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"Exact finite identifiability under declared data assumptions.",
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"This does not cover rough white-noise finite-resolution writing.",
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"title": "Held OU writing crossover",
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"section_title": "A colored-noise experiment with an exact crossover",
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"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.",
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"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."
}
}
|