{ "schemaVersion": "1.6", "slug": "hidden-architecture-exact-signal", "title": "Hidden architecture and the thermodynamic cost of an exact stochastic signal", "shortTitle": "Same signal, less dissipation: hidden architecture matters", "url": "https://evidencepress.org/releases/hidden-architecture-exact-signal/", "oneLine": "The smallest hidden Markov model that reproduces an exactly known two-level signal can overstate its least possible dissipation: a four-state mechanism produces exactly the same signal as every three-state one yet dissipates strictly less, and a sharp floor holds for any hidden size.", "abstract": "Experiments often see only a coarse two-level signal produced by a hidden Markov network of unknown size, and one model-based way to bound its dissipation is to fit the smallest hidden model that reproduces the signal and minimise entropy production over it. This candidate shows by an exact example that the procedure can overstate the least possible dissipation even when the signal is known perfectly. For a binary alternating-renewal family P_q (0 < q < 1), three hidden states are the fewest that realise the signal and the exact three-state entropy minimum is (1−q)log(1/q), attained uniquely by the homogeneous driven ring; for every q an explicit finite four-state model reproduces the same complete stationary observed law with strictly less entropy production. At q = 1/20 exact rational models have certified costs 2.7730766578…, 2.7659977105… (four states) and 2.7469854029… (five states), all below the three-state minimum 2.8459456598…. Over all finite architectures matching only the entrance intensity r, mean complete dwell m and initial dwell density f₀, the exact entropy infimum is 4r√(1−mf₀) artanh√(1−mf₀) when 0 < mf₀ < 1, approached by three-state models and attained by none; for mf₀ ≥ 1 a reversible model attains zero. For the benchmark this floor is about 108 times the one certified in an earlier Evidence Press candidate. The exact four-state and unrestricted minima remain open. AI-assisted, unrefereed candidate; no external peer review, independent reproduction or formal verification is claimed.", "datePublished": "2026-10-28", "dateModified": "2026-10-28", "version": "1.0.0-candidate", "doi": "10.5281/zenodo.23721621", "doiUrl": "https://doi.org/10.5281/zenodo.23721621", "conceptDoi": "10.5281/zenodo.23721620", "pdfUrl": "https://github.com/ipitchford/hidden-architecture-exact-signal/releases/download/v1.0.0-candidate/hidden-architecture-exact-signal-1.0.0-candidate.pdf", "altPdfUrl": "https://zenodo.org/records/23721621/files/hidden-architecture-exact-signal-1.0.0-candidate.pdf?download=1", "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23721621", "repoUrl": "https://github.com/ipitchford/hidden-architecture-exact-signal", "releaseUrl": "https://github.com/ipitchford/hidden-architecture-exact-signal/releases/tag/v1.0.0-candidate", "markdownUrl": "https://evidencepress.org/releases/hidden-architecture-exact-signal/index.md", "bibtexUrl": "https://evidencepress.org/releases/hidden-architecture-exact-signal/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/hidden-architecture-exact-signal.mp3", "imageUrl": "https://evidencepress.org/assets/og/hidden-architecture-exact-signal.png?v=aaeac0da4e", "coverArtUrl": "https://evidencepress.org/assets/art/hidden-architecture-exact-signal.svg?v=1ceb3829bf", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/hidden-architecture-exact-signal.mp3", "name": "Plain-English audio briefing", "description": "Communication aid; not additional research evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/hidden-architecture-exact-signal.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. Every theorem has a written proof; the q = 1/20 witnesses rest on exact rational certificates; the four- and five-state optima are numerical discovery evidence only. Internal AI-assisted review only, including adversarial reviews by a different model and a targeted proof audit. External specialist review, independent reproduction and formal verification have not been 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/23721621", "note": "The versioned research package and manuscript are publicly archived on GitHub and Zenodo; availability does not establish 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": "replay_all.py reruns all eight certificates and checks from a fresh copy of the frozen archive and compares every record and log; six semantic negative controls are rejected; GitHub CI repeats these." }, { "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 has been established." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "Review checks were written within the same producer workflow; no unaffiliated reimplementation." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No proof-assistant formalisation." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "AI-assisted internal review and correctness audits are 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 editorial peer review." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "passed", "note": "Python 3.11 standard library for every certificate, check, replay and control; NumPy, SciPy and Matplotlib only for figures and numerical exploration." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted mathematical research", "AI-assisted internal review (five simulated roles), adversarial reviews by a different model and a targeted proof audit", "Claude Code: publication packaging and release" ], "humanRole": "Publication authority only; no human research contribution inferred.", "reviewStatus": "Internal AI-assisted review, not external peer review." }, "attributionBoundary": null, "problem": null, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Prepared from the final manuscript (dated 28 October 2026, 20 pages), its certificate outputs and the frozen release archive.", "grandfatheredAtSchemaVersion": null, "keywords": [ "stochastic thermodynamics", "entropy production", "hidden Markov models", "phase-type distributions", "thermodynamic inference", "alternating renewal process", "exact certificate" ], "keyResults": [ "Three hidden states are the fewest that produce the signal P_q, and the exact three-state minimum entropy production is (1−q)log(1/q), attained uniquely by the homogeneous driven ring (Theorem 1, proof).", "For every 0 < q < 1 an explicit four-state model reproduces exactly the same complete observed law and dissipates strictly less: V₄(P_q) < V₃(P_q) (Theorem 1, proof).", "At q = 1/20, exact rational models cost 2.7730766578… and 2.7659977105… with four states and 2.7469854029… with five, against 2.8459456598… for any three-state model (Theorem 1, Proposition 6, exact certificates).", "For any hidden size, entropy production exceeds 4r√(1−mf₀) artanh√(1−mf₀) when 0 < mf₀ < 1, with no renewal assumption; this is the exact infimum given (r, m, f₀) and is attained by no finite model (Theorems 2 and 5, proof).", "Hence (2/3)(1−q)log(1/q) ≤ V∞(P_q) ≤ V₄(P_q) < V₃(P_q); at q = 1/20 the floor 1.8973 is about 108 times the earlier certified floor (Corollary 4).", "Numerically the four-state optimum at q = 1/20 is about 2.765996 and a fifth state lowers the cost further (Section 6, numerical only); the exact V₄ and V∞ remain open." ], "reviews": [], "evidencePackage": "Written proofs of every theorem; standard-library exact rational certificates for the q = 1/20 four-state, improved four-state and five-state models (generators, stationary vectors, dwell-transform identities and rational logarithm enclosures); exact and high-precision checks of the three-state parametrisation, the all-q construction and the short-dwell bound; a replay driver; six semantic negative controls; CI.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Ehrich, J. 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