{
  "schemaVersion": "1.6",
  "slug": "centroidal-equilibrium-creation",
  "title": "Smoothing can create new balance points",
  "shortTitle": "Centroidal equilibrium creation",
  "url": "https://evidencepress.org/releases/centroidal-equilibrium-creation/",
  "oneLine": "A smooth, strictly convex body gains four centroidal equilibria under inward curvature flow: 22 become 26.",
  "abstract": "An explicit polynomial support-function family remains uniformly strictly convex and centrally symmetric. For every sufficiently small positive parameter, genuine forward mean-curvature flow creates two antipodal minimum–saddle pairs, changing the total centroidal equilibrium count from 22 to 26. The written argument extends to nonnegative Bloore-type speeds and an open set of asymmetric initial bodies. A separate four-outcome probability law exposes a moment-to-sign inference gap without identifying a physical abrasion ensemble.",
  "datePublished": "2026-10-05",
  "dateModified": "2026-10-05",
  "version": "1.1.0-candidate",
  "doi": "10.5281/zenodo.23167004",
  "doiUrl": "https://doi.org/10.5281/zenodo.23167004",
  "conceptDoi": "10.5281/zenodo.23167003",
  "pdfUrl": "https://github.com/ipitchford/mosaics-and-abrasion-counterexamples/releases/download/v1.1.0-candidate/abrasion.pdf",
  "altPdfUrl": "https://zenodo.org/records/23167004/files/abrasion.pdf?download=1",
  "altPdfLabel": null,
  "zenodoUrl": "https://zenodo.org/records/23167004",
  "repoUrl": "https://github.com/ipitchford/mosaics-and-abrasion-counterexamples",
  "releaseUrl": "https://github.com/ipitchford/mosaics-and-abrasion-counterexamples/releases/tag/v1.1.0-candidate",
  "markdownUrl": "https://evidencepress.org/releases/centroidal-equilibrium-creation/index.md",
  "bibtexUrl": "https://evidencepress.org/releases/centroidal-equilibrium-creation/cite.bib",
  "audioUrl": "https://evidencepress.org/assets/audio/centroidal-equilibrium-creation.mp3",
  "imageUrl": "https://evidencepress.org/assets/og/centroidal-equilibrium-creation.png?v=7c945f3213",
  "coverArtUrl": "https://evidencepress.org/assets/art/centroidal-equilibrium-creation.svg?v=ec9391ad61",
  "media": [
    {
      "type": "audio",
      "url": "https://evidencepress.org/assets/audio/centroidal-equilibrium-creation.mp3",
      "name": "Centroidal equilibrium creation — audio briefing",
      "description": "Synthetic explanation, not additional evidence.",
      "transcriptUrl": "https://evidencepress.org/assets/audio/centroidal-equilibrium-creation.txt"
    },
    {
      "type": "video",
      "url": "https://youtu.be/5GOPKErq-as",
      "name": "Smoothing Can Create New Balance Points",
      "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": "Unrefereed mathematical candidate with supplied review actioned and internal exact finite checks. No authenticated external review, unaffiliated reproduction or formal verification."
  },
  "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/23167004",
      "note": "GitHub and this Zenodo record are public; all five assets downloaded and matched to the frozen local bytes."
    },
    {
      "dimension": "internalReplay",
      "label": "Internal replay",
      "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?",
      "state": "passed",
      "note": "Fresh archive exact finite replay, two positive controls, nine corruption controls and five optimized-Python rejection guards passed. Universal analytic arguments remain written proofs."
    },
    {
      "dimension": "independentRerun",
      "label": "Independent rerun",
      "question": "Has someone else run the supplied implementation and obtained the stated result?",
      "state": "not-assessed",
      "note": "Not established by this workflow."
    },
    {
      "dimension": "independentReimplementation",
      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed",
      "note": "Not established by this workflow."
    },
    {
      "dimension": "formalVerification",
      "label": "Formal verification",
      "question": "Is a formalised statement machine-checked, and over which trusted base?",
      "state": "not-assessed",
      "note": "Not established by this workflow."
    },
    {
      "dimension": "specialistReview",
      "label": "Specialist review",
      "question": "Has a domain specialist assessed the argument?",
      "state": "not-assessed",
      "note": "Not established by this workflow."
