| {"record_id":"AVGMP-I001","title":"Supplied Avenyra finite-rule inputs","kind":"inherited_input","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.","report_reference_json":"{\"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\":[]}","assumptions_json":"[\"Real finite-dimensional skew register; exact own-area update and Aa=0 gate.\",\"The source manuscript is the supplied research input.\"]","proof_status_json":"\"Input claims from the supplied manuscript; no external proof certification is asserted.\"","evidence_json":"[{\"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_json":"[\"This release does not certify the source manuscript or establish its literature priority.\"]","priority_json":"{\"status\":\"supplied_manuscript_input_priority_not_certified\",\"established_ingredients\":[],\"candidate_scope\":null}","independent_review_focus_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-T001","title":"Gate timing budget and adjoint inverse","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"Real skew A and Euclidean metric.\",\"D=|x|²|a|²-(x dot a)²; exact finite update.\"]","proof_status_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"D is dimensionless geometry, not thermodynamic heat.\",\"An adjoint inverse is a different gate policy except at the midpoint or zero area.\"]","priority_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-T002","title":"Congruence, midpoint spectrum and endpoint rank","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"Singular values do not determine orientation or full reachability.\",\"The congruence formula must not be substituted at theta=0.\"]","priority_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-T003","title":"Sharp full-rank impulse threshold","kind":"theorem","statement":"The resolvent parameterization yields the stated sharp minimum nonzero impulse norm for an invertible skew register and nonzero endpoint.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"A invertible; x nonzero; theta nonzero.\",\"Finite impulse rather than a continuous trajectory.\"]","proof_status_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"The singular case and zero endpoint require separate treatment.\",\"This is not a universal physical actuator speed or energy bound.\"]","priority_json":"{\"status\":\"candidate_model_specific_priority_unverified\",\"established_ingredients\":[\"Skew resolvents\"],\"candidate_scope\":\"Exact gate-specific impulse feasibility\"}","independent_review_focus_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-T004","title":"Continuous legal motion is isospectral","kind":"theorem","statement":"Absolutely continuous exact legal evolution conserves every skew-matrix power trace, hence spectrum and rank.","report_reference_json":"{\"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\":[]}","assumptions_json":"[\"dot x=v, dot A=x wedge v and Av=0 almost everywhere.\",\"Real finite-dimensional state with absolute continuity.\"]","proof_status_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"path\":\"research/reviews/v1/arrow_audit.md\",\"kind\":\"AI_audit\",\"role\":\"Supporting finite calculation or AI audit; not independent theorem certification.\"}]","limits_json":"[\"This does not cover rough white-noise finite-resolution writing.\",\"Continuous legality must not be interchanged with sample-and-hold legality.\"]","priority_json":"{\"status\":\"candidate_model_specific_priority_unverified\",\"established_ingredients\":[\"Trace calculus and isospectral flows\"],\"candidate_scope\":\"Exact own-area continuous-limit exclusion\"}","independent_review_focus_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-S001","title":"Seeded three-dimensional pulse and diffusion closure","kind":"theorem","statement":"The exact U,R,Q pulse recurrence closes and its independent Gaussian-stroke limit has pathwise nondecreasing U and R.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"Dimension three; U0=|b0|²>0.\",\"Legal held scalar strokes; independent Gaussian variance 2nu h for the Ito model.\"]","proof_status_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"Three scalars do not close arbitrary higher-rank or multidriver geometry.\",\"The zero-memory entrance is not supplied by these seeded theorems.\"]","priority_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-S002","title":"Held OU writing crossover","kind":"theorem","statement":"Stationary integrated OU strokes with h/tau=c converge to the controller with resolved clock fraction f(c)=1-(1-exp(-c))/c.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"Different input spectra or intra-stroke policies can give different laws.\",\"The crossover is not a universal material constant or a notation convention.\"]","priority_json":"{\"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_json":"[\"Check prop:ou and lem:pulse-limit before thm:colored.\"]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-P001","title":"Thermal probe work, free energy and heat","kind":"theorem","statement":"The specified stable harmonic probe has exact equilibrium quench-work/free-energy formulas, including positive irreversible work for isospectral orientation writes.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"Positive stiffness and calibrated physical parameters.\",\"Initial equilibrium and the specified quench/relax schedule.\",\"Controller and probe are distinct systems.\"]","proof_status_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"No universal heat or joules per geometric area is derived.\",\"Equilibration, contact fluctuations and all controller resources require independent experimental calibration.\"]","priority_json":"{\"status\":\"candidate_model_specific_priority_unverified\",\"established_ingredients\":[\"Gaussian equilibrium thermodynamics and quench work\"],\"candidate_scope\":\"Explicit geometric-controller thermal readout\"}","independent_review_focus_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-P002","title":"Passive completely positive readout and projection telescope","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-R001","title":"Exact ridge monotone and gap-free gate-error certificate","kind":"theorem","statement":"Every fixed positive ridge resolution is exactly nondecreasing under legal strokes; an approximate gate has the explicit dimension-free residual allowance.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"Exact rank and the lambda=0 projector are not robust under fixed noise.\",\"Small lambda amplifies the declared residual penalty.\"]","priority_json":"{\"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_json":"[\"Check thm:ridge-error together with the exact increment.\"]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-Q001","title":"Strong loss reads angular quadratic variation","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-E001","title":"No seed-independent Feller boundary extension","kind":"theorem","statement":"The off-zero controller semigroup has no extension continuous across all zero-memory seed approaches for f in [0,1].","report_reference_json":"{\"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\":[]}","assumptions_json":"[\"nu>0; stated seeded off-zero diffusion.\",\"A candidate extension must agree with every off-zero seed approach.\"]","proof_status_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"Selected weak entrances still exist.\",\"This is not a blanket prohibition on memory nucleation or on discontinuous boundary policies.