{
  "schemaVersion": "1.6",
  "slug": "hc4-five-support-structural-reductions",
  "title": "Structural reductions toward the quartic Hessian conjecture in dimension four",
  "shortTitle": "HC4 structural reductions",
  "url": "https://evidencepress.org/releases/hc4-five-support-structural-reductions/",
  "oneLine": "Exact five-support and tangent-orbit reductions, a three-step secant colon chain, and sixteen rational fourth-block source syzygies sharply narrow one HC4 normal-layer programme without proving HC4 or JC2.",
  "abstract": "This anonymous, AI-assisted, unrefereed computer-assisted candidate packages exact structural reductions for a quartic Hessian problem in dimension four. It excludes every clean binary-decimic restriction with exactly five support points, proves that all 31 generators of the multiplicity-six binary-decimic locus vanish on the tangent normal layer, and gives three exact rational localized-colon elements on the unresolved secant chart. A prospectively selected 16-column experiment then lifts through 173^4, reconstructs all 585,392 coordinates uniquely over the rationals, replays against 85,688 equations, and passes a separate direct-polynomial audit. The closing result is a source-kernel theorem, not membership of the inhomogeneous fourth target. Secant-orbit closure, colon equality, saturation, fourth-target membership, HC4 and JC2 remain open. Internal five-role review passed after repair, but unaffiliated reproduction, formal verification, external specialist review and peer review have not occurred.",
  "datePublished": "2026-09-01",
  "dateModified": "2026-09-01",
  "version": "0.1.0-candidate",
  "doi": "10.5281/zenodo.22216400",
  "doiUrl": "https://doi.org/10.5281/zenodo.22216400",
  "conceptDoi": "10.5281/zenodo.22216399",
  "pdfUrl": "https://github.com/ipitchford/hc4-five-support-structural-reductions/releases/download/v0.1.0-candidate/paper.pdf",
  "altPdfUrl": "https://zenodo.org/records/22216400/files/paper.pdf?download=1",
  "altPdfLabel": null,
  "zenodoUrl": "https://zenodo.org/records/22216400",
  "repoUrl": "https://github.com/ipitchford/hc4-five-support-structural-reductions",
  "releaseUrl": "https://github.com/ipitchford/hc4-five-support-structural-reductions/releases/tag/v0.1.0-candidate",
  "markdownUrl": "https://evidencepress.org/releases/hc4-five-support-structural-reductions/index.md",
  "bibtexUrl": "https://evidencepress.org/releases/hc4-five-support-structural-reductions/cite.bib",
  "audioUrl": "https://evidencepress.org/assets/audio/hc4-five-support-structural-reductions.mp3?v=713f88f27d",
  "imageUrl": "https://evidencepress.org/assets/og/hc4-five-support-structural-reductions.png?v=4b34767a04",
  "coverArtUrl": "https://evidencepress.org/assets/art/hc4-five-support-structural-reductions.svg?v=d680377695",
  "media": [
    {
      "type": "audio",
      "url": "https://evidencepress.org/assets/audio/hc4-five-support-structural-reductions.mp3",
      "name": "Audio briefing — HC4 five-support structural reductions",
      "description": "Plain-English OpenAI API synthetic-voice summary of the exact five-support and tangent reductions, unresolved secant boundary, and prospectively frozen 16-column result; a communication aid, not additional evidence.",
      "transcriptUrl": "https://evidencepress.org/assets/audio/hc4-five-support-structural-reductions.txt"
    }
  ],
  "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 structural-reductions candidate. The exact five-support, tangent-orbit, colon-element and 16-column source-kernel claims have producer-side rational or characteristic-zero replay. The direct-polynomial audit bypasses the sparse row encoding but remains producer-coordinated. The 16-column selection rule was frozen before transfer computation. A fixed-gauge fourth target lifts through 173^96, but rational recovery failed under the preregistered hierarchy; this is not evidence of non-membership. No unaffiliated rerun, independent reimplementation, proof-assistant formalization, external specialist review, journal peer review, absolute priority determination or impact evaluation has occurred. The release does not prove HC4 or JC2."
