| { |
| "schema_version": "1.0", |
| "release_version": "3.0.0", |
| "date": "2026-10-08", |
| "research_program": "VELORYN", |
| "artifact_type": "Mathematical research report, executable finite checks and proposed controller physics; not a trained ML model.", |
| "path_convention": "All artifact and evidence paths are relative to the public repository root; research/ contains the unpacked v3.0.0 research bundle.", |
| "basis": { |
| "report": "research/Avenyra_Geometric_Memory_Physics.pdf", |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "status": "research/STATUS.json", |
| "report_pages": 56, |
| "source_sha256": "a3e9a40c61ad64af5a5e18725ddfa11821b1bc6c9685cd2afad7ba9b432cf689", |
| "status_sha256": "a6730658180526d9e07b228696d63d7f6521be841c07b8989a24c184afb7173e", |
| "supplied_input": "research/source/Avenyra_Area_Feedback_v1.0.0.pdf" |
| }, |
| "verification_notice": { |
| "review_level": "Six specialist AI agents plus lead; AI cross-audits only.", |
| "external_human_review": false, |
| "external_peer_review": false, |
| "proof_assistant_checked": false, |
| "laboratory_measurements": false, |
| "fabricated_prototype": false, |
| "finite_checks_are_proofs": false, |
| "interpretation": "The report contains scoped analytic arguments claimed complete. Finite exact/numerical checks support those arguments, and do not formally certify them." |
| }, |
| "release_claim_policy": { |
| "appropriate": [ |
| "We derive the stated scoped model theorem.", |
| "Exact finite identifiability under declared data assumptions.", |
| "Candidate model-specific contribution; priority unverified.", |
| "Proposed powered controller and conventional passive readout." |
| ], |
| "not_supported": [ |
| "Established fundamental physics breakthrough.", |
| "Externally peer-reviewed or proof-assistant-certified.", |
| "New quantum mechanics, quantum advantage or noiseless learning of an unknown signal.", |
| "A universal energy per area, replacement second law or cosmological arrow.", |
| "Full reachability classification or stable noisy tomography.", |
| "A generic no-Hamiltonian or no-quantization theorem." |
| ] |
| }, |
| "claims": [ |
| { |
| "id": "AVGMP-I001", |
| "title": "Supplied Avenyra finite-rule inputs", |
| "kind": "inherited_input", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": null, |
| "section_title": "What is inherited and what is added", |
| "statement_label": null, |
| "statement_name": null, |
| "statement_number": null, |
| "pdf_page_anchor": null, |
| "equation_labels": [] |
| }, |
| "statement": "The pre-gated reachability, kernel transport, rank schedules, exterior-volume order and skew spectral reduction are credited as inputs from the supplied Avenyra manuscript.", |
| "assumptions": [ |
| "Real finite-dimensional skew register; exact own-area update and Aa=0 gate.", |
| "The source manuscript is the supplied research input." |
| ], |
| "proof_status": "Input claims from the supplied manuscript; no external proof certification is asserted.", |
| "evidence": [ |
| { |
| "path": "research/source/Avenyra_Area_Feedback_v1.0.0.pdf", |
| "kind": "supplied_source", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "This release does not certify the source manuscript or establish its literature priority." |
| ], |
| "priority": { |
| "status": "supplied_manuscript_input_priority_not_certified", |
| "established_ingredients": [], |
| "candidate_scope": null |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-T001", |
| "title": "Gate timing budget and adjoint inverse", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": null, |
| "section_title": "Gate timing controls spectrum, rank, and reversal", |
| "statement_label": "thm:budget", |
| "statement_name": "Exact timing budget and adjoint gate", |
| "statement_number": "3.1", |
| "pdf_page_anchor": 5, |
| "equation_labels": [ |
| "eq:theta", |
| "eq:timing-budget" |
| ] |
| }, |
| "statement": "For (A+theta x wedge a)a=0, the squared memory-norm increment is (1-2theta)D; the algebraic inverse uses gate 1-theta.", |
| "assumptions": [ |
| "Real skew A and Euclidean metric.", |
| "D=|x|²|a|²-(x dot a)²; exact finite update." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/verify_physics.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/results/verification.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v1/arrow_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "D is dimensionless geometry, not thermodynamic heat.", |
| "An adjoint inverse is a different gate policy except at the midpoint or zero area." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Skew rank updates and finite inverse algebra" |
| ], |
| "candidate_scope": "Timing-dependent own-area classification" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-T002", |
| "title": "Congruence, midpoint spectrum and endpoint rank", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": null, |
| "section_title": "Gate timing controls spectrum, rank, and reversal", |
| "statement_label": "thm:congruence", |
| "statement_name": "Congruence and midpoint isospectrality", |
| "statement_number": "3.2", |
| "pdf_page_anchor": 5, |
| "equation_labels": [ |
| "eq:congruence", |
| "eq:pfaffian" |
| ] |
| }, |
| "statement": "Nonzero theta legal strokes admit an exact congruence; midpoint updates are orthogonal conjugations. Rank and ordered skew-frequency classifications follow, with pre/post endpoint exceptions and a Pfaffian orientation factor.", |
| "assumptions": [ |
| "Exact theta gate; nonzero stroke for its normalized projector.", |
| "Theta=0 and theta=1 treated separately; full-rank even dimension for Pfaffian claims." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/verify_physics.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/results/verification.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v1/arrow_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Singular values do not determine orientation or full reachability.", |
| "The congruence formula must not be substituted at theta=0." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Congruence, singular-value inequalities and Pfaffian transformation" |
| ], |
| "candidate_scope": "Complete finite gate-timing specialization" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-T003", |
| "title": "Sharp full-rank impulse threshold", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": null, |
| "section_title": "The exact full-rank impulse threshold", |
| "statement_label": "thm:threshold", |
| "statement_name": "Sharp jump threshold", |
| "statement_number": "3.4", |
| "pdf_page_anchor": 6, |
| "equation_labels": [ |
| "eq:threshold" |
| ] |
| }, |
| "statement": "The resolvent parameterization yields the stated sharp minimum nonzero impulse norm for an invertible skew register and nonzero endpoint.", |
