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mathematics
information-theory
experimental-design
memory-compression
linear-algebra
quantum-information
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"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": []
}
]
}
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