  },
  "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/22216400",
      "note": "The published Zenodo record and tagged GitHub release expose the exact PDF, deterministic ZIP and hash sidecar; public downloads match local SHA-256 hashes."
    },
    {
      "dimension": "internalReplay",
      "label": "Internal replay",
      "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?",
      "state": "passed",
      "note": "The sealed package passes status, manifest, rational reconstruction and direct-polynomial C16 replay gates in a fresh extraction.",
      "evidenceUrl": "https://github.com/ipitchford/hc4-five-support-structural-reductions/blob/v0.1.0-candidate/receipts/hsop-j2-secant-r10-fourth-colon-c16-kernel-batch-terminal.json"
    },
    {
      "dimension": "independentRerun",
      "label": "Independent rerun",
      "question": "Has someone else run the supplied implementation and obtained the stated result?",
      "state": "not-assessed",
      "note": "No unaffiliated party has reported rerunning the immutable package in a separately provisioned environment."
    },
    {
      "dimension": "independentReimplementation",
      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed",
      "note": "The separate polynomial audit remains producer-coordinated; no independently authored implementation has reconstructed the results."
    },
    {
      "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 normal-layer reductions, radical certificates or source-kernel identities."
    },
    {
      "dimension": "specialistReview",
      "label": "Specialist review",
      "question": "Has a domain specialist assessed the argument?",
      "state": "not-assessed",
      "note": "The five-role reports and confirmation are internal AI editorial quality control, not external 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 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/hc4-five-support-structural-reductions/blob/v0.1.0-candidate/ENVIRONMENT.txt",
      "note": "Tool versions, scripts, matrices, receipts and replay commands are public, but no unaffiliated declarative environment reconstruction is reported."
    }
  ],
  "provenance": {
    "aiGenerated": true,
    "aiAssisted": true,
    "generatedBy": [
      "AI systems under human direction",
      "OpenAI Codex",
      "SageMath 10.9",
      "SymPy 1.14.0",
      "LinBox 1.7.1",
      "Macaulay2 1.26.06",
      "Singular 4.4.1"
    ],
    "humanRole": "Research direction, mediation, claim-boundary decisions and publication authorization by the human creator; scholarly attribution remains Anonymous.",
    "disclosure": "AI systems contributed proof exploration, code, review, editing, replay and release engineering in one producer-coordinated workflow. Exact replay, implementation diversity, review reports, matching public hashes and publication are not independent mathematical reproduction or peer review."
  },
  "attributionBoundary": null,
  "problem": {
    "name": "Quartic Hessian conjecture in dimension four",
    "url": "https://arxiv.org/abs/math/0409534"
  },
  "orderedProductAverage": null,
  "corrections": [],
  "publicCorrections": [],
  "publicCorrectionIndexes": null,
  "pageStructureVersion": "2.0",
  "pageStructureVariant": "reader-first-reference",
  "pageStructureWaivers": [],
  "recordMaturity": "current",
  "metadataProvenance": "Authored prospectively for reader-first schema 2.0 against immutable GitHub and Zenodo identities, the sealed 16-column receipt, clean-extraction replay and frozen internal review record.",
  "grandfatheredAtSchemaVersion": null,
  "keywords": [
    "Hessian nilpotent polynomial",
    "Jacobian Conjecture",
    "quartic Hessian conjecture",
    "binary decimic",
    "coincident-root locus",
    "colon ideal",
    "p-adic reconstruction",
    "computer-assisted mathematics",
    "unrefereed candidate"
  ],
  "keyResults": [
    "Every clean nonzero binary-decimic restriction with exactly five distinct projective roots is excluded by exact characteristic-zero certificates.",
    "All 31 generators of the multiplicity-six binary-decimic locus lie in the radical of the tangent normal-layer ideal.",
    "Three explicit rational quartics are certified as successive localized-colon elements on the remaining secant chart.",
    "Sixteen prospectively selected fourth-block free columns extend to exact rational source-module syzygies; all 585,392 reconstructed coordinates and 85,688 equations replay exactly.",
    "The fixed-gauge fourth target lifts through 173^96 but the frozen rational-recovery hierarchy fails closed; no target membership or non-membership conclusion follows."
