{
  "schemaVersion": "1.4",
  "slug": "certified-three-item-jrp-gap",
  "title": "A Candidate Exact Three-Item Independent-Cap Oracle",
  "shortTitle": "Certified three-item JRP gap",
  "url": "https://evidencepress.org/releases/certified-three-item-jrp-gap/",
  "oneLine": "A producer-side candidate exact oracle gives a rational three-item max-frequency relaxation-gap lower bound of 1.1487291464748206... and a verifier-checked route to instance-specific logistics stress tests.",
  "abstract": "This anonymous unrefereed successor candidate constructs an exact three-item independent-cap oracle for continuous-time common-origin fixed-interval joint replenishment. A finite primitive-triple enumeration and strict global tail candidate theorem support an exact rational bundled-instance ratio of 1.1487291464748205845..., 3.3132 percent above the producer-side unrefereed two-item upper endpoint. A monotonicity lemma propagates the candidate lower bound to every fixed item count of at least three. An exact five-policy family explains the witness, while sixteen exact vertex certificates prove two conservative inner boxes under simultaneous relative holding-cost perturbation only. The bundled five-policy sets are synthetic regression fixtures; every fitted logistics instance must regenerate and verifier-check its own candidate set across primitive and boundary regimes. The 14.8729 percent lower-bound optimism is not a savings claim. Independent rerun, reimplementation, formal verification, external specialist review, external editorial peer review, operational validation, and field impact are not assessed.",
  "datePublished": "2026-08-22",
  "dateModified": "2026-08-22",
  "version": "0.3.1-candidate",
  "doi": "10.5281/zenodo.22057665",
  "doiUrl": "https://doi.org/10.5281/zenodo.22057665",
  "conceptDoi": "10.5281/zenodo.22057664",
  "pdfUrl": "https://github.com/ipitchford/certified-three-item-jrp-gap/releases/download/v0.3.1-candidate/three-item-jrp-gap-and-logistics-v0.3.1-paper.pdf",
  "altPdfUrl": null,
  "altPdfLabel": null,
  "zenodoUrl": "https://doi.org/10.5281/zenodo.22057665",
  "repoUrl": "https://github.com/ipitchford/certified-three-item-jrp-gap",
  "releaseUrl": "https://github.com/ipitchford/certified-three-item-jrp-gap/releases/tag/v0.3.1-candidate",
  "markdownUrl": "https://evidencepress.org/releases/certified-three-item-jrp-gap/index.md",
  "bibtexUrl": "https://evidencepress.org/releases/certified-three-item-jrp-gap/cite.bib",
  "audioUrl": "https://evidencepress.org/assets/audio/certified-three-item-jrp-gap.mp3?v=2c416261a3",
  "imageUrl": "https://evidencepress.org/assets/og/certified-three-item-jrp-gap.png",
  "coverArtUrl": "https://evidencepress.org/assets/art/certified-three-item-jrp-gap.svg?v=7c606b77d2",
  "media": [
    {
      "type": "audio",
      "url": "https://evidencepress.org/assets/audio/certified-three-item-jrp-gap.mp3",
      "name": "Audio briefing — certified three-item JRP gap",
      "description": "Plain-English OpenAI API synthetic-voice summary of the exact three-item certificate, logistics stress-test handoff and assurance boundary; a communication aid, not additional mathematical or operational evidence.",
      "transcriptUrl": "https://evidencepress.org/assets/audio/certified-three-item-jrp-gap.txt"
    }
  ],
  "authors": [
    "Anonymous"
  ],
  "license": "CC0-1.0",
  "status": "unrefereed-candidate",
  "verification": {
    "peerReviewed": false,
    "independentlyReproduced": false,
    "formallyVerified": false,
    "internallyReplayed": true,
    "detail": "Identity-bearing Anonymous unrefereed successor candidate at PASS_WITH_NOTES after bounded Editor closure. Version 0.3.1 passes final-identity ordinary and optimized 21-test same-producer replay, the 61-file generated ledger, final fresh-extraction replay, and public GitHub Actions replay. The immutable GitHub prerelease and Zenodo version DOI expose six byte-identical assets under public readback. The canonical Evidence Press HTML, paper.json, audio, art, graph, operating ledgers and protocol subtree passed exact post-deploy readback after one bounded custom-domain cache-convergence retry. Unaffiliated rerun, independent reimplementation, formal verification, external specialist review, external editorial peer review, operational validation, and impact evidence remain 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://evidencepress.org/releases/certified-three-item-jrp-gap/",
      "note": "The immutable GitHub prerelease, Zenodo version and canonical Evidence Press release passed public identity and byte readback. Availability and byte identity do not establish correctness."
