CLAIMS.md

Claim and implementation ledger

Proofs mean written mathematical arguments under explicit hypotheses, not proof-assistant or external certification.

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