  ],
  "reviews": [],
  "evidencePackage": "A 10-page manuscript and accessible Markdown; seven machine-readable claim units; exact characteristic-zero certificates for seven five-support partitions and all 31 tangent target generators; three rational colon identities; a frozen 85,688 by 36,587 integer matrix interface; four canonical 16-right-hand-side LinBox solves; unique rational reconstruction of 585,392 coordinates from 173^4; exact row replay and a direct-polynomial replay with sixteen zero residuals; a complete 1,180-file manifest; failed and inconclusive recovery receipts; a five-role producer-coordinated internal review, response matrix and bounded confirmation; clean-extraction replay; and byte-identical GitHub and Zenodo ZIP and PDF assets. These establish availability, producer-side replay, integrity and the stated bounded results—not fourth-target membership, secant closure, HC4, JC2, independent reproduction or peer review.",
  "openProblems": [
    "Use the exact 16-dimensional rational source-kernel slice to derive and test a rational gauge action on the inhomogeneous fourth target.",
    "Prove or falsify full colon equality or saturation on the remaining secant chart.",
    "Transfer multiplicity-six nullcone containment from the tangent residual orbit to the secant residual orbit.",
    "Close the six-or-more-support and polynomial-level lifting gates required for the global quartic Hessian programme.",
    "Obtain unaffiliated specialist reconstruction and a separately authored implementation while preserving corrections as versioned successors."
  ],
  "mathObjects": [
    {
      "id": "five-support-exclusion",
      "kind": "statement",
      "status": "claimed-result",
      "label": "Five-support exclusion",
      "plainText": "No clean nonzero binary-decimic restriction with exactly five projective roots satisfies the frozen double-conic normal-layer equation in characteristic zero.",
      "scope": "Exactly five support points on the clean double-conic normal layer; computer-assisted exact certificates."
    },
    {
      "id": "tangent-nullcone-containment",
      "kind": "statement",
      "status": "claimed-result",
      "label": "Tangent nullcone containment",
      "plainText": "All 31 generators of the multiplicity-six binary-decimic locus lie in the radical of the tangent normal-layer ideal.",
      "scope": "Tangent residual orbit only; no secant transfer."
    },
    {
      "id": "sixteen-source-syzygies",
      "kind": "identity",
      "status": "claimed-result",
      "label": "Sixteen rational source syzygies",
      "plainText": "For the frozen fourth block there is a rational matrix T satisfying B T plus C16 equals zero.",
      "latex": "BT+C_{16}=0",
      "scope": "Sixteen selected source columns only; not the inhomogeneous fourth target."
    },
    {
      "id": "secant-fourth-target",
      "kind": "obstruction",
      "status": "open-problem",
      "label": "Secant fourth-target obstruction",
      "plainText": "Prove rational fourth-target membership or a full secant colon or saturation statement.",
      "scope": "Remaining secant chart; required before normal-layer closure, HC4, or JC2."
