Fixed-correction and gradient-ambiguity review evidence
This bounded review covers two units:
FPRD-T78, the fixed-state sequential-correction separation.FPRD-T79/T80, the letter-bounded gradient criterion and the exact ambiguity-three series.
The executable checker independently tests the finite identities, hostile boundaries, and small cases used during review. It does not replace the universal proofs.
Mathematical boundaries
T78uses two separate infima over baseline/presentation pairs. The zero baseline proves the optimized residual raw-height upper bound; every allowed baseline satisfies the residual canonical lower bound. No single baseline is asserted to attain both infima.- The
T78target is undefined outsideb^+ c a^* # Code Code. Its equality challenge is load-bearing for the forced-access argument. The horizon presentation may use polynomially many states. - The target is not max-plus rational at any ambiguity level. After fixing an address, a hypothetical finite automaton would have to realize unary slopes
1/(i+1)with unbounded reduced denominators, whereas ann-state unary integer max-plus automaton obtains asymptotic slopes from cycle means with denominator at mostn. T79imports the classical theorem that a unary max-plus rational sequence is eventually affine on each residue class. Finite testing cannot prove that theorem.- The residue modulus in
T79need not be bounded by the number of states: disjoint cycles of lengths two and three use five states but have least support period six. T80needs only the three open full-dimensional cones. Boundary rays, axes, and ties do not affect the lower bound. Its three-component automaton supplies the matching upper bound.
Reproduction
Run:
python3 audit_fixed_correction_gradient.py
The published JSON output is the exact stdout of that command.