\"]","priority_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-E002","title":"Selected scalar writing entrance","kind":"theorem","statement":"The nonzero-anchor writing boundary has a unique global causal scalar entrance via the proved Volterra contraction and bounds.","report_reference_json":"{\"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\":[]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"The r0=0 origin cannot be inserted into this contraction.\",\"Uniqueness is within the declared writing boundary class.\"]","priority_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-E003","title":"Unique nonzero-anchor immediate-writing weak vector law","kind":"theorem","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.","report_reference_json":"{\"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\":[]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-E004","title":"Positive selfsimilar origin law and vector weak existence","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-H001","title":"Arbitrary seeded-rank intrinsic polynomial closure","kind":"theorem","statement":"The intrinsic scalar quotient at seeded rank 2m has an exact finite polynomial pulse closure and a global continuous-driver coefficient limit.","report_reference_json":"{\"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\":[]}","assumptions_json":"[\"Positive seeded gap; intrinsic single transported kernel-line input.\",\"Cumulative additive driver and resolved square clock converge with vanishing cubic remainders.\"]","proof_status_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-H002","title":"Multidriver obstructions and valid matrix OU sectors","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-D001","title":"Finite-duration powered endpoint realization","kind":"physical_proposal","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.","report_reference_json":"{\"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\":[]}","assumptions_json":"[\"Known positive filter constants; initial filter currents zero.\",\"Held direction, permitted signed compensation and calibrated finite-state powered sequencer.\"]","proof_status_json":"\"Model equations and proposed implementation; no fabricated device or laboratory validation.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-C001","title":"Exact endpoint weighted spectral transport","kind":"theorem","statement":"The post-stroke positive displacement measure is the rank-one probe measure multiplied by 1+s²q²/ell, including repeated modes and rank birth.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"Real finite-dimensional skew state and exact pre-gated stroke.\",\"Active spectral reduction and zero/inactive blocks treated as in the theorem.\"]","proof_status_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"Transport is for this displacement-weighted measure, not a universal order on arbitrary probe vectors.\",\"Spectral order does not characterize finite reachability.\"]","priority_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-C002","title":"Aligned nonsmooth rank-one order lemma","kind":"theorem","statement":"For B=C+c vv^T, the aligned quadratic spectral probe increases for every nondecreasing finite-valued scalar weight, including discontinuities.","report_reference_json":"{\"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\":[]}","assumptions_json":"[\"Finite nonnegative symmetric matrices; c>0.\",\"Probe vector exactly aligned with the rank-one update.\"]","proof_status_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"Scalar monotonicity is not operator monotonicity.\",\"A different probe vector can violate the inequality.\"]","priority_json":"{\"status\":\"established_trace_order_specialization\",\"established_ingredients\":[\"Generalized Klein inequality; Mackey et al. Proposition 3.5\"],\"candidate_scope\":null}","independent_review_focus_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-C003","title":"Complete quadratic scalar spectral cone","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"Finite-valued scalar phi; real finite-dimensional skew A.\",\"Exact own-area pre-gate; universal quantification over allowed states and dimensions.\"]","proof_status_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-C004","title":"Exact finite visible-spectrum tomography and samples-alone minimality","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[\"Do not apply the 2m necessity statement after supplying extra normalization data.\"]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-Q002","title":"Seeded OU positive joint-loss endpoint integral","kind":"theorem","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))).","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-Q003","title":"Finite-MA endpoint nonidentifiability comparison","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"path\":\"research/reviews/v3/final_structural_audit.md\",\"kind\":\"AI_derivation\",\"role\":\"Supporting finite calculation or AI audit; not independent theorem certification.\"}]","limits_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-Q004","title":"Correlation-response identifiability and limits","kind":"theorem","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.","report_reference_json":"{\"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\":[]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-G001","title":"Exact metric-bundle inheritance","kind":"theorem","statement":"Orthogonal connection transport inherits every metric/conjugacy-invariant finite pulse statement exactly.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"Real metric vector bundle and metric-compatible connection.\",\"Specified pulse path and parallel transport; x is an internal fibre register.\"]","proof_status_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"Internal developed displacement is not generally physical position or Log(q).\",\"The extension does not derive its connection, clock or microscopic fields.\"]","priority_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-G002","title":"Short-history spatial certificate","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"No global spatial exclusion follows; flat-torus loops are an exact counterexample.\",\"No Lorentzian or relativistic field theory is supplied.\"]","priority_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-G003","title":"Axiomatic wedge form and endpoint-robust norm gate","kind":"theorem","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.","report_reference_json":"{\"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\":[]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-G004","title":"Conditional canonical Jacobi obstruction and auxiliary action","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-F001","title":"Adjoint reverse and finite-fuel thermal completion","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-F002","title":"Observable writing/reversal entropy certificate","kind":"theorem","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.","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
| {"record_id":"AVGMP-F003","title":"Finite preparation-resource reverse floor","kind":"theorem","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).","report_reference_json":"{\"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\"]}","assumptions_json":"[\"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_json":"\"Scoped analytic argument in the report, reviewed only by AI agents; not externally certified.\"","evidence_json":"[{\"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_json":"[\"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_json":"{\"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_json":"[]","evidence_kind":"source_authored_claim_annotation","source_file":"CLAIM_LEDGER.json"} |
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