{ "schemaVersion": "1.6", "slug": "central-configuration-kernel-rigidity", "title": "Certified convex reconstruction and kernel exclusion for central configurations", "shortTitle": "Reconstructing gravitational configurations", "url": "https://evidencepress.org/releases/central-configuration-kernel-rigidity/", "oneLine": "Exact certificates separate a uniquely reconstructed metric from a genuine gravitational central configuration—and exclude two whole seven-body parameter boxes.", "abstract": "This methods candidate develops quantitative and certified refinements of classical fixed-support convex reconstruction for central configurations. It gives an explicit Gram-matrix separation estimate in complete-kernel projector distance, primal–dual reconstruction error bounds, and a bounded 41-chart reduction retaining every possible stress rank for spatial seven-body configurations. Exact arithmetic certifies 54 local metric reconstructions and parameter patches, 15 higher-rank exclusion regions, and two full-dimensional singular-fibre boxes with noncentral rank-one PSD optimizers. The qualitative convex reconstruction and kernel-rigidity mechanism is attributed to Yoccoz and Albouy. The planar-eight and spatial-seven inventories remain lower bounds of twenty, not complete classifications.", "datePublished": "2026-10-01", "dateModified": "2026-10-01", "version": "1.2.0-candidate", "doi": "10.5281/zenodo.23074985", "doiUrl": "https://doi.org/10.5281/zenodo.23074985", "conceptDoi": "10.5281/zenodo.23074984", "pdfUrl": "https://github.com/ipitchford/central-configuration-kernel-rigidity/releases/download/v1.2.0-candidate/manuscript.pdf", "altPdfUrl": "https://zenodo.org/records/23074985/files/manuscript.pdf?download=1", "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23074985", "repoUrl": "https://github.com/ipitchford/central-configuration-kernel-rigidity", "releaseUrl": "https://github.com/ipitchford/central-configuration-kernel-rigidity/releases/tag/v1.2.0-candidate", "markdownUrl": "https://evidencepress.org/releases/central-configuration-kernel-rigidity/index.md", "bibtexUrl": "https://evidencepress.org/releases/central-configuration-kernel-rigidity/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/central-configuration-kernel-rigidity.mp3?v=0a3876d196", "imageUrl": "https://evidencepress.org/assets/og/central-configuration-kernel-rigidity.png?v=b63b4bba01", "coverArtUrl": "https://evidencepress.org/assets/art/central-configuration-kernel-rigidity.svg?v=1b0f74e947", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/central-configuration-kernel-rigidity.mp3", "name": "A metric is not yet a central configuration", "description": "A synthetic OpenAI fable briefing in the house British style. This explanation is not additional scientific evidence.", "durationLabel": "2 min 11 sec", "transcriptUrl": "https://evidencepress.org/assets/audio/central-configuration-kernel-rigidity.txt" }, { "type": "video", "url": "https://youtu.be/oql9vFpghyE", "name": "Reconstructing Gravitational Configurations", "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 methods candidate. Classical fixed-support convexity, qualitative kernel rigidity and cone optimality are not claimed as new. Local certificates do not establish exhaustive target counts, global thickness, a complete singular-branch classification or solver speedup. Supplied reviewer independence is unauthenticated." }, "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/23074985", "note": "The versioned GitHub release and published Zenodo record expose the manuscript, exact archive, replay summary and manifest. Full asset downloads from both providers match the frozen local files. Site-delivery readback is a separate publication record." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Current twelve-stage exact replay passed, including two whole singular boxes; supplied alternative cap and singular implementations also replayed. Finite checks are distinct from universal written proofs." }, { "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 rerun; coordinated agents and supplied reports do not establish independence." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "Supplied alternative arithmetic and positivity tests provide implementation diversity; unaffiliated provenance is unauthenticated." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No proof-assistant verification of the entire analytic or computational chain." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "Supplied review is not authenticated as 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 other external venue peer review is claimed." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "partial", "note": "Exact replay uses Python standard-library integer/rational arithmetic with retained inputs and receipts; the full environment and PDF build are not hermetic." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted research; originating identities not fully authenticated", "Codex mathematical extension, exact checking, bounded revisions and publication", "Supplied review and alternative checker; unaffiliated provenance unauthenticated" ], "humanRole": "Publication authority and supplied materials only; no human scientific contribution is inferred. Scholarly creator remains Anonymous.", "disclosure": "Internal replay and supplied separately written checks do not establish authenticated independent reproduction, institutional audit or editorial peer review." }, "attributionBoundary": null, "problem": { "name": "Certified reconstruction and exclusion in central-configuration searches", "url": "https://doi.org/10.1007/s10569-019-9920-6" }, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Corrected manuscript and exact certificate package; supplied 1 October review and alternative implementation were used within producer-coordinated verification. Classical antecedents are explicitly restored.", "grandfatheredAtSchemaVersion": null, "keywords": [ "central configurations", "many-body problem", "convex reconstruction", "stress kernels", "interval arithmetic", "positive semidefinite metrics" ], "keyResults": [ "Explicit quantitative separation of normalized central Gram matrices by complete-kernel projector distance, with fixed masses and stated distance bounds.", "A semidefinite-constrained dual with a factorized gap and certified reconstruction errors, including the closed PSD boundary.", "Two rational seven-body kernel-chart boxes, of dimensions eight and five and half-width 2^−34, have unique rank-one noncentral PSD optimizers throughout; neither box contains a realizable complete kernel.", "54 local reconstruction and parameter-patch certificates, 15 higher-rank exclusion regions, and a 41-chart domain reduction retaining the spatial-seven singular branches." ], "reviews": [], "evidencePackage": "Written proofs; twelve-stage exact producer replay; rational and outward-rounded interval certificates; semantic rejection controls; separately supplied alternative checks replayed with provenance limitations.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Yoccoz (1986), Description conjecturale des configurations centrales dans le problème planaire des 4 corps, §1.5, pp.2–3. Classical affine reduction, strict convexity and the distinction between positive distances and positive metrics.", "url": "https://carlos.matheus.perso.math.cnrs.fr/yoccoz/JC-4-corps-final.pdf", "doi": null }, { "citation": "Albouy (1997), Recherches sur le problème des N corps, Part 5, §§2.4 and 2.9, p.77. Fixed-support convex uniqueness is the decisive antecedent; qualitative complete-kernel rigidity follows from this framework.", "url": "https://perso.imcce.fr/alain-albouy/Albouy_habilitation.pdf", "doi": null }, { "citation": "Moczurad and Zgliczyński (2019), Central configurations in planar n-body problem with equal masses for n=5,6,7. The complete planar-seven catalogue is an external premise of the seven-body boundary application.", "url": "https://doi.org/10.1007/s10569-019-9920-6", "doi": "10.1007/s10569-019-9920-6" }, { "citation": "Chenciner (2016), Non-avoided crossings for n-body balanced configurations in R³ near a central configuration, Lemma 1. Reconstruction from the full force operator, distinct from comparing complete kernels.", "url": "https://doi.org/10.1007/s40598-016-0041-y", "doi": "10.1007/s40598-016-0041-y" }, { "citation": "Dias (2026), Brehm–Wintner–Conley dimension, Plücker coordinates, and generalized Dziobek–Williams equations. Actual-rank stratification and the complete-kernel Grassmannian invariant.", "url": "https://arxiv.org/abs/2608.07771", "doi": "10.48550/arXiv.2608.07771" }, { "citation": "Albouy and Sun (2025), On the eigenvalues of a central configuration. Spectral context, including the classical collinear separation attributed to Conley; not a global seven-body spectral theorem.", "url": "https://arxiv.org/abs/2512.00661", "doi": "10.48550/arXiv.2512.00661" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:central-configuration-kernel-rigidity", "attemptIds": [ "ep-attempt:central-configuration-kernel-rigidity-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "method-demonstration" ], "lineageId": null, "accelerationPrimitives": [ "certificate-first", "structural-compression", "adversarial-controls", "productive-failure", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "certificate", "description": "Quantitative reconstruction and exact whole-region complete-kernel exclusion certificates.", "scope": "Normalized attractive central configurations; explicit equal-mass Newtonian seven/eight-body corpus and two seven-body singular support boxes." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "Convex metric optimality, restricted slack, physical force equations and complete-kernel realization are kept separate; exact finite certificates connect to stated quantified propositions.", "remainingRisks": [ "Universal prose arguments and Python semantics are not formally verified.", "The root-existence chain partly uses inherited code.", "Two excluded boxes do not cover the singular branches or solve either counting problem." ] }, "humanJudgmentGates": [ "Publication authorisation only; no human research contribution or external review status is inferred." ], "parentLinks": [], "assuranceTarget": { "dimensions": [ "independentRerun", "independentReimplementation", "formalVerification", "semanticValidation", "noveltyAssessment", "priorityAssessment" ], "nextAction": "Challenge the proof-to-certificate bridge and independently reproduce the exact boxes; a complete smaller benchmark would test the reduction's practical reach.", "claimCeiling": "Unrefereed methods candidate with exact producer-side replay, not a completed classification." }, "impactClaims": [ { "id": "central-configuration-kernel-rigidity-no-impact", "aim": "science", "outcome": "Reusable convex reconstruction and exclusion certificates", "setting": "Producer-coordinated mathematical candidate publication", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "None.", "estimand": "No research-speed, solver-speed or impact effect 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. 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