| "assumptions": [ |
| "A invertible; x nonzero; theta nonzero.", |
| "Finite impulse rather than a continuous trajectory." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/verify_physics.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v1/arrow_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "The singular case and zero endpoint require separate treatment.", |
| "This is not a universal physical actuator speed or energy bound." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Skew resolvents" |
| ], |
| "candidate_scope": "Exact gate-specific impulse feasibility" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-T004", |
| "title": "Continuous legal motion is isospectral", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": null, |
| "section_title": "Continuous motion and the origin of the operational arrow", |
| "statement_label": "thm:continuous", |
| "statement_name": "Complete continuous isospectrality", |
| "statement_number": "4.1", |
| "pdf_page_anchor": 7, |
| "equation_labels": [] |
| }, |
| "statement": "Absolutely continuous exact legal evolution conserves every skew-matrix power trace, hence spectrum and rank.", |
| "assumptions": [ |
| "dot x=v, dot A=x wedge v and Av=0 almost everywhere.", |
| "Real finite-dimensional state with absolute continuity." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/reviews/v1/arrow_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "This does not cover rough white-noise finite-resolution writing.", |
| "Continuous legality must not be interchanged with sample-and-hold legality." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Trace calculus and isospectral flows" |
| ], |
| "candidate_scope": "Exact own-area continuous-limit exclusion" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-S001", |
| "title": "Seeded three-dimensional pulse and diffusion closure", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": null, |
| "section_title": "A seeded three-dimensional noisy controller", |
| "statement_label": "thm:closure", |
| "statement_name": "Exact scalar pulse closure", |
| "statement_number": "5.1", |
| "pdf_page_anchor": 8, |
| "equation_labels": [ |
| "eq:closure", |
| "eq:ito-closure" |
| ] |
| }, |
| "statement": "The exact U,R,Q pulse recurrence closes and its independent Gaussian-stroke limit has pathwise nondecreasing U and R.", |
| "assumptions": [ |
| "Dimension three; U0=|b0|²>0.", |
| "Legal held scalar strokes; independent Gaussian variance 2nu h for the Ito model." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/verify_physics.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/finite_resolution_check.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/results/verification.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v1/finite_resolution.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Three scalars do not close arbitrary higher-rank or multidriver geometry.", |
| "The zero-memory entrance is not supplied by these seeded theorems." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Diffusion scaling and Ito calculus" |
| ], |
| "candidate_scope": "Endogenous own-area scalar closure and locking" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-S002", |
| "title": "Held OU writing crossover", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": null, |
| "section_title": "A colored-noise experiment with an exact crossover", |
| "statement_label": "thm:colored", |
| "statement_name": "Sample-held colored-noise locking", |
| "statement_number": "6.3", |
| "pdf_page_anchor": 11, |
| "equation_labels": [ |
| "eq:core" |
| ] |
| }, |
| "statement": "Stationary integrated OU strokes with h/tau=c converge to the controller with resolved clock fraction f(c)=1-(1-exp(-c))/c.", |
| "assumptions": [ |
| "Seeded U0>0; stationary scalar OU preparation.", |
| "h,tau tend to zero at fixed c>0; direction held during each stroke.", |
| "Cumulative driver, square clock and cubic-remainder hypotheses of lem:pulse-limit." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/colored_crossover.py", |
| "kind": "finite_simulation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/finite_resolution_check.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/results/colored_crossover.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/results/independent_finite_resolution.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Different input spectra or intra-stroke policies can give different laws.", |
| "The crossover is not a universal material constant or a notation convention." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "OU covariance integration, homogenization and Ito/Stratonovich corrections" |
| ], |
| "candidate_scope": "Resolved noise clock tied to exact area-memory response" |
| }, |
| "independent_review_focus": [ |
| "Check prop:ou and lem:pulse-limit before thm:colored." |
| ] |
| }, |
| { |
| "id": "AVGMP-P001", |
| "title": "Thermal probe work, free energy and heat", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": null, |
| "section_title": "A stable thermal probe with exact work and heat", |
| "statement_label": "thm:thermal", |
| "statement_name": "Exact thermal writing law", |
| "statement_number": "8.1", |
| "pdf_page_anchor": 13, |
| "equation_labels": [ |
| "eq:probe", |
| "eq:wirr", |
| "eq:midpoint-heat" |
| ] |
| }, |
| "statement": "The specified stable harmonic probe has exact equilibrium quench-work/free-energy formulas, including positive irreversible work for isospectral orientation writes.", |
| "assumptions": [ |
| "Positive stiffness and calibrated physical parameters.", |
| "Initial equilibrium and the specified quench/relax schedule.", |
| "Controller and probe are distinct systems." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/verify_physics.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/results/verification.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v1/thermodynamics.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "No universal heat or joules per geometric area is derived.", |
| "Equilibration, contact fluctuations and all controller resources require independent experimental calibration." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Gaussian equilibrium thermodynamics and quench work" |
| ], |
| "candidate_scope": "Explicit geometric-controller thermal readout" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-P002", |
| "title": "Passive completely positive readout and projection telescope", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": null, |
| "section_title": "A completely positive dark-mode readout", |
| "statement_label": "thm:survival", |
| "statement_name": "Exact relaxed-stage survival", |
| "statement_number": "10.1", |
| "pdf_page_anchor": 16, |
| "equation_labels": [ |