    }
  ],
  "relatedWorks": [
    {
      "citation": "Zhao, W. (2004). Hessian Nilpotent Polynomials and the Jacobian Conjecture.",
      "url": "https://arxiv.org/abs/math/0409534",
      "doi": null
    },
    {
      "citation": "van den Essen, A., & Zhao, W. (2007). Two Results on Homogeneous Hessian Nilpotent Polynomials.",
      "url": "https://arxiv.org/abs/0704.1690",
      "doi": "10.48550/arXiv.0704.1690"
    },
    {
      "citation": "Brouwer, A. E., & Popoviciu, M. (2010). The invariants of the binary decimic.",
      "url": "https://arxiv.org/abs/1002.1008",
      "doi": "10.48550/arXiv.1002.1008"
    },
    {
      "citation": "Chipalkatti, J. V. (2003). On equations defining coincident root loci.",
      "url": "https://arxiv.org/abs/math/0110224",
      "doi": null
    },
    {
      "citation": "Lee, H., & Sturmfels, B. (2016). Duality of Multiple Root Loci.",
      "url": "https://arxiv.org/abs/1508.00202",
      "doi": "10.48550/arXiv.1508.00202"
    }
  ],
  "claimAssurance": null,
  "operatingModel": {
    "version": "1.0",
    "workId": "ep-work:hc4-five-support-structural-reductions",
    "attemptIds": [
      "ep-attempt:hc4-five-support-structural-reductions"
    ],
    "aims": [
      "science"
    ],
    "artifactRoles": [
      "research-output",
      "evidence-assessment",
      "method-demonstration",
      "communication"
    ],
    "lineageId": null,
    "accelerationPrimitives": [
      "certificate-first",
      "structural-compression",
      "adversarial-controls",
      "productive-failure",
      "assurance-vector",
      "agent-readable-research-object"
    ],
    "decisionObject": {
      "type": "executable-open-problem",
      "description": "A sharply bounded secant fourth-target and rational gauge-action research handoff following exact five-support, tangent and source-kernel reductions.",
      "scope": "The clean normal-layer five-support theorem, tangent nullcone containment, three secant colon elements, fixed-gauge recovery failure and sixteen rational source syzygies; not fourth-target membership, secant closure, HC4 or JC2."
    },
    "bottleneckTargeted": [
      "discovery",
      "assurance",
      "publication"
    ],
    "semanticBridge": {
      "state": "explicit",
      "description": "The package maps the quartic Hessian normal layer through binary-decimic support and residual-orbit geometry to an unresolved secant saturation, then isolates an exact rational 16-direction source-kernel slice for the next gauge-action test.",
      "remainingRisks": [
        "The normal-layer reductions have not been reconstructed by an unaffiliated specialist.",
        "Source-kernel freedom may not move the inhomogeneous fourth target into a rationally simple gauge.",
        "Tangent containment need not transfer to the secant residual orbit.",
        "Normal-layer closure would still require polynomial-level and full-family lifting."
      ]
    },
    "humanJudgmentGates": [
      "Check the invariant-theoretic and normal-layer reductions as mathematics rather than inferring them from successful replay.",
      "Keep source syzygies separate from inhomogeneous target membership and colon elements separate from colon equality.",
      "Keep tangent-orbit containment separate from the unresolved secant orbit.",
      "Require external specialist assessment before any HC4, JC2, first, priority or field-acceptance language."
    ],
    "parentLinks": [],
    "assuranceTarget": {
      "dimensions": [
        "independentRerun",
        "independentReimplementation",
        "formalVerification",
        "specialistReview",
        "dataEnvironmentReproducibility",
        "semanticValidation",
        "noveltyAssessment",
        "priorityAssessment"
      ],
      "nextAction": "Obtain an unaffiliated reconstruction of the tangent and secant reductions, then use the exact 16-direction kernel slice to prove or decisively falsify rational fourth-target membership.",
      "claimCeiling": "An anonymous unrefereed computer-assisted structural-reductions candidate with exact characteristic-zero and rational certificates, a prospectively frozen 16-column source-kernel theorem, fail-closed negative routes and internal editorial closure; not fourth-target membership, secant closure, HC4, JC2, independent validation, formal verification, external specialist or editorial peer review, absolute priority or demonstrated workflow impact."