    },
    {
      "dimension": "internalReplay",
      "label": "Internal replay",
      "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?",
      "state": "passed",
      "note": "Final-identity ordinary and optimized same-producer replay pass all 21 tests and the same 61-file generated ledger; final archive extraction is recorded externally after sealing.",
      "evidenceUrl": "https://github.com/ipitchford/certified-three-item-jrp-gap/actions/runs/32576989590"
    },
    {
      "dimension": "independentRerun",
      "label": "Independent rerun",
      "question": "Has someone else run the supplied implementation and obtained the stated result?",
      "state": "not-assessed"
    },
    {
      "dimension": "independentReimplementation",
      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed"
    },
    {
      "dimension": "formalVerification",
      "label": "Formal verification",
      "question": "Is a formalised statement machine-checked, and over which trusted base?",
      "state": "not-assessed"
    },
    {
      "dimension": "specialistReview",
      "label": "Specialist review",
      "question": "Has a domain specialist assessed the argument?",
      "state": "not-assessed"
    },
    {
      "dimension": "editorialPeerReview",
      "label": "Editorial peer review",
      "question": "Has a journal or venue run peer review to a decision?",
      "state": "not-assessed"
    },
    {
      "dimension": "dataEnvironmentReproducibility",
      "label": "Data and environment reproducibility",
      "question": "Are data and computational environment pinned well enough to rebuild?",
      "state": "partial"
    }
  ],
  "provenance": {
    "aiGenerated": true,
    "aiAssisted": true,
    "generatedBy": [
      "AI systems under human direction",
      "OpenAI Codex"
    ],
    "humanRole": "The user set the objective. Ian Pitchford supplied research direction and is the intended maintainer and publisher. The scholarly creator is cited as Anonymous.",
    "disclosure": "AI systems assisted mathematical audit, code hardening, source research, logistics translation, drafting, and replay within one producer-coordinated workflow. These activities are not independent review."
  },
  "attributionBoundary": null,
  "problem": null,
  "orderedProductAverage": null,
  "corrections": [],
  "publicCorrections": [],
  "publicCorrectionIndexes": null,
  "pageStructureVersion": "1.0",
  "pageStructureVariant": "tailored-legacy",
  "pageStructureWaivers": [],
  "recordMaturity": "grandfathered-legacy",
  "metadataProvenance": "Authored before page-structure schema 2.0. Current display metadata may be renderer-derived; unrecorded historical evidence has not been reconstructed.",
  "grandfatheredAtSchemaVersion": "1.3",
  "keywords": [
    "joint replenishment",
    "inventory",
    "exact optimisation",
    "integrality gap",
    "resource constraints",
    "logistics",
    "certificate",
    "unrefereed candidate"
  ],
  "keyResults": [
    "The bundled rational instance has exact gap 7732648297718008589674913778809/6731480890380196637385597557508 = 1.1487291464748205845....",
    "The lower bound is 3.3132 percent above the producer-side unrefereed two-item upper endpoint and propagates to every fixed item count n at least 3, subject to the candidate proof boundary.",
    "The finite closure enumerates 49,981 primitive triples at minimal cutoff S=21 and proves a strict omitted-triple tail margin.",
    "Sixteen exact vertex certificates prove two conservative simultaneous holding-cost inner boxes; the frozen five-policy sets are synthetic regression fixtures only.",
    "The exact oracle is proposed as a logistics stress test and regression benchmark; no field saving or operational impact is claimed."