| "eq:lindblad", |
| "eq:errorbound", |
| "eq:two-pulse" |
| ] |
| }, |
| "statement": "The stated loss channels form a completely positive passive readout; complete relaxed stages give exact survival U0/U, with a separate finite-dwell error budget.", |
| "assumptions": [ |
| "Seeded three-dimensional controller; independent probe.", |
| "Loss blanked during each write and held at its endpoint.", |
| "Initial photon is in the known dark mode; projection telescope assumes complete relaxation." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/quantum_protocol_check.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/results/quantum_protocol_check.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v1/quantum_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Finite dwell is not exact projection.", |
| "Coherent transport can remove attenuation; classical waves have the same amplitude law.", |
| "No unknown-state learning, new quantum rule or quantum advantage follows." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Lindblad loss, Kraus channels, dark modes and projection products" |
| ], |
| "candidate_scope": "Exact endogenous memory-survival telescope" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-R001", |
| "title": "Exact ridge monotone and gap-free gate-error certificate", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:ridge", |
| "section_title": "A rank-continuous family of robust geometric certificates", |
| "statement_label": "thm:ridge", |
| "statement_name": "Resolved exclusion is exactly monotone", |
| "statement_number": "12.1", |
| "pdf_page_anchor": 18, |
| "equation_labels": [ |
| "eq:ridge", |
| "eq:ridge-increment", |
| "eq:ridge-error", |
| "eq:ridge-readout" |
| ] |
| }, |
| "statement": "Every fixed positive ridge resolution is exactly nondecreasing under legal strokes; an approximate gate has the explicit dimension-free residual allowance.", |
| "assumptions": [ |
| "Real finite-dimensional skew A; Euclidean metric.", |
| "Exact own-area write; positive fixed lambda.", |
| "Measured gate residual |Aa|≤epsilon|a| for the error theorem." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v2/robust_radius_check.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v2/results/robust_radius_results.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v2/robust_radius.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Exact rank and the lambda=0 projector are not robust under fixed noise.", |
| "Small lambda amplifies the declared residual penalty." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Resolvent/Woodbury identities and matrix perturbation bounds" |
| ], |
| "candidate_scope": "Exact own-area ridge gain and nearest-legal finite-error construction" |
| }, |
| "independent_review_focus": [ |
| "Check thm:ridge-error together with the exact increment." |
| ] |
| }, |
| { |
| "id": "AVGMP-Q001", |
| "title": "Strong loss reads angular quadratic variation", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:continuous-dark", |
| "section_title": "Continuous stochastic dark-space transport", |
| "statement_label": "thm:strong-loss", |
| "statement_name": "Strong loss detects angular quadratic variation", |
| "statement_number": "13.1", |
| "pdf_page_anchor": 19, |
| "equation_labels": [ |
| "eq:strong-loss", |
| "eq:two-exponents" |
| ] |
| }, |
| "statement": "For a rank-one semimartingale dark line, finite continuous loss followed by strong loss converges to attenuation from its angular quadratic variation. The colored Avenyra exponent is 1/f.", |
| "assumptions": [ |
| "Positive seeded memory lower bound.", |
| "Continuous rank-one semimartingale projector; localized integrable/bounded coefficients as stated.", |
| "Fixed finite loss continuum limit is taken before the strong-loss limit." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v2/colored_readout_check.py", |
| "kind": "finite_simulation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v2/readout_stress_check.py", |
| "kind": "finite_simulation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v2/results/colored_readout_check.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v2/quantum_continuum.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Order of limits changes the response.", |
| "Not a theorem for arbitrary kernel rank, arbitrary bath schedules or zero-memory dark initialization.", |
| "Finite loss and projection must remain separate." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Stochastic moving-projector and Zeno attenuation methods" |
| ], |
| "candidate_scope": "Controlled endogenous area-memory exponent and uniform loss bounds" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-E001", |
| "title": "No seed-independent Feller boundary extension", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:zero", |
| "section_title": "Zero memory: a selected entrance and a universal obstruction", |
| "statement_label": null, |
| "statement_name": "No seed-independent Feller extension", |
| "statement_number": null, |
| "pdf_page_anchor": 21, |
| "equation_labels": [] |
| }, |
| "statement": "The off-zero controller semigroup has no extension continuous across all zero-memory seed approaches for f in [0,1].", |
| "assumptions": [ |
| "nu>0; stated seeded off-zero diffusion.", |
| "A candidate extension must agree with every off-zero seed approach." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/reviews/v2/zero_memory.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v2/vector_entrance_independent_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Selected weak entrances still exist.", |
| "This is not a blanket prohibition on memory nucleation or on discontinuous boundary policies." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Feller continuity and separating observables" |
| ], |
| "candidate_scope": "Explicit parallel/transverse and full-origin boundary counterexamples" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-E002", |
| "title": "Selected scalar writing entrance", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:zero", |
| "section_title": "Zero memory: a selected entrance and a universal obstruction", |
| "statement_label": "thm:entrance", |
| "statement_name": "Unique scalar writing entrance", |
| "statement_number": "14.2", |
| "pdf_page_anchor": 22, |
| "equation_labels": [] |
| }, |
| "statement": "The nonzero-anchor writing boundary has a unique global causal scalar entrance via the proved Volterra contraction and bounds.", |
| "assumptions": [ |
| "x0 nonzero; r0=|x0|²>0; nu>0 and f>0.", |
| "Continuous Holder writing input; U0=Q0=0 and R tends to r0." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/reviews/v2/zero_memory.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v2/vector_uniqueness_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "The r0=0 origin cannot be inserted into this contraction.", |
