "label": "Arbitrary-deletion strict interlacing", "plainText": "Deleting any chosen entry from a positive alphabet of size two through five produces a polynomial that strictly interlaces the original one.", "scope": "Strictly positive alphabets with 2 <= n <= 5; symmetry reduces a chosen deletion to rho = (X,y)." }, { "id": "degree-five-bezout-certificate", "kind": "identity", "status": "computed-finite", "label": "Degree-five positive Bezout certificate", "plainText": "Every coefficient in each of the five leading degree-five Bezout minors is a positive integer.", "scope": "Exactly 61,192 exponent-coefficient terms across the five degree-five minors, regenerated by Singular and checked by a standard-library verifier." }, { "id": "fisk-all-degree-conjecture", "kind": "statement", "status": "open-problem", "label": "Fisk all-degree conjecture", "plainText": "Determine whether the 3x3 Toeplitz-minor transform preserves real negative zeros in every degree.", "scope": "The unrestricted parent problem, including degrees beyond five and its required limiting or boundary analysis." } ], "relatedWorks": [ { "citation": "Fisk, S. (2008). Questions about determinants and polynomials. arXiv:0808.1850.", "url": "https://arxiv.org/abs/0808.1850", "doi": "10.48550/arXiv.0808.1850" }, { "citation": "Branden, P. (2011). Iterated sequences and the geometry of zeros. Journal fur die reine und angewandte Mathematik 658, 115-131.", "url": "https://doi.org/10.1515/CRELLE.2011.063", "doi": "10.1515/CRELLE.2011.063" }, { "citation": "Yoshida, R. (2013). On some questions of Fisk and Branden. Complex Variables and Elliptic Equations 58(7), 933-945.", "url": "https://doi.org/10.1080/17476933.2011.603418", "doi": "10.1080/17476933.2011.603418" }, { "citation": "American Institute of Mathematics. (2023). Theory and applications of total positivity: workshop report.", "url": "https://aimath.org/pastworkshops/totalposrep.pdf", "doi": null }, { "citation": "OpenTorus. (2026). Campaign: Fisk's 3x3 Toeplitz-minor conjecture, public status and computation audit.", "url": "https://github.com/maximilianbehr/OpenTorus/tree/main/examples/fisk-toeplitz-minors", "doi": null } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:fisk-toeplitz-deletion-interlacing-through-five", "attemptIds": [ "ep-attempt:fisk-toeplitz-deletion-interlacing-through-five-publication-completion" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "evidence-assessment", "method-demonstration", "communication" ], "lineageId": null, "accelerationPrimitives": [ "certificate-first", "structural-compression", "adversarial-controls", "counterexample-proxy-first", "productive-failure", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "executable-open-problem", "description": "A complete finite deletion-interlacing certificate through five positive alphabet entries and a sharply bounded all-degree research handoff.", "scope": "Exact real-rootedness and arbitrary-deletion strict interlacing for positive alphabets of size at most five, plus a degree-six first-three-minor boundary; not zero-boundary cases, all degrees, independent validation, novelty or priority." }, "bottleneckTargeted": [ "discovery", "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "The package fixes the signed Bezout convention, maps F_(X,y) and F_X to a symmetric matrix, proves that positivity of all leading minors makes that matrix positive definite, and invokes the matching strict-interlacing criterion. Complete term streams bind the degree-five coefficient claim to the exact computation.", "remainingRisks": [ "The finite proof and classical interlacing bridge have not been reconstructed by an unaffiliated specialist.", "Positive coefficient expansions may fail at a higher degree even if the parent conjecture remains true by another mechanism.", "Strict positivity on the open orthant does not by itself settle zero entries, degree drops or multiple-root limits.", "The targeted literature and GitHub search may miss differently phrased, unindexed or unpublished prior work." ] }, "humanJudgmentGates": [ "Check the sign convention and Bezout-to-interlacing theorem as mathematics rather than inferring them from positive coefficient files.", "Keep the finite theorem through five separate from the degree-six partial calculation and Fisk's unrestricted conjecture.", "Treat the exact grid and seeded searches as reconnaissance rather than proof or counterexample evidence.", "Keep internal review, public replay and archive availability separate from unaffiliated validation, peer review, novelty and priority." ], "parentLinks": [ { "relation": "depends-on-claim", "workId": null, "legacyReleaseSlug": null, "externalUrl": "https://arxiv.org/abs/0808.1850", "inheritedClaim": "Fisk defines the higher Toeplitz-minor transform and asks whether its output preserves real negative zeros.", "inheritedAssuranceCeiling": "The source fixes the parent target and attribution but does not establish this finite theorem, its certificate, correctness, novelty or priority." }, { "relation": "extends-result", "workId": null, "legacyReleaseSlug": null, "externalUrl": "https://doi.org/10.1515/CRELLE.2011.063", "inheritedClaim": "Branden proves the corresponding two-by-two transform and develops adjacent real-rootedness-preserver context.", "inheritedAssuranceCeiling": "The published result supplies mathematical context, not the three-by-three finite certificate or all-degree conclusion." } ], "assuranceTarget": { "dimensions": [ "independentRerun", "independentReimplementation", "formalVerification", "specialistReview", "dataEnvironmentReproducibility", "semanticValidation", "noveltyAssessment", "priorityAssessment" ], "nextAction": "Obtain an unaffiliated reconstruction of the Bezout sign and interlacing bridge, then complete or refute the degree-six coefficient-positivity route in a separately authored stack.", "claimCeiling": "An anonymous, AI-assisted, unrefereed computer-assisted finite theorem candidate through five positive alphabet entries with complete exact coefficient streams, hostile controls, producer replay, internal editorial closure and public immutable assets; not the all-degree or zero-boundary conjecture, independent validation, formal verification, external specialist or editorial peer review, historical priority or demonstrated workflow impact." }, "impactClaims": [ { "id": "fisk-deletion-interlacing-science-no-impact", "aim": "science", "outcome": "Faster or more reliable resolution and assurance of open real-rootedness conjectures", "setting": "AI-assisted symmetric-function proof search, exact algebra, adversarial replay, internal review and guarded candidate publication", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "No matched conventional research, theorem-review or publication workflow was registered.", "estimand": "No effect on discovery time, active human effort, compute, correction rate, proof quality, independent-assurance time, uptake, citation or field outcomes was estimated.", "evidenceRefs": [], "registeredDesignRef": null, "independentAssessment": null } ] }, "researchMetrics": { "schemaVersion": "1.0", "policyUrl": "https://evidencepress.org/api/research-metrics-policy.json", "workLedgerUrl": "https://evidencepress.org/api/work-ledger.json", "claimCeiling": "These records describe scoped workflow inputs and outcomes. They support calibration and reference-class construction, but do not by themselves establish research acceleration, theorem correctness, novelty, independent assurance or impact.", "attempts": [ { "attemptId": "ep-attempt:fisk-toeplitz-deletion-interlacing-through-five-publication-completion", "status": "published", "resultClass": "partial", "metrics": { "schemaVersion": "1.0", "measurementScope": "publication-only", "scopeBoundary": "From registration after reviewed GitHub and Zenodo identity plus initial local page drafting through release media, composite sealing, hosted site CI, merge, guarded zero-cost deployment and exact canonical readback or a preserved stop. All research, review, identity and initial-authoring work is excluded and not reconstructed.", "forecast": { "frozenAt": "2026-09-01T15:09:32.000Z", "procedureClass": "canonical-site-media-seal-deploy-and-readback", "targetOutcome": "Publish a reader-first Evidence Press release with provenance-bound fable audio, deterministic art and thumbnail, reciprocal method and work ledgers, green composite CI, guarded zero-cost deployment and exact canonical HTML, paper.json and media readback.", "expectedActiveMinutes": 95, "plausibleLowMinutes": 55, "plausibleHighMinutes": 160, "expectedUnattendedWaitMinutes": 25, "referenceClass": { "label": "Recent Evidence Press publication-completion releases", "sampleSize": 5, "basis": "Recent mathematics releases used the same media generators, composite protocol seal, four-job hosted CI, guarded deployment and canonical readback architecture." }, "fermiComponents": [ { "component": "Claim-disciplined art, OG, thumbnail and fable audio", "count": 1, "lowMinutesPerUnit": 15, "centralMinutesPerUnit": 25, "highMinutesPerUnit": 40, "basis": "One new mathematical slug using established deterministic renderers and the house TTS profile." }, { "component": "Composite