claim_id stringlengths 8 8 | title stringlengths 24 47 | status stringclasses 3
values | statement stringlengths 54 153 | assumptions listlengths 1 4 | proof_path stringclasses 2
values | proof_anchor stringlengths 0 9 | code_paths listlengths 0 2 | evidence_paths listlengths 0 2 | limitations listlengths 1 1 | novelty stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
EDD2-T01 | Information-conditioned quadratic accessibility | PROVED | Optimal gross adaptation benefit is 1/2 tr[W(W+eta I)^(-1) E[m m^T]], m=E[r|I]. | [
"Finite second moments",
"Fixed conditional control map K",
"Positive quadratic effort price eta",
"Allowed nonanticipative information"
] | MATHEMATICAL_SUPPLEMENT.md | s-bayes | [
"research/v2/src/joint.py"
] | [
"research/v2/results/verification.json"
] | [
"A local quadratic decision value; not universal nonlinear reachability."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-P02 | Information and control monotonicity | PROVED | Nested information and PSD-greater control Gramians cannot decrease the exact value. | [
"Nested information sigma fields or fixed information",
"Effort and behavioral metrics transported"
] | MATHEMATICAL_SUPPLEMENT.md | s-mono | [
"research/v2/src/joint.py"
] | [
"research/v2/results/verification.json"
] | [
"Changing the learning operator or cost invalidates a mere coordinate comparison."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-P03 | Evidence-control principal-angle matching | PROVED | For rank-r isotropic evidence/control subspaces, gain is vec/2 times the sum of squared principal-angle cosines. | [
"Orthonormal bases",
"Specified isotropic nonzero spectra"
] | MATHEMATICAL_SUPPLEMENT.md | s-angles | [
"research/v2/src/joint.py"
] | [
"research/v2/results/summary.json"
] | [
"Equal ranks alone do not ensure overlap."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-P04 | Gaussian explained covariance | PROVED | Explained covariance equals Sigma-(Sigma^(-1)+F)^(-1). | [
"SPD Gaussian prior",
"Independent linear Gaussian observation noise",
"PSD evidence precision F"
] | MATHEMATICAL_SUPPLEMENT.md | s-gauss | [
"research/v2/src/joint.py"
] | [
"research/v2/results/verification.json"
] | [
"For singular priors restrict to support."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-T05 | Sharp Holder reserve-birth threshold | PROVED | A s/(1+s) t/(1+t)-as-bt has a positive optimum iff A>(a^(1/3)+b^(1/3))^3. | [
"s,t initially absent nonnegative normalized resources",
"a,b strictly positive linear prices",
"Gaussian/quadratic scalar reduction"
] | MATHEMATICAL_SUPPLEMENT.md | s-birth | [
"research/v2/src/joint.py"
] | [
"research/v2/results/verification.json"
] | [
"Existing evidence and nonlinear storage prices change the threshold."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-C06 | Coordinate-greedy empty-reserve trap | PROVED | Coordinate maximization and projected first-order ascent initialized at the empty pair stay there even above the profitable joint-birth threshold. | [
"Exact stated scalar objective",
"Zero initialization",
"Specified coordinate or projected-gradient rule"
] | MATHEMATICAL_SUPPLEMENT.md | s-trap | [
"research/v2/src/joint.py"
] | [
"research/v2/results/verification.json"
] | [
"A restricted algorithmic comparison, not a lower bound against all neural optimizers."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-T07 | Exact scalar access-cost frontier | PROVED | Minimum cost for joint retained fraction q is ((a+b)q+2 sqrt(abq))/(1-q). | [
"0<q<1",
"a,b>0",
"Specified two-resource saturation"
] | MATHEMATICAL_SUPPLEMENT.md | s-front | [
"research/v2/src/joint.py"
] | [
"research/v2/results/verification.json"
] | [
"Precision and mobility units are not bytes or FLOPs."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-T08 | Noncommuting uniform joint-reserve bound | PROVED | The minimum trace cost for E^(1/2) C E^(1/2)>=qI equals d times the scalar frontier, including noncommuting matrix candidates. | [
"Finite PSD S,T",
"E=S(I+S)^(-1), C=T(I+T)^(-1)",
"Isotropic normalized trace prices"
] | MATHEMATICAL_SUPPLEMENT.md | s-matrix | [
"research/v2/src/joint.py"
] | [
"research/v2/results/verification.json"
] | [