    },
    "impactClaims": [
      {
        "id": "hc4-structural-science-no-impact",
        "aim": "science",
        "outcome": "Faster or more reliable resolution and assurance of difficult algebraic conjectures",
        "setting": "AI-assisted invariant theory, exact algebra and p-adic reconstruction around a quartic Hessian programme",
        "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 or citation 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:hc4-five-support-structural-reductions",
        "status": "published",
        "resultClass": "partial",
        "metrics": {
          "schemaVersion": "1.0",
          "measurementScope": "research-through-publication",
          "scopeBoundary": "From prospective registration through one frozen 16-column characteristic-173 experiment, manuscript construction, bounded editorial repair, immutable GitHub and Zenodo identity, reader-first Evidence Press publication and canonical readback or a preserved stop. Every earlier HC4 discovery, scan, lift, recovery attempt and support census is left-censored and excluded rather than reconstructed.",
          "forecast": {
            "frozenAt": "2026-08-31T21:45:53.688Z",
            "procedureClass": "left-censored-hc4-structural-reductions-new-falsification-through-publication",
            "targetOutcome": "Complete and replay the preregistered 16-column test, then publish an exact claim-bounded HC4 structural-reductions candidate with deterministic package, five-role internal review, immutable archive identity, reader-first media, composite sealing, hosted CI, guarded zero-cost deployment and exact canonical readback.",
            "expectedActiveMinutes": 390,
            "plausibleLowMinutes": 240,
            "plausibleHighMinutes": 600,
            "expectedUnattendedWaitMinutes": 80,
            "referenceClass": {
              "label": "Audited LinBox multi-right-hand-side kernel tests plus recent exact-mathematics full-candidate publications",
              "sampleSize": 7,
              "basis": "One closely related 114-column canonical-section solve completed in about 189 seconds, while six recent Evidence Press mathematics candidates exercised the same package, review, immutable identity, media, CI, deployment and readback architecture; no previous attempt combines both classes prospectively."
            },
            "fermiComponents": [
              {
                "component": "16-column system export, modular solve, replay and first p-adic lift gate",
                "count": 1,
                "lowMinutesPerUnit": 25,
                "centralMinutesPerUnit": 50,
                "highMinutesPerUnit": 90,
                "basis": "The nearest 114-column canonical-section solve took about 189 seconds, but the row-normalization export and independent replay are new engineering surfaces."
              },
              {
                "component": "Evidence recovery, theorem-boundary synthesis and manuscript/package construction",
                "count": 1,
                "lowMinutesPerUnit": 70,
                "centralMinutesPerUnit": 120,
                "highMinutesPerUnit": 190,
                "basis": "The frozen campaign is extensive and exact but distributed across receipts; one concise manuscript must reconstruct dependencies without upgrading bounded evidence into HC4."
              },
              {
                "component": "Five-role internal editorial review, one repair batch and confirmation",
                "count": 1,
                "lowMinutesPerUnit": 45,
                "centralMinutesPerUnit": 80,
                "highMinutesPerUnit": 130,
                "basis": "The candidate has several adjacent claim boundaries and one new experiment, making scientific scope review more demanding than a short finite theorem."
              },
              {
                "component": "Public GitHub repository, deterministic archive, Zenodo identity and cross-service byte readback",
                "count": 1,
                "lowMinutesPerUnit": 35,
                "centralMinutesPerUnit": 55,
                "highMinutesPerUnit": 85,
                "basis": "Established automation is available, but a new repository, DOI-bearing rebuild and immutable asset comparison are required."
              },
              {
                "component": "Evidence Press authoring, provenance-bound media, operating records, composite seals, hosted CI, deployment and readback",
                "count": 1,
                "lowMinutesPerUnit": 65,
                "centralMinutesPerUnit": 85,
                "highMinutesPerUnit": 105,
                "basis": "Recent releases use stable generators and deployment tooling, while this new slug still requires method assignment, audio, art, Open Graph image, thumbnail and two append-only ledger closures."
              }
            ],
            "probabilityPositiveSignal": 0.72,
            "probabilityTargetClosure": 0.6,
            "probabilityHorizonMinutes": 600,
            "assumptions": [
              "The frozen p=173 matrix, free-column descriptors and LinBox environment remain byte-readable and semantically consistent with the registered test design.",
              "The selected 16 characteristic-173 directions can be exported under the original row normalization without rebuilding the entire campaign from undocumented state.",
              "GitHub, Zenodo, OpenAI TTS, hosted CI and zero-cost Cloudflare credentials remain available without weakening a gate or exposing a secret.",
              "No manuscript audit discovers a fatal mismatch between the frozen receipts and the proposed structural-reductions claim ceiling."
            ],
            "reforecastTriggers": [
              "The frozen matrix cannot be reproduced or the selected free-column descriptors do not bind to the claimed rows and columns.",
              "The 16-column modular nullspace fails the all-row replay or exposes a rank/normalization inconsistency rather than a mathematically classified lift outcome.",
              "Editorial review finds a load-bearing theorem, provenance, citation or assurance defect requiring more than one bounded repair batch.",
              "Public identity, site CI, Cloudflare or canonical readback remains unavailable after bounded recovery."