    },
    {
      "dimension": "editorialPeerReview",
      "label": "Editorial peer review",
      "question": "Has a journal or venue run peer review to a decision?",
      "state": "not-assessed",
      "note": "Not established by this workflow."
    },
    {
      "dimension": "dataEnvironmentReproducibility",
      "label": "Data and environment reproducibility",
      "question": "Are data and computational environment pinned well enough to rebuild?",
      "state": "partial",
      "note": "Pinned Python dependencies; no unaffiliated reproduction."
    }
  ],
  "provenance": {
    "aiGenerated": true,
    "aiAssisted": true,
    "generatedBy": [
      "Supplied research package; original model identity not established",
      "Codex review revisions and publication checks"
    ],
    "humanRole": "Publication authorization only; no scientific contribution inferred.",
    "disclosure": "Anonymous is scholarly creator. Supplied review identity and external independence are not authenticated. Two distinct papers share one computational archive."
  },
  "attributionBoundary": null,
  "problem": {
    "name": "Centroidal equilibrium monotonicity under curvature-driven abrasion",
    "url": "https://arxiv.org/abs/1308.4779"
  },
  "orderedProductAverage": null,
  "corrections": [],
  "publicCorrections": [],
  "publicCorrectionIndexes": null,
  "pageStructureVersion": "2.0",
  "pageStructureVariant": "canonical-theorem",
  "pageStructureWaivers": [],
  "recordMaturity": "current",
  "metadataProvenance": "Supplied candidate and review, bounded source comparison and explicit review response; no reconstructed discovery metrics.",
  "grandfatheredAtSchemaVersion": null,
  "keywords": [
    "curvature flow",
    "abrasion",
    "centroidal equilibria",
    "bifurcation",
    "stochastic drift"
  ],
  "keyResults": [
    "A globally convex support family has 22 equilibria before and 26 after positive-time births.",
    "The mechanism extends to nontrivial nonnegative mean/Gaussian-curvature combinations.",
    "Endpoint counts persist for an open set of asymmetric initial bodies.",
    "Zero means and covariance do not determine the sign drift; stronger probability conditions are required."
  ],
  "reviews": [],
  "evidencePackage": "Exact symbolic flow jets, rational Sturm root isolation and four-outcome probability arithmetic. The common-time PDE and Morse-persistence arguments remain written proofs, not numerical simulation or formal verification.",
  "openProblems": [],
  "mathObjects": [],
  "relatedWorks": [
    {
      "citation": "Domokos, Monotonicity of spatial critical points evolving under curvature-driven flows. Expected-count conjecture and distinct stochastic assumptions.",
      "url": "https://doi.org/10.1007/s00332-014-9228-3",
      "doi": "10.1007/s00332-014-9228-3"
    },
    {
      "citation": "Damon, Local Morse theory for solutions to the heat equation and Gaussian blurring. Earlier local creation mechanism.",
      "url": "https://doi.org/10.1006/jdeq.1995.1019",
      "doi": "10.1006/jdeq.1995.1019"
    },
    {
      "citation": "Huisken, Flow by mean curvature of convex surfaces into spheres. Convex-flow background.",
      "url": "https://doi.org/10.4310/jdg/1214438998",
      "doi": "10.4310/jdg/1214438998"
    },
    {
      "citation": "Huang, The Cauchy problem for fully nonlinear parabolic systems on manifolds, version 8. Local existence and Schauder input.",
      "url": "https://arxiv.org/abs/1506.05030v8",
      "doi": "10.48550/arXiv.1506.05030"
    }
  ],
  "claimAssurance": null,
  "operatingModel": {
    "version": "1.0",
    "workId": "ep-work:centroidal-equilibrium-creation",
    "attemptIds": [
      "ep-attempt:centroidal-equilibrium-creation-publication"
    ],
    "aims": [
      "science"
    ],
    "artifactRoles": [
      "research-output"
    ],
    "lineageId": null,
    "accelerationPrimitives": [
      "certificate-first",
      "structural-compression",
      "adversarial-controls",
      "assurance-vector",
      "agent-readable-research-object"
    ],
    "decisionObject": {
      "type": "counterexample",
      "description": "A smooth, strictly convex body gains four centroidal equilibria under inward curvature flow: 22 become 26.",
      "scope": "Smooth uniformly convex support functions; sufficiently small positive parameter, local forward time, specified curvature speeds. No physical sampling law."