| "Uniqueness is within the declared writing boundary class." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Volterra equations and Banach contraction" |
| ], |
| "candidate_scope": "Explicit own-area singular scalar entrance with controlled constants" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-E003", |
| "title": "Unique nonzero-anchor immediate-writing weak vector law", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:zero", |
| "section_title": "Zero memory: a selected entrance and a universal obstruction", |
| "statement_label": "thm:vector-entrance", |
| "statement_name": "Canonical immediate-writing vector law", |
| "statement_number": "14.3", |
| "pdf_page_anchor": 24, |
| "equation_labels": [] |
| }, |
| "statement": "Every continuous immediate-writing entrance at a nonzero anchor has the same joint law with its Brownian driver; it is not strong for that specified driver.", |
| "assumptions": [ |
| "x0 nonzero; nu>0; f>0; continuous causal weak solution.", |
| "U(t)>0 for every positive time; Brownian motion remains Brownian in the solution filtration." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/reviews/v2/vector_uniqueness.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v2/vector_entrance_independent_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Nonwriting and delayed-writing boundary policies remain distinct.", |
| "No-strong means relative to the specified innovation, not no possible generating Brownian filtration.", |
| "This does not establish full-origin vector uniqueness." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Emery-Schachermayer eternal circular Brownian motion and integrable linear SDEs" |
| ], |
| "candidate_scope": "Model-specific automatic scalar selection, polar reduction and regular reconstruction" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-E004", |
| "title": "Positive selfsimilar origin law and vector weak existence", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:zero", |
| "section_title": "Zero memory: a selected entrance and a universal obstruction", |
| "statement_label": "thm:origin", |
| "statement_name": "Unique selfsimilar scalar origin writing law", |
| "statement_number": "14.4", |
| "pdf_page_anchor": 25, |
| "equation_labels": [ |
| "eq:origin-foster", |
| "eq:origin-means" |
| ] |
| }, |
| "statement": "The log-time scalar diffusion has a unique positive invariant law, yielding a unique selfsimilar positive scalar origin entrance and a rotationally invariant vector weak entrance. Its c_star lies strictly between 1 and 2.", |
| "assumptions": [ |
| "nu>0 and f>0.", |
| "Positive selfsimilar scalar entrance class and the stated log-time domain.", |
| "Proper Foster function, hypoellipticity and accessibility assumptions verified in the report." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v2/origin_foster_check.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v2/results/origin_foster_check.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v2/origin_selfsimilar.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v2/final_prior_art.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "All nonselfsimilar origin laws and vector uniqueness are unresolved.", |
| "No explicit invariant density or certified numeric c_star is supplied.", |
| "c_star is a model constant, not a universal constant of nature." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Lamperti scaling, Foster-Lyapunov control, hypoellipticity and support arguments" |
| ], |
| "candidate_scope": "Explicit singular controller barrier, invariant-law construction and entrance" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-H001", |
| "title": "Arbitrary seeded-rank intrinsic polynomial closure", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:multi", |
| "section_title": "Multiple drivers: valid limits and rank-burst collapse", |
| "statement_label": "thm:polynomial", |
| "statement_name": "Complete intrinsic spectral closure", |
| "statement_number": "15.1", |
| "pdf_page_anchor": 30, |
| "equation_labels": [] |
| }, |
| "statement": "The intrinsic scalar quotient at seeded rank 2m has an exact finite polynomial pulse closure and a global continuous-driver coefficient limit.", |
| "assumptions": [ |
| "Positive seeded gap; intrinsic single transported kernel-line input.", |
| "Cumulative additive driver and resolved square clock converge with vanishing cubic remainders." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v2/multidriver_checks.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v2/results/multidriver_check_results.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v2/multidriver.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Externally labelled directions require orientation data.", |
| "Minimality of the 2m+1 coefficient count is not claimed.", |
| "This does not provide every multidriver or rank-changing limit." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Skew normal form, bordered resolvents and positive-clock convergence" |
| ], |
| "candidate_scope": "Exact finite intrinsic own-area spectral hierarchy" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-H002", |
| "title": "Multidriver obstructions and valid matrix OU sectors", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:multi", |
| "section_title": "Multiple drivers: valid limits and rank-burst collapse", |
| "statement_label": null, |
| "statement_name": "Multiple drivers: valid limits and rank-burst collapse", |
| "statement_number": null, |
| "pdf_page_anchor": 27, |
| "equation_labels": [ |
| "eq:tangency", |
| "eq:matrix-ou" |
| ] |
| }, |
| "statement": "The report identifies the projector-tangency obstruction, generic even-dimensional rank-burst freeze, failure of three-scalar closure and a matrix OU limit in a valid smooth seeded sector.", |
| "assumptions": [ |
| "Each obstruction or limit uses its separately stated rank, dimension and driving hypotheses.", |
| "Stationary stable matrix OU bath and valid smooth tangent sector for the matrix law." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v2/multidriver_checks.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v2/results/multidriver_check_results.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v2/multidriver.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v2/final_prior_art.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "No universal arbitrary-rank Brownian projector equation is asserted.", |
| "Odd-dimensional singular burst laws, adaptive/non-Gaussian input and invalid tangency sectors remain unresolved." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Tangent diffusions and enhanced colored-noise/area limits" |
| ], |
