{
  "schemaVersion": "1.6",
  "slug": "debt-disclosure-bounds",
  "title": "What Public Debt Statistics Establish About Interest-Rate Exposure",
  "shortTitle": "Same average, different exposure",
  "url": "https://evidencepress.org/releases/debt-disclosure-bounds/",
  "oneLine": "Exact model bounds show what debt summaries determine—and which missing repayment and funding details prevent a fiscal interpretation.",
  "abstract": "Published totals and average maturities can leave very different interest-rate exposures compatible with the same debt statistics. This methods candidate applies established moment and linear-programming techniques to compute sharp bounds under a declared refinancing model, with 4,576 exact endpoint certificates. It characterises when additional annual disclosures identify costs, verifies 105 gilt records against an official dated export, and reconciles a historical APF accounting example. Synthetic holdings-runoff scenarios remain distinct from actual consolidated fiscal exposure; neither a complete UK forecast nor measured policy benefit is established.",
  "datePublished": "2026-10-13",
  "dateModified": "2026-10-13",
  "version": "1.1.0-candidate",
  "doi": "10.5281/zenodo.23337976",
  "doiUrl": "https://doi.org/10.5281/zenodo.23337976",
  "conceptDoi": "10.5281/zenodo.23337975",
  "pdfUrl": "https://github.com/ipitchford/debt-disclosure-bounds/releases/download/v1.1.0-candidate/debt-disclosure-bounds-v1.1.0-candidate.pdf",
  "altPdfUrl": "https://zenodo.org/records/23337976/files/debt-disclosure-bounds-v1.1.0-candidate.pdf?download=1",
  "altPdfLabel": null,
  "zenodoUrl": "https://zenodo.org/records/23337976",
  "repoUrl": "https://github.com/ipitchford/debt-disclosure-bounds",
  "releaseUrl": "https://github.com/ipitchford/debt-disclosure-bounds/releases/tag/v1.1.0-candidate",
  "markdownUrl": "https://evidencepress.org/releases/debt-disclosure-bounds/index.md",
  "bibtexUrl": "https://evidencepress.org/releases/debt-disclosure-bounds/cite.bib",
  "audioUrl": "https://evidencepress.org/assets/audio/debt-disclosure-bounds.mp3",
  "imageUrl": "https://evidencepress.org/assets/og/debt-disclosure-bounds.png?v=ff197737f1",
  "coverArtUrl": "https://evidencepress.org/assets/art/debt-disclosure-bounds.svg?v=9b06c0fdf7",
  "media": [
    {
      "type": "audio",
      "url": "https://evidencepress.org/assets/audio/debt-disclosure-bounds.mp3",
      "name": "Audio briefing — Same average, different exposure",
      "description": "Synthetic explanation of the methods and accounting boundary; not additional scientific evidence.",
      "transcriptUrl": "https://evidencepress.org/assets/audio/debt-disclosure-bounds.txt"
    }
  ],
  "authors": [
    "Anonymous"
  ],
  "license": "CC0-1.0",
  "status": "unrefereed-candidate",
  "verification": {
    "peerReviewed": false,
    "independentlyReproduced": false,
    "formallyVerified": false,
    "internallyReplayed": true,
    "detail": "Unrefereed, AI-assisted methods candidate. Internal exact checking is not independent reproduction, formal verification or external peer review. Bounds apply to declared models, not a complete fiscal forecast; no policy impact or priority is established."
  },
  "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/23337976",
      "note": "Public GitHub and Zenodo archive, manuscript and checksum files match local frozen assets by full downloads. This establishes availability, not correctness or peer review."
    },
    {
      "dimension": "internalReplay",
      "label": "Internal replay",
      "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?",
      "state": "passed",
      "note": "All 4,576 recorded endpoint certificates linked to their reported values in producer-side exact checking. This checks declared programmes, not institutional validity.",
      "evidenceUrl": "https://github.com/ipitchford/debt-disclosure-bounds/blob/v1.1.0-candidate/REPLAY_RECEIPT.md"
    },
    {
      "dimension": "independentRerun",
      "label": "Independent rerun",
      "question": "Has someone else run the supplied implementation and obtained the stated result?",
      "state": "not-assessed",
      "note": "Producer-coordinated checks do not establish unaffiliated reproduction."
    },
    {
      "dimension": "independentReimplementation",
      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed",
      "note": "A separate evaluator shares the producer workflow and model conventions."
    },
    {
      "dimension": "formalVerification",
      "label": "Formal verification",
      "question": "Is a formalised statement machine-checked, and over which trusted base?",
      "state": "not-assessed",
      "note": "No end-to-end proof-assistant formalisation."
    },
    {
      "dimension": "specialistReview",
      "label": "Specialist review",
      "question": "Has a domain specialist assessed the argument?",
      "state": "not-assessed",
      "note": "Internal AI-assisted review is 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 external journal editorial peer review established."
