{ "schemaVersion": "1.6", "slug": "prophet-over-time-limit", "title": "The long-run price of committing before seeing the future", "shortTitle": "Rent today, or commit for the season?", "url": "https://evidencepress.org/releases/prophet-over-time-limit/", "oneLine": "An unrefereed candidate proves a limiting guarantee for i.i.d. prophet inequalities over time, with certified bounds below the inverse golden ratio.", "abstract": "An online decision maker rents one resource over a finite horizon, observing independent nonnegative offers from a known common distribution with finite positive mean. The optimal expected reward is compared with a prophet who knows every offer. This candidate proves that the worst-case ratio converges as the horizon grows, identifies the limit with a continuum minimax value, and shows that deterministic threshold schedules approach that value arbitrarily closely. Explicit Arb-certified witnesses give 0.60922 <= gamma* <= 0.609816, strictly below the inverse golden ratio. No exact constant or attainment by a bounded schedule is established. Atomic distributions may require randomised threshold-tie handling. A separate million-period instance gives ratio at most 0.6123450.", "datePublished": "2026-10-17", "dateModified": "2026-10-17", "version": "0.1.0-candidate", "doi": "10.5281/zenodo.23442742", "doiUrl": "https://doi.org/10.5281/zenodo.23442742", "conceptDoi": "10.5281/zenodo.23442741", "pdfUrl": "https://zenodo.org/records/23442742/files/paper.pdf", "altPdfUrl": null, "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23442742", "repoUrl": "https://github.com/ipitchford/prophet-over-time-limit", "releaseUrl": "https://github.com/ipitchford/prophet-over-time-limit/releases/tag/v0.1.0-candidate", "markdownUrl": "https://evidencepress.org/releases/prophet-over-time-limit/index.md", "bibtexUrl": "https://evidencepress.org/releases/prophet-over-time-limit/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/prophet-over-time-limit.mp3", "imageUrl": "https://evidencepress.org/assets/og/prophet-over-time-limit.png?v=cc8e688da7", "coverArtUrl": "https://evidencepress.org/assets/art/prophet-over-time-limit.svg?v=b99cec78a0", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/prophet-over-time-limit.mp3", "name": "Plain-English audio briefing", "description": "Communication aid; not additional research evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/prophet-over-time-limit.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed AI-assisted mathematical candidate. No external peer review, unaffiliated reproduction, formal verification or exhaustive priority clearance 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/23442742", "note": "Versioned GitHub and public Zenodo record 23442742 verified by full downloads of the archive, manuscript and checksum manifest against frozen local hashes." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Final archive clean-extraction normal and optimized certifiers passed, including five excessive-target rejection controls. CI passed at the tagged payload. Numerical replay does not certify the universal written proof." }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "No unaffiliated rerun established." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "Coordinated producer checking is not independent reimplementation." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "Written proofs and ball arithmetic are not proof-assistant verification." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "Internal AI scrutiny 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 journal 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 rational witness inputs, pinned python-flint 0.9.0, checking code, replay instructions and normal/optimized receipts are included. Unaffiliated reproduction remains unestablished." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "OpenAI Codex coordinated mathematical development, checking and drafting" ], "humanRole": "Publication authority only; no human research contribution inferred from account ownership.", "reviewStatus": "Internal AI-assisted proof and source checking; not external peer review or independent reproduction." }, "attributionBoundary": null, "problem": null, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Prepared from the integrated manuscript and frozen version 0.1.0-candidate archive, SHA-256 06e55af3c307d46d2f792522b26cecc5a4444824f273617d0073208c94d31048. Research repository payload f5d4e7181e3fc5253465fa90539ae76b7bb80347. Numerical and analytic assurance remain distinct.", "grandfatheredAtSchemaVersion": null, "keywords": [ "prophet inequalities over time", "online commitment", "iid arrivals", "continuum minimax", "deterministic thresholds", "certified bounds" ], "keyResults": [ "The worst-case optimal-online-to-prophet ratio has a limit as the number of periods tends to infinity.", "The limit equals a