| "candidate_scope": "Own-area rank exhaustion and valid-sector covariance specialization" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-D001", |
| "title": "Finite-duration powered endpoint realization", |
| "kind": "physical_proposal", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:finite-rate", |
| "section_title": "Exact finite-duration realization in a powered hybrid model", |
| "statement_label": null, |
| "statement_name": "Finite-bandwidth endpoint realization", |
| "statement_number": null, |
| "pdf_page_anchor": 31, |
| "equation_labels": [] |
| }, |
| "statement": "A shaped finite-duration command realizes the exact endpoint write with zero final filter currents in the specified latched two-filter model; speed, error and energy budgets are apparatus dependent.", |
| "assumptions": [ |
| "Known positive filter constants; initial filter currents zero.", |
| "Held direction, permitted signed compensation and calibrated finite-state powered sequencer." |
| ], |
| "proof_status": "Model equations and proposed implementation; no fabricated device or laboratory validation.", |
| "evidence": [ |
| { |
| "path": "research/v2/finite_rate_check.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v2/results/finite_rate_check.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v2/finite_rate_realization.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "No fabricated circuit or passive material is reported.", |
| "Compact-time commands are not strictly Fourier band limited.", |
| "Bounded-power fixed-bandwidth hardware does not justify an arbitrarily fast white-noise limit." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Filter compensation, shaped control and first-law accounting" |
| ], |
| "candidate_scope": "Exact finite-rate realization of the stipulated area endpoint" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-C001", |
| "title": "Exact endpoint weighted spectral transport", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:spectral-cone", |
| "section_title": "The complete cone of quadratic spectral memory observables", |
| "statement_label": "thm:spectral-transport", |
| "statement_name": "Exact own-area spectral transport", |
| "statement_number": "17.1", |
| "pdf_page_anchor": 33, |
| "equation_labels": [ |
| "eq:spectral-transport", |
| "eq:spectral-mass" |
| ] |
| }, |
| "statement": "The post-stroke positive displacement measure is the rank-one probe measure multiplied by 1+s²q²/ell, including repeated modes and rank birth.", |
| "assumptions": [ |
| "Real finite-dimensional skew state and exact pre-gated stroke.", |
| "Active spectral reduction and zero/inactive blocks treated as in the theorem." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v3/spectral_order_check.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/results/spectral_order_check.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/spectral_order.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/foundational_geometry.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Transport is for this displacement-weighted measure, not a universal order on arbitrary probe vectors.", |
| "Spectral order does not characterize finite reachability." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Rank-one skew reduction and spectral functional calculus" |
| ], |
| "candidate_scope": "Exact own-area endpoint probe-weight amplification" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-C002", |
| "title": "Aligned nonsmooth rank-one order lemma", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:spectral-cone", |
| "section_title": "The complete cone of quadratic spectral memory observables", |
| "statement_label": "lem:rankone-order", |
| "statement_name": "Aligned rank-one spectral order", |
| "statement_number": "17.2", |
| "pdf_page_anchor": 33, |
| "equation_labels": [] |
| }, |
| "statement": "For B=C+c vv^T, the aligned quadratic spectral probe increases for every nondecreasing finite-valued scalar weight, including discontinuities.", |
| "assumptions": [ |
| "Finite nonnegative symmetric matrices; c>0.", |
| "Probe vector exactly aligned with the rank-one update." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v3/spectral_order_check.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/results/spectral_order_check.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Scalar monotonicity is not operator monotonicity.", |
| "A different probe vector can violate the inequality." |
| ], |
| "priority": { |
| "status": "established_trace_order_specialization", |
| "established_ingredients": [ |
| "Generalized Klein inequality; Mackey et al. Proposition 3.5" |
| ], |
| "candidate_scope": null |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-C003", |
| "title": "Complete quadratic scalar spectral cone", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:spectral-cone", |
| "section_title": "The complete cone of quadratic spectral memory observables", |
| "statement_label": "thm:complete-cone", |
| "statement_name": "Complete quadratic spectral cone", |
| "statement_number": "17.3", |
| "pdf_page_anchor": 34, |
| "equation_labels": [ |
| "eq:complete-cone", |
| "eq:cone-increment" |
| ] |
| }, |
| "statement": "M_phi=x^T phi(-A²)x increases under every legal own-area stroke in every finite dimension exactly when phi(0)=0 and phi is nonnegative and nondecreasing on positive arguments.", |
| "assumptions": [ |
| "Finite-valued scalar phi; real finite-dimensional skew A.", |
| "Exact own-area pre-gate; universal quantification over allowed states and dimensions." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v3/spectral_order_check.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/results/spectral_order_check.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/final_claim_review.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Only quadratic scalar spectral observables are classified.", |
| "Other Lyapunov functions, full reachability and a universal physical entropy are not classified.", |
| "No general strictness for thresholds or projectors is claimed." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Aligned rank-one trace order and spectral measures" |
| ], |
| "candidate_scope": "Necessary-and-sufficient cone for this exact own-area endpoint law" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-C004", |
| "title": "Exact finite visible-spectrum tomography and samples-alone minimality", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:finite-tomography", |
| "section_title": "Finite tomography of the observable spectral geometry", |
| "statement_label": "thm:finite-tomography", |
| "statement_name": "Exact finite observable tomography", |
| "statement_number": "17.4", |
| "pdf_page_anchor": 35, |
| "equation_labels": [ |
| "eq:tomographic-response" |
| ] |
| }, |