    },
    "bottleneckTargeted": [
      "assurance",
      "publication"
    ],
    "semanticBridge": {
      "state": "explicit",
      "description": "Global convexity and central symmetry connect the exact support-function jets to centroidal equilibria; forward parabolic dependence and complete critical-point enumeration supply the count transition.",
      "remainingRisks": [
        "Written analytic arguments not formalized.",
        "Producer-side checking, not independent reproduction.",
        "Bounded priority audit and no empirical validation."
      ]
    },
    "humanJudgmentGates": [
      "Publication is authorized; no human scientific contribution inferred.",
      "Future independent specialist assessment remains possible."
    ],
    "parentLinks": [
      {
        "relation": "depends-on-claim",
        "workId": null,
        "legacyReleaseSlug": null,
        "externalUrl": "https://arxiv.org/abs/1506.05030v8",
        "inheritedClaim": "Local uniformly parabolic existence and linear Schauder theory.",
        "inheritedAssuranceCeiling": "Source hypotheses retained; no external assurance inherited for the new application."
      }
    ],
    "assuranceTarget": {
      "dimensions": [
        "independentRerun",
        "independentReimplementation",
        "specialistReview",
        "formalVerification",
        "noveltyAssessment",
        "priorityAssessment"
      ],
      "nextAction": "Unaffiliated audit of the exact construction and the analytic proof interfaces.",
      "claimCeiling": "Unrefereed written candidate with internal exact finite checking."
    },
    "impactClaims": [
      {
        "id": "centroidal-equilibrium-creation-no-impact",
        "aim": "science",
        "outcome": "A smooth, strictly convex body gains four centroidal equilibria under inward curvature flow: 22 become 26.",
        "setting": "AI-assisted mathematical research and publication",
        "status": "NO_IMPACT_EVIDENCE",
        "designClass": "none",
        "comparator": "No matched-assurance comparison is registered.",
        "estimand": "No discovery-speed, cost, adoption or impact effect is 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:centroidal-equilibrium-creation-publication",
        "status": "result-ready",
        "resultClass": "positive",
        "metrics": {
          "schemaVersion": "1.0",
          "measurementScope": "publication-only",
          "scopeBoundary": "Remaining publication only; two outputs share packaging. No duplicated total effort estimate.",
          "forecast": {
            "frozenAt": "2026-10-05T16:27:48.121Z",
            "procedureClass": "review-revision-and-full-publication",
            "targetOutcome": "An exact-version candidate archive with GitHub and Zenodo identities, standard page and media, and canonical Evidence Press readback.",
            "expectedActiveMinutes": 30,
            "plausibleLowMinutes": 15,
            "plausibleHighMinutes": 60,
            "expectedUnattendedWaitMinutes": 15,
            "referenceClass": {
              "label": "Remaining two-output publication, allocated planning prior",
              "sampleSize": 0,
              "basis": "Task decomposition, not measured historical calibration."
            },
            "fermiComponents": [
              {
                "component": "Allocated remaining package and media",
                "count": 1,
                "lowMinutesPerUnit": 10,
                "centralMinutesPerUnit": 20,
                "highMinutesPerUnit": 40,
                "basis": "Two outputs share archive and provider setup."
              },
              {
                "component": "Allocated guarded site delivery",
                "count": 1,
                "lowMinutesPerUnit": 5,
                "centralMinutesPerUnit": 10,
                "highMinutesPerUnit": 20,
                "basis": "Shared CI and two-cycle deployment, unattended time separate."
              }
            ],
            "probabilityPositiveSignal": 0.9,
            "probabilityTargetClosure": 0.85,
            "probabilityHorizonMinutes": 120,
            "assumptions": [
              "No new proof gap",
              "Providers available"
            ],
            "reforecastTriggers": [
              "A load-bearing proof, attribution or licensing defect changes the payload.",
              "Provider failure, archive mismatch or site preservation defect delays delivery."
            ],
            "stopRule": "Timing is planning telemetry. Continue authorized work unless an unresolved integrity, rights or provider-access defect blocks publication; never promote an unchecked claim to meet the forecast."
          },
          "outcome": null
        },
        "missingnessReason": null
      }
    ]
  }
}