Datasets:
Formats:
json
Languages:
English
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< 1K
Tags:
mathematics
nonlinear-systems
model-reduction
state-representation
exterior-algebra
exact-arithmetic
| {"boundary": "Known finite library of strictly positive linear maps, followed by normalization; positive-denominator linear-fractional readouts", "claim": "Finite exterior closure characterizes every finite conditional continuation", "evidence": "Complete proof; exact compiler and word-membership checks", "id": "claim-001", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "This is an information ordering, not a minimum bit count for arbitrary real encodings", "claim": "Coarsest information partition among arbitrary encoders", "evidence": "Equivalence and minimality proof", "id": "claim-002", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Local regular neighborhoods; no globally minimal chart asserted in general", "claim": "Least local continuous dimension equals regular signature rank", "evidence": "Constant-rank upper chart and invariance-of-dimension lower bound", "id": "claim-003", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Snapshot coordinates do not have to update from themselves", "claim": "Affine snapshot dimension is between r and 2r", "evidence": "Ratio lemma, local-dependence proof, sharp examples", "id": "claim-004", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Compared with fixed global affine encoders, not all conventional methods", "claim": "Two nonlinear coordinates versus n−1 fixed affine recurrent coordinates", "evidence": "Explicit positive instrument; exact closure proof", "id": "claim-005", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Matches the conditional outputs; no recursive advantage claimed", "claim": "Equal-evidence mode-aware conventional controller", "evidence": "Exact word tests", "id": "claim-006", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Exact behavior; effects of deep hidden coordinates can be arbitrarily small", "claim": "Rank-one rewrite raises nonlinear minimum to n−1", "evidence": "Explicit inverse from finite conditional readouts; exact matrix checks", "id": "claim-007", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "For the explicit family, not every rank-one edit", "claim": "Spectra, branch probabilities, and uniform aggregate stationary state are unchanged", "evidence": "Direct triangular-coordinate proof and rational checks", "id": "claim-008", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Specified perturbation family and protected output", "claim": "Compact old controller has error at most 8δ/3 after rewrite", "evidence": "Direct pathwise proof; 72 histories and vertex tests", "id": "claim-009", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Deterministic worst-state output guarantee; excludes code/model/acquisition costs", "claim": "All-horizon quantized implementation needs 2 log2(1/ε)+O(1) state bits", "evidence": "Contraction bound and matching two-dimensional packing argument", "id": "claim-010", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "General quantifier elimination not implemented and may be expensive", "claim": "Exact new-branch compatibility is a quadratic implication on feasible pairs", "evidence": "Necessary-and-sufficient proof", "id": "claim-011", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "A rejected span test alone is not an impossibility certificate", "claim": "Linear exterior transport is not necessary for compatibility", "evidence": "Explicit full-state counterexample", "id": "claim-012", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Restricted libraries and approximate memory are not ruled out", "claim": "Arbitrary positive stochastic future edits require full exact state information", "evidence": "Explicit separation for every distinct state pair", "id": "claim-013", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Requires valid denominator bounds, feasible represented states, and contraction for lifetime stability", "claim": "Robust exterior residual certificate", "evidence": "Direct cross-product/denominator bound", "id": "claim-014", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Valid common model, genuine uniform errors, common evaluation anchor, operational permissions", "claim": "Adaptive promotion can use one valid uncertainty event", "evidence": "Standard uniform-confidence composition", "id": "claim-015", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Full gain infimum must actually be bounded", "claim": "Checking only vertices may accept a harmful revision", "evidence": "Exact bounded linear-fractional counterexample", "id": "claim-016", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "Test counts are not proofs of asymptotic claims or novelty", "claim": "40 tests pass and numerical residuals match recorded files", "evidence": "Executed logs and raw data", "id": "claim-017", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "source_claim_with_stated_evidence"} | |
| {"boundary": "No LLM training or external benchmark run", "claim": "Improved frontier-agent or terminal-benchmark performance", "evidence": "Not established", "id": "claim-018", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "not_established"} | |
| {"boundary": "Theorems concern specific complete mathematical contracts", "claim": "Universal superiority or T9 significance", "evidence": "Not established", "id": "claim-019", "source_path": "CLAIMS.md", "source_sha256": "c27b862fde4471767c6ff43b8de2ca55ab3d8711bc8c2002c5f071db8abb87ba", "status": "not_established"} | |