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mathematics
information-theory
experimental-design
memory-compression
linear-algebra
quantum-information
| { | |
| "schema": "EVE-OQAIVAEI-claims-1", | |
| "version": "1.0.0", | |
| "date": "2026-10-20", | |
| "scope": "Finite mathematical theorems and synthetic constructions; no universal superiority or physical validation claim.", | |
| "claims": [ | |
| { | |
| "id": "C01", | |
| "title": "Exact continuation quotient and invariant row space", | |
| "source": "manuscript/chapters/01_foundations.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:finite-quotient", | |
| "number": "1.3", | |
| "printed_page": "2" | |
| }, | |
| { | |
| "label": "thm:linear-closure", | |
| "number": "2.2", | |
| "printed_page": "4" | |
| } | |
| ], | |
| "contract": "Finite states or finite-dimensional linear actions; exact future task values.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Classical realization foundation, reproved.", | |
| "evidence_files": [ | |
| "src/oqaivaei/continuation.py", | |
| "results/continuation_results.json" | |
| ] | |
| }, | |
| { | |
| "id": "C02", | |
| "title": "Minimal supplemental memory for contract enlargement", | |
| "source": "manuscript/chapters/01_foundations.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:finite-upgrade", | |
| "number": "1.5", | |
| "printed_page": "2" | |
| }, | |
| { | |
| "label": "thm:linear-upgrade", | |
| "number": "2.4", | |
| "printed_page": "5" | |
| } | |
| ], | |
| "contract": "Old archive is retained; a finite-alphabet or linear supplement is added.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Constructive formulation; historical priority not claimed.", | |
| "evidence_files": [ | |
| "tests/test_continuation.py" | |
| ] | |
| }, | |
| { | |
| "id": "C03", | |
| "title": "Two reversible interventions activate a full state", | |
| "source": "manuscript/chapters/02_activation.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:activation", | |
| "number": "3.1", | |
| "printed_page": "9" | |
| } | |
| ], | |
| "contract": "Permutation involutions and a coordinate task over a finite-dimensional state.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Explicit synthesis construction; priority unverified.", | |
| "evidence_files": [ | |
| "results/continuation_results.json" | |
| ] | |
| }, | |
| { | |
| "id": "C04", | |
| "title": "Sharp rank/error frontier sqrt(1-k/n)", | |
| "source": "manuscript/chapters/02_activation.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:rank-error", | |
| "number": "3.5", | |
| "printed_page": "11" | |
| } | |
| ], | |
| "contract": "Linear archive of a Euclidean unit-ball state; query-dependent arbitrary decoders.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Uses classical balanced-projection geometry.", | |
| "evidence_files": [ | |
| "results/continuation_results.json" | |
| ] | |
| }, | |
| { | |
| "id": "C05", | |
| "title": "Exact shared-sensor minimax precision", | |
| "source": "manuscript/chapters/03_repair.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:repair-shared", | |
| "number": "4.6", | |
| "printed_page": "17" | |
| } | |
| ], | |
| "contract": "Unbiased exact linear recovery of leakage; whitened unit sensor noise; trace gain budget.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Inverse-information design has classical predecessors; operational synthesis.", | |
| "evidence_files": [ | |
| "results/repair/exact_certificate.json", | |
| "results/repair/optimization.csv" | |
| ] | |
| }, | |
| { | |
| "id": "C06", | |
| "title": "Deterministic announcement and bit tradeoff", | |
| "source": "manuscript/chapters/03_repair.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:repair-partition", | |
| "number": "4.9", | |
| "printed_page": "20" | |
| }, | |
| { | |
| "label": "cor:repair-bits", | |
| "number": "4.10", | |
| "printed_page": "21" | |
| } | |
| ], | |
| "contract": "Action-only message before sensing; exact action at decoding; per-selected-sensor gain budget.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Proposed timing formulation and sharp construction; priority unverified.", | |
| "evidence_files": [ | |
| "results/repair/partitions.csv" | |
| ] | |
| }, | |
| { | |
| "id": "C07", | |
| "title": "Dynamic, biased and robust repair bounds", | |
| "source": "manuscript/chapters/03_repair.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:repair-dynamics", | |
| "number": "5.1", | |
| "printed_page": "22" | |
| }, | |
| { | |
| "label": "prop:repair-bias", | |
| "number": "5.8", | |
| "printed_page": "27" | |
| }, | |
| { | |
| "label": "thm:repair-robust", | |
| "number": "5.9", | |
| "printed_page": "29" | |
| } | |
| ], | |
| "contract": "Predictable switching and conditional centering for stochastic recurrence; stated uncertainty set.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Derived finite-model bounds; classical stability/robustness ingredients.", | |
| "evidence_files": [ | |
| "results/repair/dynamics.csv", | |
| "results/repair/robustness.csv" | |
| ] | |
| }, | |
| { | |
| "id": "C08", | |
| "title": "Exact and dimension-factor one-matrix certificate reuse", | |
| "source": "manuscript/chapters/04_certificates.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:cert-principal", | |
| "number": "6.4", | |
| "printed_page": "33" | |
