The sampled raw digit and carry blocks were maximally diverse at tested scales

Exact statement

Across the states $T^k(196)$ , $0\le k<4{,}000$ , every within-state decimal digit block through length $4$ and every incoming-carry block through length $12$ occurs. The pinned replay gives carry-in density $0.499366103113$ , mirrored-digit mutual information $0.563591475633$ bits, and mirrored carry-in mutual information $0.000013795714$ bits.

StatusExact finite window and estimators independently replayed

External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

Raw block diversity was used to test whether a low-complexity substitution hierarchy was visible in the sampled orbit.

Proof or evidence

The published certificate pins a 4,000-state window, excludes row-crossing subwords, uses least-significant-first incoming carries, and is reproduced exactly by integer and digit-list implementations.

Raw-complexity observation →

Verification notes

The source's carry density 0.5009 came from an unspecified later window and was not silently treated as reproduced. The public claim now uses the independently pinned window's 0.499366103113 value; the qualitative saturation and mutual-information observations agree.

Limitations

Maximum observed p(k) for finitely many k is compatible with later structure.
Random-like summary statistics do not prove anti-concentration on one deterministic infinite orbit.

Open work

Add explicit control sequences under the same estimators before making comparative complexity claims.