| "statement": "Any 2m distinct exact positive ridge samples determine a visible at-most-m-mode weighted measure. With unrestricted positive weights and distinct unknown frequencies, fewer samples fail locally when samples are the only data.", |
| "assumptions": [ |
| "Exact scalar ridge response values; known bound m on visible distinct positive modes.", |
| "Local minimality uses unrestricted frequency/weight parameters and no independent known normalization.", |
| "Common factors are canceled when the mode count is overestimated." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v3/tomography_check.py", |
| "kind": "exact_Fraction_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/results/tomography_check.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/tomography_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Independent normalization or other prior constraints can reduce the parameter count.", |
| "Known |x| recovers aggregate kernel weight, not its orientation.", |
| "Invisible modes, multiplicities, full A, permission kernel and stable noisy reconstruction are not determined." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Rational interpolation, poles/residues and implicit-function local identifiability" |
| ], |
| "candidate_scope": "Operational visible measure reconstruction from this ridge readout" |
| }, |
| "independent_review_focus": [ |
| "Do not apply the 2m necessity statement after supplying extra normalization data." |
| ] |
| }, |
| { |
| "id": "AVGMP-Q002", |
| "title": "Seeded OU positive joint-loss endpoint integral", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:joint-loss", |
| "section_title": "Joint controller and loss scaling: the covariance-filter endpoint law", |
| "statement_label": "thm:joint-loss", |
| "statement_name": "Positive joint loss scaling", |
| "statement_number": "18.1", |
| "pdf_page_anchor": 37, |
| "equation_labels": [ |
| "eq:jendpoint", |
| "eq:jrate", |
| "eq:jmax", |
| "eq:jconfidence" |
| ] |
| }, |
| "statement": "For stationary held OU strokes and post-write dwell with gamma_h h tending to positive ell or infinity, survival converges uniformly to the stated covariance-filter endpoint integral; a localized log-error is O_P(sqrt(h log(1/h))).", |
| "assumptions": [ |
| "c=h/tau fixed positive; stationary OU preparation; U0>0.", |
| "Initially dark independent signal and ordered write-then-dwell protocol.", |
| "ell_h bounded below for the uniform rate; exact bright attenuation exp(-ell_h U/2)." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v3/joint_loss_check.py", |
| "kind": "finite_simulation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/joint_loss_simulation.py", |
| "kind": "finite_simulation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/results/joint_loss_checks.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/results/joint_loss_simulation.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/joint_loss.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/foundational_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Arbitrary ell_h tending to zero is not covered; fixed gamma_h is a counterexample to conflating that regime with strong loss.", |
| "Changing bath ratios, loss during a write and general kernels require new estimates.", |
| "The rate is localized and finite simulation does not certify its exponent." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Kofman-Kurizki-Opatrny covariance-weighted partial absorption; Gaussian Poisson equations" |
| ], |
| "candidate_scope": "Controlled homogenization with endogenous BV weights and the U-endpoint conversion" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-Q003", |
| "title": "Finite-MA endpoint nonidentifiability comparison", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:finite-ma", |
| "section_title": "A proved finite-MA comparison: endpoint budgets do not identify the bath", |
| "statement_label": "cor:finite-ma", |
| "statement_name": "Two baths with identical sequential endpoints", |
| "statement_number": "18.2", |
| "pdf_page_anchor": 41, |
| "equation_labels": [ |
| "eq:ma-controller", |
| "eq:ma-loss" |
| ] |
| }, |
| "statement": "Two explicit Gaussian MA sources have C0=1 and total variance 7/5, hence the same scalar diffusion and two sequential survival exponents, but chi_m(q)=1+(2/5)q^m for m=1,2 produces different positive-joint-loss survival functions at the same U endpoint.", |
| "assumptions": [ |
| "The explicit stationary iid-Gaussian MA construction with alpha²+beta²=1 and alpha beta=1/5.", |
| "Seeded held controller; initially dark signal; gamma_h h tends to ell>0.", |
| "Comparison of S1(U) and S2(U) at identical U0 and the same U>U0, not different finite-grid endpoints." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/reviews/v3/final_structural_audit.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Raw resolved lag records distinguish the sources.", |
| "Only retained continuum state and sequential endpoint budgets are nonidentifying.", |
| "No dedicated MA path simulation is bundled; proof verifies its finite-state averaging." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Finite Gaussian MA processes and the same Gaussian Lyapunov/Poisson averaging method" |
| ], |
| "candidate_scope": "Explicit endogenous controller/readout endpoint counteridentifiability" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-Q004", |
| "title": "Correlation-response identifiability and limits", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:joint-loss", |
| "section_title": "Broader covariance law and its precise limits", |
| "statement_label": null, |
| "statement_name": "Joint controller and loss scaling: the covariance-filter endpoint law", |
| "statement_number": null, |
| "pdf_page_anchor": 36, |
| "equation_labels": [] |
| }, |
| "statement": "Under verified lag-budget and quadratic-averaging hypotheses, chi(q)=C0+2 sum Ck q^k is the response. Exact open-interval knowledge determines its coefficients, and its covariance spectral representation is nonnegative.", |
| "assumptions": [ |
| "General joint-loss extension hypotheses including a verified uniform-q quadratic maximal bound.", |
| "Exact continuum response data on an open interval for all-lag identifiability." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v3/tomography_check.py", |
| "kind": "exact_covariance_identity_checks", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/results/tomography_check.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/foundational_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Covariance summability alone is insufficient for quadratic averaging.", |
| "Finite noisy scans do not stably identify infinitely many unrestricted lags.", |
| "OU loss monotonicity and its exponent interval are not universal for negative correlations." |