build, protocol seal and local accessibility checks", "count": 1, "lowMinutesPerUnit": 15, "centralMinutesPerUnit": 25, "highMinutesPerUnit": 40, "basis": "One reader-first release with reciprocal work and method records on the current schema." }, { "component": "Push, pull request, hosted CI and merge", "count": 1, "lowMinutesPerUnit": 10, "centralMinutesPerUnit": 20, "highMinutesPerUnit": 35, "basis": "One isolated site branch using the established four-job Evidence Press workflow." }, { "component": "Post-merge ledger reseal, guarded deploy and canonical readback", "count": 1, "lowMinutesPerUnit": 15, "centralMinutesPerUnit": 25, "highMinutesPerUnit": 45, "basis": "One zero-cost Cloudflare deployment with exact release, media, protocol and preservation checks." } ], "probabilityPositiveSignal": 0.98, "probabilityTargetClosure": 0.9, "probabilityHorizonMinutes": 160, "assumptions": [ "The already public GitHub and Zenodo identities remain reachable and byte-stable.", "OpenAI fable TTS, hosted CI and zero-cost Cloudflare credentials remain available without weakening a gate.", "Origin main does not acquire an irreconcilable overlapping release or ledger change.", "The current reader-first and protocol schemas accept the new record without migration." ], "reforecastTriggers": [ "A media, accessibility, registry, manifest or preservation gate finds a release-blocking conflict.", "Hosted CI, TTS, Cloudflare or canonical readback remains unavailable after bounded recovery.", "Origin main advances with overlapping release or append-only ledger edits requiring reconciliation." ], "stopRule": "Stop on a fatal claim, licence, authentication, preservation, CI, accessibility or exact-readback failure. At 95 active minutes prioritize load-bearing gates; at 160 active minutes preserve the exact blocker rather than weaken a gate." }, "outcome": { "measuredAt": "2026-09-01T15:27:40.000Z", "calendarElapsedMinutes": 18, "activeAgentMinutes": 13, "activeHumanMinutes": null, "computeMinutes": 0, "unattendedWaitMinutes": 5, "blockedMinutes": 0, "reworkMinutes": 3, "agentRuns": 1, "maxParallelAgents": 1, "modelTurns": 1, "deduplicatedModelTokens": null, "uncachedInputTokens": null, "researchCycles": { "positive": 0, "negative": 0, "inconclusive": 0 }, "falsificationGatesRun": 0, "candidateArchitecturesTested": 0, "candidateArchitecturesRejected": 0, "substantiveReviewRounds": 0, "p0Findings": 0, "p1Findings": 0, "prepublicationClaimCorrections": 0, "resultState": "target-closed", "resultSummary": "The honestly left-bounded publication-completion attempt closed with provenance-bound fable narration, deterministic art and thumbnail, reciprocal method and work records, an exact protocol seal, green Node 18, 20 and 22 plus accessibility CI, merge commit fcf34c15467dff5b9b51287b15a253d5f614ae80, guarded zero-cost Cloudflare deployment, byte-identical canonical HTML, paper.json, audio, art and Open Graph readback, full 49-release and 31-institutional-artifact preservation, and accepted IndexNow submission. A stale mechanically derived Atlas baseline and an initially unpinned standalone protocol rebuild were corrected without changing the theorem, research package or media. The published result remains an anonymous, AI-assisted, unrefereed finite theorem candidate through five positive alphabet entries; Fisk's all-degree conjecture, zero-boundary cases, degree six beyond three leading minors, independent reconstruction, formal verification, external specialist review, peer review, novelty and priority remain open or unassessed.", "positiveSignalObserved": true, "targetReached": true, "forecastErrorMinutes": -82, "forecastRatio": 0.14, "withinForecastInterval": false, "varianceReason": "The attempt began only after research, review, public GitHub and Zenodo identity and initial page drafting were complete; established media, composite-seal, CI and deployment tooling then closed the remaining publication route below the 55-minute lower active-time bound, with two bounded local integration corrections and no research-package change.", "missingFields": [ { "field": "activeHumanMinutes", "reason": "No instrument captured human direction or review time inside the prospective publication-only boundary." }, { "field": "deduplicatedModelTokens", "reason": "No active fork-aware task counter exposed exact task-local model-token usage at or after the 15:09:32Z publication boundary, so tokens are not reconstructed from conversation context." }, { "field": "uncachedInputTokens", "reason": "The runtime does not expose an uncached-input token counter." } ] } }, "missingnessReason": null } ] } }