    },
    {
      "dimension": "dataEnvironmentReproducibility",
      "label": "Data and environment reproducibility",
      "question": "Are data and computational environment pinned well enough to rebuild?",
      "state": "partial",
      "note": "Exact model snapshots support offline certificate checking; full source reconstruction requires third-party inputs obtained under their own terms. Producer-side source checks are distinct from independent reproduction.",
      "evidenceUrl": "https://github.com/ipitchford/debt-disclosure-bounds/blob/v1.1.0-candidate/data/EXTERNAL_INPUTS.md"
    }
  ],
  "provenance": {
    "aiGenerated": true,
    "aiAssisted": true,
    "generatedBy": [
      "AI-assisted research workflow",
      "OpenAI Codex: review action, accounting/source checks, bounded revisions and publication preparation"
    ],
    "humanRole": "Publication authority only; no human research contribution asserted.",
    "reviewStatus": "Internal AI-assisted review only; external peer review and unaffiliated reproduction not established."
  },
  "attributionBoundary": null,
  "problem": {
    "name": "What do aggregate debt disclosures identify about a specified interest-rate shock?",
    "url": "https://github.com/ipitchford/debt-disclosure-bounds"
  },
  "orderedProductAverage": null,
  "corrections": [],
  "publicCorrections": [],
  "publicCorrectionIndexes": null,
  "pageStructureVersion": "2.0",
  "pageStructureVariant": "canonical-theorem",
  "pageStructureWaivers": [],
  "recordMaturity": "current",
  "metadataProvenance": "Supplied debt-disclosure bundle and review, revised 13 October 2026; exact frozen archive and public-provider identities verified. Research assurance and subsequent canonical site delivery are recorded separately. Earlier discovery effort is not reconstructed.",
  "grandfatheredAtSchemaVersion": null,
  "keywords": [
    "public debt",
    "interest-rate exposure",
    "partial identification",
    "maturity disclosure",
    "linear programming",
    "exact certificates",
    "APF accounting"
  ],
  "keyResults": [
    "A finite breakpoint programme and rational primal-dual certificates bound the stated maturity-ledger model exactly on its declared daily grid.",
    "Identification is constancy over the full feasible set; total and mean maturity alone need not determine even first-year cost.",
    "Annual amounts and first moments identify the specified annual windows; disclosure vectors and their incremental ranks are recorded explicitly.",
    "A February 2026 historical APF account reconciles, while October holdings and loan snapshots do not identify a matched future net-funding path."
  ],
  "reviews": [],
  "evidencePackage": "Written model and reduction arguments; 4,576 exact endpoint certificates replayed in normal and optimized Python from the frozen archive and linked to reported values; source reconstruction checked internally; 105 gilt rows matched to the official dated DMO export. Separate historical accounting and recursive-financing checks. No unaffiliated reproduction or fiscal-model validation asserted.",
  "openProblems": [],
  "mathObjects": [],
  "relatedWorks": [
    {
      "citation": "Barrett and Johns (2024), Parameterizing debt maturity. Parametric maturity modelling; the present disclosure bounds answer a different question.",
      "url": "https://doi.org/10.1111/jmcb.13116",
      "doi": "10.1111/jmcb.13116"
    },
    {
      "citation": "Bank of England APF Annual Report and Accounts 2025/26. Source of the dated February accounting reconciliation.",
      "url": "https://www.bankofengland.co.uk/-/media/boe/files/asset-purchase-facility/2026/apf-annual-report-2025-26.pdf",
      "doi": null
    },
    {
      "citation": "Bank of England weekly report, 7 October 2026. Dated APF loan observation, not a full-month or future-path account.",
      "url": "https://www.bankofengland.co.uk/weekly-report/2026/7-october-2026",
      "doi": null
    },
    {
      "citation": "UK Debt Management Office, Gilts in Issue. Official dated export used for the 105-row computational-field comparison.",
      "url": "https://www.dmo.gov.uk/data/pdfdatareport?reportCode=D1A",
      "doi": null
    },
    {
      "citation": "Evidence Press, Stocks Are Not Flows. A thematic antecedent on accounting and identification, not independent confirmation.",
      "url": "https://evidencepress.org/releases/stocks-are-not-flows/",
      "doi": null
    }
  ],
  "claimAssurance": null,
  "operatingModel": {
    "version": "1.0",
    "workId": "ep-work:debt-disclosure-bounds",
    "attemptIds": [
      "ep-attempt:debt-disclosure-bounds-publication"
    ],
    "aims": [
      "science",
      "policy"
    ],
    "artifactRoles": [
      "research-output",
      "method-demonstration",
      "evidence-assessment",
      "communication"
    ],
    "lineageId": null,
    "accelerationPrimitives": [
      "identification-gate",
      "partial-identification",
      "certificate-first",
      "adversarial-controls",
      "assurance-vector",
      "agent-readable-research-object"
    ],
    "decisionObject": {
      "type": "bound",
      "description": "Sharp model exposure bounds, disclosure diagnostics and an explicit accounting stop boundary.",
      "scope": "Declared debt ledgers, daily-grid refinancing kernels and specified accounting conventions; not a national fiscal forecast."