| ], |
| "priority": { |
| "status": "established_filter_with_model_specific_response_connection", |
| "established_ingredients": [ |
| "Poisson kernel, covariance spectral measures and optical correlation filtering" |
| ], |
| "candidate_scope": "Covariance-generating response through endogenous area memory" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-G001", |
| "title": "Exact metric-bundle inheritance", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:intrinsicgeometry", |
| "section_title": "Intrinsic geometry and the limits of a fundamental-force interpretation", |
| "statement_label": null, |
| "statement_name": "Exact inheritance", |
| "statement_number": null, |
| "pdf_page_anchor": 43, |
| "equation_labels": [ |
| "eq:bundlepulse", |
| "eq:antidevelopment" |
| ] |
| }, |
| "statement": "Orthogonal connection transport inherits every metric/conjugacy-invariant finite pulse statement exactly.", |
| "assumptions": [ |
| "Real metric vector bundle and metric-compatible connection.", |
| "Specified pulse path and parallel transport; x is an internal fibre register." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v3/foundational_geometry_checks.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/results/foundational_geometry_checks.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/foundational_geometry.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Internal developed displacement is not generally physical position or Log(q).", |
| "The extension does not derive its connection, clock or microscopic fields." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Metric connections, parallel transport and functional calculus" |
| ], |
| "candidate_scope": "Exact own-area bundle completion" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-G002", |
| "title": "Short-history spatial certificate", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:intrinsicgeometry", |
| "section_title": "Intrinsic geometry and the limits of a fundamental-force interpretation", |
| "statement_label": null, |
| "statement_name": "Short-history spatial certificate", |
| "statement_number": null, |
| "pdf_page_anchor": 43, |
| "equation_labels": [ |
| "eq:curvaturecertificate" |
| ] |
| }, |
| "statement": "For geodesic pulses from x0=0 in the stipulated normal ball, physical distance is bounded below by an earlier internal rho minus K L³.", |
| "assumptions": [ |
| "Total path length L below injectivity radius at q0.", |
| "Curvature operator bound |R(u,v)|≤K|u wedge v| throughout the radial normal ball.", |
| "K L²≤1/4; internal x0=0." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v3/foundational_geometry_checks.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/results/foundational_geometry_checks.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/foundational_geometry.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "No global spatial exclusion follows; flat-torus loops are an exact counterexample.", |
| "No Lorentzian or relativistic field theory is supplied." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Jacobi fields, normal coordinates and connection variation" |
| ], |
| "candidate_scope": "Controlled curvature error coupled to the own-area certificate" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-G003", |
| "title": "Axiomatic wedge form and endpoint-robust norm gate", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:intrinsicgeometry", |
| "section_title": "Intrinsic geometry and the limits of a fundamental-force interpretation", |
| "statement_label": null, |
| "statement_name": "Endpoint-robust passivity and preceding bilinear uniqueness", |
| "statement_number": null, |
| "pdf_page_anchor": 43, |
| "equation_labels": [] |
| }, |
| "statement": "Full O(d) equivariance and bilinearity select gamma x wedge a; for nonzero gamma, no decrease of the stipulated Frobenius memory norm for every x selects ker A as the maximal endpoint-independent stroke set.", |
| "assumptions": [ |
| "d≥2; full O(d), not merely SO(d).", |
| "Bilinear skew write; gamma nonzero for nontrivial writing.", |
| "Specified Frobenius memory certificate; permission depends only on A,a and must hold for every endpoint x." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v3/foundational_geometry_checks.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/results/foundational_geometry_checks.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/final_structural_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Gain magnitude/sign and finite timing are not selected.", |
| "Physical energetic passivity needs a separate work/supply relation.", |
| "Oriented, nonlinear, endpoint-dependent or differently energized laws are outside the axioms." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Orthogonal-equivariant tensor classification and quadratic minimization" |
| ], |
| "candidate_scope": "Declared constitutive axioms specialized to the area gate" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-G004", |
| "title": "Conditional canonical Jacobi obstruction and auxiliary action", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:intrinsicgeometry", |
| "section_title": "Intrinsic geometry and the limits of a fundamental-force interpretation", |
| "statement_label": null, |
| "statement_name": "Intrinsic geometry and the limits of a fundamental-force interpretation", |
| "statement_number": null, |
| "pdf_page_anchor": 43, |
| "equation_labels": [ |
| "eq:intrinsic3dflow" |
| ] |
| }, |
| "statement": "The stated identification of x as commuting canonical positions and b as mechanical momenta violates Poisson/commutator Jacobi for the proposed flow; a doubled cotangent Hamiltonian still realizes the chosen vector field formally.", |
| "assumptions": [ |
| "Same six variables and canonical mixed bracket/commutator identification.", |
| "Common invariant domain for associative operator commutators.", |
| "The auxiliary cotangent lift may add variables and unbounded momentum energy." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/v3/foundational_geometry_checks.py", |
| "kind": "finite_verifier", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/v3/results/foundational_geometry_checks.json", |
| "kind": "finite_results", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/foundational_geometry.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Not a general no-Hamiltonian or no-quantization theorem.", |
| "Other physical identifications, auxiliary fields and controlled plants remain possible.", |
| "The cotangent action enforces rather than derives the selected dynamics." |
| ], |
| "priority": { |
| "status": "established_Jacobi_obstruction_specialization", |
| "established_ingredients": [ |