| }, | |
| { | |
| "label": "thm:cert-dbound", | |
| "number": "6.11", | |
| "printed_page": "37" | |
| } | |
| ], | |
| "contract": "Common positive-semidefinite lower region; determinant-maximizing feasible matrix.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Convex matrix analysis foundation and explicit constructions.", | |
| "evidence_files": [ | |
| "results/certificates/certificate_report.json" | |
| ] | |
| }, | |
| { | |
| "id": "C09", | |
| "title": "Exponential feasible-matrix menu bounds", | |
| "source": "manuscript/chapters/04_certificates.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:cert-exponential", | |
| "number": "7.5", | |
| "printed_page": "42" | |
| }, | |
| { | |
| "label": "thm:cert-hamming", | |
| "number": "7.7", | |
| "printed_page": "44" | |
| } | |
| ], | |
| "contract": "Static menu entries must be feasible; multiplicative Loewner-order coverage. Not a bound on arbitrary symbolic encodings.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Candidate bound construction with classical concentration ingredients; priority unverified.", | |
| "evidence_files": [ | |
| "results/certificates/menu_bounds.json" | |
| ] | |
| }, | |
| { | |
| "id": "C10", | |
| "title": "Quantum continuation and robust algebra memory", | |
| "source": "manuscript/chapters/05_quantum.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:quant_finite", | |
| "number": "8.2", | |
| "printed_page": "51" | |
| }, | |
| { | |
| "label": "thm:quant_profile", | |
| "number": "8.7", | |
| "printed_page": "54" | |
| }, | |
| { | |
| "label": "thm:quant_robust", | |
| "number": "8.8", | |
| "printed_page": "55" | |
| } | |
| ], | |
| "contract": "Finite-dimensional quantum channels; common restoration and stated quadratic calibration for algebra conclusions.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Quantum compression foundations acknowledged; quantitative synthesis.", | |
| "evidence_files": [ | |
| "results/quantum_results.json" | |
| ] | |
| }, | |
| { | |
| "id": "C11", | |
| "title": "Response-only/common-restoration separation", | |
| "source": "manuscript/chapters/05_quantum.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:quant_mub", | |
| "number": "8.11", | |
| "printed_page": "58" | |
| }, | |
| { | |
| "label": "thm:quant_response", | |
| "number": "8.12", | |
| "printed_page": "59" | |
| } | |
| ], | |
| "contract": "Two mutually unbiased bases and the stated projector-error metrics; different output contracts.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Established related quantum information literature credited; no priority claim.", | |
| "evidence_files": [ | |
| "results/quantum_results.json" | |
| ] | |
| }, | |
| { | |
| "id": "C12", | |
| "title": "Joint archive/sensor endpoint optima", | |
| "source": "manuscript/chapters/06_codesign.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:codesign-main", | |
| "number": "9.1", | |
| "printed_page": "65" | |
| } | |
| ], | |
| "contract": "Exact rank-p hidden archive, q coordinates, freely designed linear sensing, isotropic trace gain B.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Classical frame geometry; joint operational interpretation.", | |
| "evidence_files": [ | |
| "results/codesign_results.json" | |
| ] | |
| }, | |
| { | |
| "id": "C13", | |
| "title": "Announcement lower bound and divisible optima", | |
| "source": "manuscript/chapters/06_codesign.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:codesign-partition-lower", | |
| "number": "9.3", | |
| "printed_page": "66" | |
| }, | |
| { | |
| "label": "thm:codesign-blocks", | |
| "number": "9.4", | |
| "printed_page": "67" | |
| } | |
| ], | |
| "contract": "At most k action cells; archive and selected sensor jointly designed. Exactness restricted to stated integer families.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Proposed synthesis; historical priority unverified.", | |
| "evidence_files": [ | |
| "results/codesign_results.json" | |
| ] | |
| }, | |
| { | |
| "id": "C14", | |
| "title": "Exact nondivisible optimum and nonblock advantage", | |
| "source": "manuscript/chapters/06_codesign_nondivisible.tex", | |
| "locations": [ | |
| { | |
| "label": "thm:codesign-codim-one", | |
| "number": "9.5", | |
| "printed_page": "69" | |
| } | |
| ], | |
| "contract": "q=r+1>=3; one stored linear coordinate; at most r deterministic cells; unbiased repair and gain B.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Most sharply isolated candidate contribution; bounded prior-art search does not certify novelty.", | |
| "evidence_files": [ | |
| "results/announcement_family.json" | |
| ] | |
| }, | |
| { | |
| "id": "C15", | |
| "title": "Vertex reduction for robust exact continuation", | |
| "source": "manuscript/chapters/06_synthesis.tex", | |
| "locations": [ | |
| { | |
| "label": "prop:vertex-closure", | |
| "number": "10.1", | |
| "printed_page": "75" | |
| } | |
| ], | |
| "contract": "Independent transitions selected from finite convex matrix families; transition identity known when applying reduced maps.", | |
| "proof_status": "Complete written proof under stated hypotheses; internally reviewed, not proof-assistant verified.", | |
| "novelty_status": "Elementary extension; historical priority not claimed.", | |
| "evidence_files": [] | |
| } | |
| ] | |
| } | |