  ],
  "reviews": [],
  "evidencePackage": "The versioned package contains the 16-page manuscript and Markdown source, three point certificates, sixteen holding-cost vertex certificates, two holding-box reports, exact portfolio reconstruction across 49,981 primitive triples and four boundary regimes per witness, a 61-file generated-artifact ledger, a 143-file package manifest, 21 deterministic tests with mutation and path-containment controls, ordinary and optimized replay, a final fresh-extraction replay, the complete internal five-role review record, response matrix, failed confirmation decision and bounded Editor closure. These are producer-side exact-computation, software and internal editorial records—not unaffiliated independent reproduction, formal verification, external peer review, operational validation or impact evidence.",
  "openProblems": [
    "Obtain an unaffiliated mathematical audit of the finite primitive-triple generator, global tail theorem, active-envelope elimination and holding-box vertex argument.",
    "Independently rerun the exact DOI archive and reimplement the oracle and checker without importing the released package.",
    "Formalize the generator, totality, tail, monotonicity and vertex lemmas in a proof assistant.",
    "Determine the exact three-item independent-cap constant and construct a universal upper certificate over the parameter space.",
    "Extend the executable oracle to directly accept arbitrary coupled resource rows while preserving exact assurance.",
    "Measure the distribution of relaxation gaps in representative eligible logistics triplets and retain null or ineligible cases.",
    "Run preregistered simulation, shadow and field evaluations with service stop rules, implementation costs and a defensible comparator before any savings or impact claim."
  ],
  "relatedWorks": [
    {
      "citation": "Agent collective and I. Pitchford (2026). Exact two-item resource-constrained joint replenishment and its independent-cap relaxation gap. Evidence Press / Zenodo, v1.2.0-candidate.",
      "url": "https://doi.org/10.5281/zenodo.21855894"
    },
    {
      "citation": "Schulz, A. S., and Telha, C. (2024). Integer factorization: Why two-item joint replenishment is hard. Operations Research 72(3), 1192–1202.",
      "url": "https://doi.org/10.1287/opre.2022.2390"
    },
    {
      "citation": "Segev, D. (2025). The continuous-time joint replenishment problem: epsilon-optimal policies via pairwise alignment. Management Science 71(5), 4183–4197.",
      "url": "https://doi.org/10.1287/mnsc.2023.00705"
    },
    {
      "citation": "Segev, D. (2026; online 2025). Improved approximation guarantees for joint replenishment in continuous time. Mathematics of Operations Research 51(2), 1683–1712.",
      "url": "https://doi.org/10.1287/moor.2024.0635"
    },
    {
      "citation": "Cohen-Hillel, T., and Yedidsion, L. (2018). The periodic joint replenishment problem is strongly NP-hard. Mathematics of Operations Research 43(4), 1269–1289.",
      "url": "https://doi.org/10.1287/moor.2017.0904"
    },
    {
      "citation": "Creemers, S., and Stephan, T. (2026). Special Cases of the Joint Replenishment Problem: A Mathematical Analysis. SSRN 6674418.",
      "url": "https://doi.org/10.2139/ssrn.6674418"
    },
    {
      "citation": "Suemitsu, I., Miyashita, N., Hosoda, J., Shimazu, Y., Nishikawa, T., and Izui, K. (2024). Integration of sales, inventory, and transportation resource planning by dynamic-demand joint replenishment problem with time-varying costs. Computers & Industrial Engineering 188, 109922.",
      "url": "https://doi.org/10.1016/j.cie.2024.109922"
    },
    {
      "citation": "Bojinov, I., Simchi-Levi, D., and Zhao, J. (2023). Design and analysis of switchback experiments. Management Science 69(7), 3759–3777.",
      "url": "https://doi.org/10.1287/mnsc.2022.4583"
    }
  ],
  "operatingModel": {
    "version": "1.0",
    "workId": "ep-work:certified-three-item-jrp-gap",
    "attemptIds": [
      "ep-attempt:certified-three-item-jrp-gap"
    ],
    "aims": [
      "science",
      "productivity"
    ],
    "artifactRoles": [
      "research-output",
      "evidence-assessment",
      "method-demonstration",
      "communication"
    ],
    "lineageId": "joint-replenishment-exact-certification-programme",
    "accelerationPrimitives": [
      "certificate-first",
      "structural-compression",
      "regime-stitching",
      "adversarial-controls",
      "research-lineage-reuse",
      "certified-decision-margin",
      "staged-adoption-evaluation",
      "assurance-vector",
      "agent-readable-research-object"
    ],
    "decisionObject": {
      "type": "certificate",
      "description": "An exact rational three-item gap certificate, fixed-item monotonicity implication, exact holding-box comparison, verifier-checked instance-specific candidate-set builder, and staged decision rule for whether a logistics triplet warrants operational evaluation.",
      "scope": "Three-item stationary common-origin periodic policies with rational independent frequency caps; logistics use is diagnostic until omitted constraints and outcomes are evaluated separately."