| "Magnetic charge/Jacobi obstruction; associative commutator Jacobi; cotangent lift" |
| ], |
| "candidate_scope": "Explicit obstruction for this proposed variable identification" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-F001", |
| "title": "Adjoint reverse and finite-fuel thermal completion", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:thermal-foundations", |
| "section_title": "Thermal completion and an operational writing certificate", |
| "statement_label": "thm:adjoint-completion", |
| "statement_name": "The reverse gate is an adjoint gate", |
| "statement_number": "20.1", |
| "pdf_page_anchor": 46, |
| "equation_labels": [ |
| "eq:thermal-pair" |
| ] |
| }, |
| "statement": "Each writing pre-gate has a post-gated inverse, and a finite registry plus finite fuel has the explicit paired detailed-balance thermal rates.", |
| "assumptions": [ |
| "Declared finite exact register registry and inverse edges.", |
| "Finite full implementation energies and fuel quanta; positive bath temperature.", |
| "Actual proper reversal includes controller phase and odd controls." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/reviews/v3/thermodynamic_foundations.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/final_claim_review.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "The finite registry is a consistent model, not a fabricated autonomous material.", |
| "Channel rate ratios are not deadline success probabilities.", |
| "Repeated pre-gate alone is not a complete thermal reverse law." |
| ], |
| "priority": { |
| "status": "candidate_model_specific_priority_unverified", |
| "established_ingredients": [ |
| "Detailed balance and finite-resource Markov embedding" |
| ], |
| "candidate_scope": "Explicit own-area pre/post pair with fuel accounting" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-F002", |
| "title": "Observable writing/reversal entropy certificate", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:thermal-foundations", |
| "section_title": "Thermal completion and an operational writing certificate", |
| "statement_label": "thm:thermal-writing", |
| "statement_name": "Observable writing--reversal certificate", |
| "statement_number": "20.2", |
| "pdf_page_anchor": 46, |
| "equation_labels": [ |
| "eq:binary-writing-ep", |
| "eq:three-bin-writing-ep" |
| ] |
| }, |
| "statement": "Proper forward/reverse path relative entropy bounds the observed binary writing divergence; a stronger three-bin formula requires the additional same-law reverse compatibility.", |
| "assumptions": [ |
| "Thermodynamically resolved local detailed balance and full boundary ensembles.", |
| "Calibrated time-reversal-even certificate and writing event.", |
| "q_R is measured in the correctly prepared reverse experiment; same-run q requires the extra compatibility." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/reviews/v3/thermodynamic_foundations.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/foundational_audit.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/final_claim_review.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "Not an entropy assignment to a deterministic algorithm or to geometric area.", |
| "Stationarity alone is insufficient with unconjugated odd controls.", |
| "Zero observed reversals in finite samples does not prove zero probability." |
| ], |
| "priority": { |
| "status": "established_information_inequality_specialization", |
| "established_ingredients": [ |
| "Path entropy production and relative-entropy data processing" |
| ], |
| "candidate_scope": "Operational writing event built from the robust own-area certificate" |
| }, |
| "independent_review_focus": [] |
| }, |
| { |
| "id": "AVGMP-F003", |
| "title": "Finite preparation-resource reverse floor", |
| "kind": "theorem", |
| "report_reference": { |
| "source": "research/Avenyra_Geometric_Memory_Physics.tex", |
| "section_label": "sec:thermal-foundations", |
| "section_title": "Thermal completion and an operational writing certificate", |
| "statement_label": "thm:finite-resource-floor", |
| "statement_name": "Finite prepared resource leaves a reverse-event floor", |
| "statement_number": "20.3", |
| "pdf_page_anchor": 47, |
| "equation_labels": [ |
| "eq:finite-resource-floor" |
| ] |
| }, |
| "statement": "In the finite autonomous detailed-balance completion, full prepared free energy bounds the proper reverse-event probability below by exp(-(B+h(p))/p).", |
| "assumptions": [ |
| "Finite autonomous resolved detailed-balance apparatus.", |
| "B includes the full prepared controller/fuel free energy relative to Gibbs equilibrium.", |
| "p>0; actual transient reverse probability q_R." |
| ], |
| "proof_status": "Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.", |
| "evidence": [ |
| { |
| "path": "research/reviews/v3/thermodynamic_foundations.md", |
| "kind": "AI_derivation", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| }, |
| { |
| "path": "research/reviews/v3/final_claim_review.md", |
| "kind": "AI_audit", |
| "role": "Supporting finite calculation or AI audit; not independent theorem certification." |
| } |
| ], |
| "limits": [ |
| "A transient same-run erasure probability cannot replace q_R.", |
| "No universal heat per unit area or universal apparatus-independent resource cost follows.", |
| "Work interpretations require a fully accounted isothermal cyclic implementation." |
| ], |
| "priority": { |
| "status": "established_free_energy_information_specialization", |
| "established_ingredients": [ |
| "Nonequilibrium free energy and binary relative entropy" |
| ], |
| "candidate_scope": "Finite-resource writing/reversal floor for the explicit completion" |
| }, |
| "independent_review_focus": [] |
| } |
| ], |
| "remaining_questions": [ |
| "General nonselfsimilar complete-origin scalar classification, complete-origin vector uniqueness and preparation selection", |
| "Odd-dimensional singular rank-burst limits and adaptive/non-Gaussian driving beyond proved sectors", |
| "Arbitrary zero-loss-per-dwell joint paths, changing bath ratios and overlapping hardware write/loss limits", |
| "Stable noisy spectral/correlation inverse, invisible mode orientation and full reachability classification", |
| "Stable microscopic Hamiltonian and independent evidence for the controller constitutive axioms", |
| "Fabrication, physical clock/retained memory, contact fluctuations, calibrated reverse events, measured work and comparative benchmarks", |
| "Independent human review, broader priority investigation and reproducible experimental confirmation" |
| ], |
| "validation": { |
| "claim_count": 32, |
| "report_labels_checked": true, |
| "evidence_paths_checked": true, |
| "validation_scope": "Schema construction, anchor presence and file presence only; not mathematical proof checking." |
| } |
| } |
|
|