"Defined spectral criterion, not success on every nonlinear task."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-T09 | Sharp specialization-action-risk allocation | PROVED | Worst-direction action factor rho relative to isotropic W0 is equivalent to W>=W0/rho; optimal expected ridge access uses floored spectral water filling. | [
"Driftless quadratic action",
"Fixed trace budget",
"Isotropic reference",
"rho>=1"
] | MATHEMATICAL_SUPPLEMENT.md | s-action | [
"research/v2/src/joint.py"
] | [
"research/v2/results/verification.json",
"research/v2/results/summary.json"
] | [
"Action is not SGD iterations or measured hardware compute."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-T10 | Proper realized-accessibility witness | PROVED | The held-out score r^T S mhat-1/2 mhat^T S mhat equals deployed ridge benefit; expected regret is 1/2 E[(mhat-m)^T S(mhat-m)]. | [
"Prediction uses only available information",
"Specified ridge control",
"Finite second moments"
] | MATHEMATICAL_SUPPLEMENT.md | s-witness | [
"research/v2/src/joint.py"
] | [
"research/v2/results/verification.json"
] | [
"Only proper on reachable directions; a different deployed optimizer needs recalibration."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-P11 | Finite-candidate holdout confidence certificate | PROVED | Bounded independent witnesses admit a simultaneous Hoeffding bound and conservative net-gain admission. | [
"Candidate designs fixed before evaluation",
"Independent bounded residual/prediction norms",
"Finite candidate set"
] | MATHEMATICAL_SUPPLEMENT.md | s-conf | [
"research/v2/src/joint.py",
"research/v2/src/controller.py"
] | [
"research/v2/results/verification.json"
] | [
"Not directly applicable to unbounded Gaussian tails or repeated adaptive holdout use."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-T12 | Discrete resource portfolio | PROVED | A cost-grid dynamic program solves the separable portfolio exactly and has the supplied additive continuous error bound. | [
"Independent calibrated modes",
"Positive prices",
"Finite cost grid"
] | MATHEMATICAL_SUPPLEMENT.md | s-dp | [
"research/v2/src/joint.py"
] | [
"research/v2/results/verification.json"
] | [
"Does not solve arbitrary interacting or noncommuting anisotropic design."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-T13 | Resource-aware descendant composition | PROVED | Simulation errors add, multiplicative cost factors multiply, and additive overheads compose affinely. | [
"Uniform common environment envelope",
"Nonanticipative policy simulators",
"Every decoder/compiler/adaptation cost charged"
] | MATHEMATICAL_SUPPLEMENT.md | s-sim | [] | [] | [
"The existence of a global simulator is not implied by local Gramian checks."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
EDD2-E14 | Trainable paired Gaussian preparation | NUMERICALLY TESTABLE | In the executed 20-seed Gaussian experiment, joint preparation reached the exact matched value 1.28. | [
"Dimension 32, rank 4",
"150 projected SGD updates",
"Known Gaussian surrogate"
] | [
"research/v2/src/paired_torch.py",
"research/v2/run_experiments.py"
] | [
"research/v2/results/summary.json"
] | [
"Equal geometry/evidence budgets, not equal preparation compute; informed conventional design ties."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. | ||
EDD2-N15 | No architecture monopoly | PROVED | A conventional system with identical evidence, feasible controls, learning operator and costs can match the reserve decision problem. | [
"Identical admissible policy sets and accounting"
] | [] | [] | [
"Rules out a universal advantage based solely on branch naming or equal parameter count."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. | ||
EDD2-H16 | Large-model total training-cost gains | CONJECTURE | Paired reserves may reduce amortized training cost in neural task streams under a complete equal-resource comparison. | [
"Calibrated useful task witnesses",
"Preparation savings exceed all costs",
"Protection and shift constraints hold"
] | [
"research/v2/src/dendritic.py"
] | [] | [
"No trained Transformer or universal neural experiment supplied."
] | Independent novelty not established; see research/v2/PRIOR_ART.md. |
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