continuum profile infimum and a cumulative-coverage minimax value.", "Explicit witnesses certify 0.60922 <= gamma* <= 0.609816 < 1/phi.", "Deterministic threshold schedules approach the limit; attainment by one bounded schedule is not proved, and atomic laws may require randomised ties.", "A separate finite witness at one million periods certifies a ratio at most 0.6123450; it is not the asymptotic upper bound." ], "reviews": [], "evidencePackage": "Integrated written analytic arguments and explicit strategy/profile witnesses checked using Arb ball arithmetic. Normal and optimized replay from clean archive extraction passed, with five excessive targets rejected; GitHub CI also passed. Numerical replay certifies the stated witness inequalities, not the complete analytic proof.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Abels, Pitschmann and Schmand, Prophet Inequalities over Time: the model, optimal-online recurrence and inverse-golden-ratio upper bound.", "url": "https://arxiv.org/abs/2211.10471v2", "doi": "10.48550/arXiv.2211.10471" }, { "citation": "Perez-Salazar and Verdugo, i.i.d. prophet inequalities over time: quantile strategies and finite-horizon convex characterisation.", "url": "https://arxiv.org/abs/2408.11224v1", "doi": "10.48550/arXiv.2408.11224" }, { "citation": "Fan, Minimax theorems, Proceedings of the National Academy of Sciences 39 (1953), 42–47: minimax methodology.", "url": "https://doi.org/10.1073/pnas.39.1.42", "doi": "10.1073/pnas.39.1.42" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:prophet-over-time-limit", "attemptIds": [ "ep-attempt:prophet-over-time-limit-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "communication" ], "lineageId": null, "accelerationPrimitives": [ "certificate-first", "structural-compression", "adversarial-controls", "assurance-vector" ], "decisionObject": { "type": "bound", "description": "A long-horizon worst-case rental guarantee with explicit limiting and finite-horizon witnesses.", "scope": "Known iid nonnegative law with finite positive mean; one resource rented over time, compared with the clairvoyant optimum." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "Tail-quantile coverage and two-way finite-horizon transfer connect threshold strategies and value profiles to the limiting worst-case ratio.", "remainingRisks": [ "Analytic transfer and minimax assumptions require mathematical scrutiny.", "Arb replay certifies supplied witnesses, not the complete analytic proof.", "No exact constant, attained bounded schedule or practically useful general convergence rate is claimed." ] }, "humanJudgmentGates": [ "The user authorises publication; no scientific endorsement is inferred.", "Development-independent proof, novelty and priority scrutiny remain open." ], "parentLinks": [], "assuranceTarget": { "dimensions": [ "availability", "internalReplay", "semanticValidation", "specialistReview", "noveltyAssessment" ], "nextAction": "Seek development-independent scrutiny of the written proof and certificate-to-theorem connection; retain the archived producer checks, bounded prior-art comparison and external-assurance limits.", "claimCeiling": "Unrefereed mathematical candidate with internal producer checks; no formal verification, external peer review, priority clearance or measured impact." }, "impactClaims": [ { "id": "prophet-over-time-limit-no-impact", "aim": "science", "outcome": "Inspectable limiting characterisation and certified rental-ratio bounds", "setting": "Coordinated AI-assisted mathematical research", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "None registered.", "estimand": "No causal research-speed or real-world decision improvement estimated.", "evidenceRefs": [], "registeredDesignRef": null, "independentAssessment": null } ] }, "researchMetrics": { "schemaVersion": "1.0", "policyUrl": "https://evidencepress.org/api/research-metrics-policy.json", "outcomePolicyUrl": "https://evidencepress.org/api/v2/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:prophet-over-time-limit-publication", "status": "published", "resultClass": "positive", "metrics": { "schemaVersion": "1.0", "measurementScope": "assurance-through-publication", "scopeBoundary": "Only remaining publication from this registration; all earlier research and preparation are left-censored.", "forecast": { "frozenAt": "2026-10-16T01:30:41.638Z", "procedureClass": "remaining-candidate-site-and-archive-delivery", "targetOutcome": "Accurately scoped archived candidate and canonical site readback, if scientific and publication gates pass.", "expectedActiveMinutes": 60, "plausibleLowMinutes": 30, "plausibleHighMinutes": 120, "expectedUnattendedWaitMinutes": 20, "referenceClass": { "label": "Single mathematical candidate remaining publication", "sampleSize": 0, "basis": "Prospective planning judgement, not empirical calibration." }, "fermiComponents": [ { "component": "Content, metadata and media