            ],
            "stopRule": "Stop the positive scientific route immediately on a matrix-identity, row-normalization, modular replay or exact-certificate failure and preserve the counter-receipt. Stop publication on a fatal claim, citation, licence, authentication, preservation, CI, accessibility or exact-readback failure. At 390 active minutes prioritize load-bearing gates; at 600 active minutes preserve the exact blocker rather than weaken a theorem or publication gate."
          },
          "outcome": {
            "measuredAt": "2026-08-31T23:16:42.000Z",
            "calendarElapsedMinutes": 91,
            "activeAgentMinutes": 75,
            "activeHumanMinutes": null,
            "computeMinutes": 8,
            "unattendedWaitMinutes": 16,
            "blockedMinutes": 0,
            "reworkMinutes": 10,
            "agentRuns": 4,
            "maxParallelAgents": 4,
            "modelTurns": 4,
            "deduplicatedModelTokens": null,
            "uncachedInputTokens": null,
            "researchCycles": {
              "positive": 1,
              "negative": 0,
              "inconclusive": 0
            },
            "falsificationGatesRun": 4,
            "candidateArchitecturesTested": 1,
            "candidateArchitecturesRejected": 0,
            "substantiveReviewRounds": 1,
            "p0Findings": 0,
            "p1Findings": 1,
            "prepublicationClaimCorrections": 0,
            "resultState": "target-closed",
            "resultSummary": "The prospectively selected 16-column experiment reached a positive exact result: four characteristic-173 batch solves lifted through 173^4, all 585,392 coordinates reconstructed uniquely, all 85,688 source equations replayed with zero mismatch, and a separate direct-polynomial audit expanded sixteen residuals to zero. A 10-page anonymous unrefereed manuscript, complete deterministic ZIP, PDF and hash sidecar reached matching public GitHub and Zenodo identities under DOI 10.5281/zenodo.22216400. The reader-first Evidence Press release adds provenance-bound fable audio and transcript, deterministic art, Open Graph media, a mirrored thumbnail, method and Atlas records, composite content/control seals, green Node 18, 20 and 22 plus accessibility CI, guarded zero-cost deployment, exact 47-release and 31-institutional-artifact canonical readback, protocol parity, media hash parity and full publication preservation. The first hosted run exposed four missing reader-function headings; an additive three-heading repair and control reseal passed. The first post-upload readback was blocked by eight byte-identical iCloud duplicate files; they were verified, moved recoverably to Trash and the exact canonical readback then passed without changing tracked source. The result is a source-module syzygy theorem and structural-reductions candidate, not fourth-target membership, colon equality, saturation, secant closure, full binary-decimic nullcone closure, HC4, JC2, independent reconstruction, formal verification, external specialist review, editorial peer review, absolute priority or workflow impact.",
            "positiveSignalObserved": true,
            "targetReached": true,
            "forecastErrorMinutes": -315,
            "forecastRatio": 0.19,
            "withinForecastInterval": false,
            "varianceReason": "The frozen 240--600 minute interval intentionally included uncertainty in matrix export, manuscript recovery and public identity. The preserved campaign state proved more complete than the reference class anticipated, the shared 16-right-hand-side solve completed in 439.334 seconds, established packaging and publication tooling eliminated most engineering variance, and both site repairs were narrow presentation or filesystem-state corrections rather than scientific rework.",
            "missingFields": [
              {
                "field": "activeHumanMinutes",
                "reason": "No instrument captured human direction, mediation or review time at the prospective research-through-publication boundary."
              },
              {
                "field": "deduplicatedModelTokens",
                "reason": "No active fork-aware goal counter exposed exact task-local model-token usage for the complete prospectively registered interval, so tokens are not reconstructed from conversation context."
              },
              {
                "field": "uncachedInputTokens",
                "reason": "The runtime does not expose an uncached-input token counter."
              }
            ]
          }
        },
        "missingnessReason": null
      }
    ]
  }
}