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