    },
    "bottleneckTargeted": [
      "discovery",
      "assurance",
      "publication",
      "translation"
    ],
    "semanticBridge": {
      "state": "partial",
      "description": "Common and item-specific model coefficients map to incremental replenishment-event, handling, and deterministic holding costs only after domain validation. The exact oracle maps to a triplet benchmark, not directly to executed orders.",
      "remainingRisks": [
        "Frequency caps may be invalid proxies for pointwise transport or dock capacity.",
        "Stochastic demand, lead times, service, order rounding, minimum quantities, and nonlinear tariffs are outside the certificate.",
        "No representative company dataset or field comparison has been evaluated."
      ]
    },
    "humanJudgmentGates": [
      "Confirm that the three items share an incremental common event and every coefficient has defensible operational semantics.",
      "Keep exact synthetic lower-bound optimism separate from savings or field performance.",
      "Require simulation and shadow evaluation before any order execution.",
      "Require preregistered service stop rules and a defensible comparator before causal or net-value language.",
      "Confirm Anonymous scholarly attribution, licences, immutable identifiers, and release authority before publication."
    ],
    "parentLinks": [
      {
        "relation": "extends-result",
        "workId": null,
        "legacyReleaseSlug": "certified-two-item-jrp",
        "externalUrl": null,
        "inheritedClaim": "The parent supplies the exact two-item interval, resource-to-cap reduction, and certificate-first model boundary.",
        "inheritedAssuranceCeiling": "The parent is an unrefereed producer-side candidate. Reuse is dependency evidence, not independent confirmation."
      }
    ],
    "assuranceTarget": {
      "dimensions": [
        "independentRerun",
        "independentReimplementation",
        "formalVerification",
        "specialistReview",
        "dataEnvironmentReproducibility",
        "semanticValidation",
        "noveltyAssessment",
        "priorityAssessment"
      ],
      "nextAction": "Obtain unaffiliated mathematical review and clean-room replay; for any eligible fitted triplet, regenerate its candidate set and run the preregistered logistics stress-test and shadow protocol.",
      "claimCeiling": "A producer-side unrefereed exact-computation candidate for a bundled three-item lower bound and a proposed logistics evaluation route; not the exact global constant, independent assurance, operational validation, savings, or field impact."
    },
    "impactClaims": [
      {
        "id": "jrp3-operations-no-impact",
        "aim": "productivity",
        "outcome": "Better replenishment plans or lower net logistics cost",
        "setting": "Eligible three-SKU clusters with a shared replenishment event",
        "status": "NO_IMPACT_EVIDENCE",
        "designClass": "none",
        "comparator": "No incumbent-plan comparison has been run.",
        "estimand": "No plan-change rate, service effect, avoided loss, implementation cost, or net value has been estimated.",
        "evidenceRefs": [],
        "registeredDesignRef": null,
        "independentAssessment": null
      },
      {
        "id": "jrp3-science-no-impact",
        "aim": "science",
        "outcome": "More reliable mathematical understanding of multi-item joint-replenishment relaxation gaps",
        "setting": "Research on continuous-time common-origin fixed-interval joint replenishment with rational independent frequency caps",
        "status": "NO_IMPACT_EVIDENCE",
        "designClass": "none",
        "comparator": "No matched conventional research or theorem-review workflow was registered.",
        "estimand": "No effect on discovery time, proof quality, error rate, review effort, method uptake, citation or field outcomes was estimated.",
        "evidenceRefs": [],
        "registeredDesignRef": null,
        "independentAssessment": null
      }
    ]
  }
}