integration", "count": 1, "lowMinutesPerUnit": 15, "centralMinutesPerUnit": 30, "highMinutesPerUnit": 60, "basis": "One new release with layered explanation and pending identities." }, { "component": "Archive parity, guarded site delivery and readback", "count": 1, "lowMinutesPerUnit": 15, "centralMinutesPerUnit": 30, "highMinutesPerUnit": 60, "basis": "Mandatory exact-byte and canonical checks; external wait separate." } ], "probabilityPositiveSignal": 0.9, "probabilityTargetClosure": 0.8, "probabilityHorizonMinutes": 240, "assumptions": [ "No unresolved mathematical defect; configured providers and required CI remain available." ], "reforecastTriggers": [ "Scientific revision, provider failure or preservation mismatch." ], "stopRule": "Do not weaken gates or promote assurance to meet a forecast." }, "outcome": { "status": "unavailable", "policyVersion": "2.0", "recordedAt": "2026-10-17T22:29:51.943Z", "reason": "The publication target is evidenced by dated delivery observations, but complete scoped active effort, wait, rework and aggregate runtime telemetry was not instrumented. Earlier work remains left-censored. Individual tool receipts do not supply complete effort totals; no retrospective estimates or calibration update are made.", "missingFields": [ { "field": "calendarElapsedMinutes", "reason": "Observed opening and readback clocks are retained separately; wall time is not active effort and no numeric metrics series is emitted." }, { "field": "activeAgentMinutes", "reason": "The complete scoped activeAgentMinutes counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "activeHumanMinutes", "reason": "The complete scoped activeHumanMinutes counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "computeMinutes", "reason": "The complete scoped computeMinutes counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "unattendedWaitMinutes", "reason": "The complete scoped unattendedWaitMinutes counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "blockedMinutes", "reason": "The complete scoped blockedMinutes counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "reworkMinutes", "reason": "The complete scoped reworkMinutes counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "agentRuns", "reason": "The complete scoped agentRuns counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "maxParallelAgents", "reason": "The complete scoped maxParallelAgents counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "modelTurns", "reason": "The complete scoped modelTurns counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "deduplicatedModelTokens", "reason": "The complete scoped deduplicatedModelTokens counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "uncachedInputTokens", "reason": "The complete scoped uncachedInputTokens counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "researchCycles", "reason": "The complete scoped researchCycles counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "falsificationGatesRun", "reason": "The complete scoped falsificationGatesRun counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "candidateArchitecturesTested", "reason": "The complete scoped candidateArchitecturesTested counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "candidateArchitecturesRejected", "reason": "The complete scoped candidateArchitecturesRejected counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "substantiveReviewRounds", "reason": "The complete scoped substantiveReviewRounds counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "p0Findings", "reason": "The complete scoped p0Findings counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "p1Findings", "reason": "The complete scoped p1Findings counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "prepublicationClaimCorrections", "reason": "The complete scoped prepublicationClaimCorrections counter is unavailable; no aggregate is inferred from elapsed time, messages or selected tool receipts." }, { "field": "resultState", "reason": "Confirmed candidate delivery is recorded in statusHistory; no calibrated outcome metric is emitted with incomplete telemetry." }, { "field": "positiveSignalObserved", "reason": "Confirmed candidate delivery is recorded in statusHistory; no calibrated outcome metric is emitted with incomplete telemetry." }, { "field": "targetReached", "reason": "Confirmed candidate delivery is recorded in statusHistory; no calibrated outcome metric is emitted with incomplete telemetry." }, { "field": "forecastErrorMinutes", "reason": "Unmeasured active effort prevents comparison with the frozen active-time forecast." }, { "field": "forecastRatio", "reason": "Unmeasured active effort prevents comparison with the frozen active-time forecast." }, { "field": "withinForecastInterval", "reason": "Unmeasured active effort prevents comparison with the frozen active-time forecast." } ], "calibration": null } }, "missingnessReason": null } ] } }