    },
    "bottleneckTargeted": [
      "assurance",
      "publication"
    ],
    "semanticBridge": {
      "state": "partial",
      "description": "The finite programme represents the declared refinancing model. Official gilt-field comparison and a dated accounting reconciliation support specific input bridges, while actual APF future net funding remains unidentified.",
      "remainingRisks": [
        "Actual accounting and model perimeters can differ.",
        "UK bill timing is reconstructed; source-to-ledger checking remains producer coordinated.",
        "Synthetic IPP-funded scenarios do not validate consolidated fiscal exposure.",
        "External assurance, exhaustive originality assessment and downstream benefit remain absent."
      ]
    },
    "humanJudgmentGates": [
      "External scrutiny of accounting definitions, reporting burden and any policy use remains necessary; publication is user-authorised."
    ],
    "parentLinks": [],
    "assuranceTarget": {
      "dimensions": [
        "independentRerun",
        "specialistReview",
        "semanticValidation"
      ],
      "nextAction": "Reproduce the source-to-model bridge outside the producer workflow and reconcile a matched actual funding path before fiscal interpretation.",
      "claimCeiling": "Unrefereed methods application with exact encoded-model certificates, not verified national fiscal exposure or measured policy benefit."
    },
    "impactClaims": [
      {
        "id": "debt-disclosure-bounds-science-no-impact",
        "aim": "science",
        "outcome": "Reusable exact disclosure-bound methods",
        "setting": "Producer-coordinated model application",
        "status": "NO_IMPACT_EVIDENCE",
        "designClass": "none",
        "comparator": "None.",
        "estimand": "No measured research acceleration or downstream scientific benefit.",
        "evidenceRefs": [],
        "registeredDesignRef": null,
        "independentAssessment": null
      },
      {
        "id": "debt-disclosure-bounds-policy-no-impact",
        "aim": "policy",
        "outcome": "More explicit debt-disclosure information requirements",
        "setting": "Declared models and dated accounting examples",
        "status": "NO_IMPACT_EVIDENCE",
        "designClass": "none",
        "comparator": "None.",
        "estimand": "No measured forecast improvement, reporting adoption or policy effect.",
        "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:debt-disclosure-bounds-publication",
        "status": "result-ready",
        "resultClass": "positive",
        "metrics": {
          "schemaVersion": "1.0",
          "measurementScope": "assurance-through-publication",
          "scopeBoundary": "Remaining publication from site registration; earlier review and extensions left-censored.",
          "forecast": {
            "frozenAt": "2026-10-13T10:06:42.482Z",
            "procedureClass": "full-candidate",
            "targetOutcome": "Final candidate archive and complete canonical Evidence Press publication",
            "expectedActiveMinutes": 150,
            "plausibleLowMinutes": 100,
            "plausibleHighMinutes": 240,
            "expectedUnattendedWaitMinutes": 40,
            "referenceClass": {
              "label": "Remaining full-candidate publication",
              "sampleSize": 0,
              "basis": "Procedural forecast, not measured benchmark"
            },
            "fermiComponents": [
              {
                "component": "Final model, source and archive checks",
                "count": 1,
                "lowMinutesPerUnit": 25,
                "centralMinutesPerUnit": 40,
                "highMinutesPerUnit": 70,
                "basis": "Revised debt-disclosure methods candidate; final rights-safe archive checking pending."
              },
              {
                "component": "Provider publication and byte verification",
                "count": 1,
                "lowMinutesPerUnit": 15,
                "centralMinutesPerUnit": 25,
                "highMinutesPerUnit": 40,
                "basis": "Small archive but provider latency uncertain."
              },
              {
                "component": "Page, media and presentation QA",
                "count": 1,
                "lowMinutesPerUnit": 25,
                "centralMinutesPerUnit": 35,
                "highMinutesPerUnit": 55,
                "basis": "New release requires banner, thumbnail and audio."
              },
              {
                "component": "Both guarded deployment cycles and closeout",
                "count": 1,
                "lowMinutesPerUnit": 35,
                "centralMinutesPerUnit": 50,
                "highMinutesPerUnit": 75,
                "basis": "Required CI, preservation, canonical readback and post-readback ledger cycle."
              }
            ],
            "probabilityPositiveSignal": 0.9,
            "probabilityTargetClosure": 0.8,
            "probabilityHorizonMinutes": 480,
            "assumptions": [
              "No material proof gap and provider, CI and deployment routes remain available."
            ],
            "reforecastTriggers": [
              "A substantive integrity finding, provider failure or CI failure."
            ],
            "stopRule": "No hard cap; complete mandatory gates or report a precise blocker."
          },
          "outcome": null
        },
        "missingnessReason": null
      }
    ]
  }
}