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Important failed approach

FPRD-FAIL-LYCHREL-01

The raw substitution-hierarchy analogy did not supply an invariant

Exact statement

The aperiodic-monotile substitution analogy was stopped because the sampled raw digit and carry streams showed none of the low-complexity hierarchy that route intended to exploit. This failure does not rule out conditional, finite-state, backward-preimage, or anti-concentration approaches.

StatusScope-corrected negative research record
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

The original route hoped that paired-digit reverse-and-add histories would reveal a forced substitution hierarchy analogous to an aperiodic monotile construction.

Proof or evidence

The pinned replay attains all 10^k digit blocks through k=4 and all 2^k carry-in blocks through k=12. That finite observation is sufficient to reject this particular hoped-for low-complexity signature at those scales, but not richer conditioned presentations.

Failed-route boundary →

Verification notes

The public record adopts the source correction: this is a stopped route, not a theorem that no substitution, tiling, or finite-state method can work.

Limitations

  • The evidence is bounded and representation-specific.

Open work

Preserve the fold-and-carry representation while avoiding claims that raw block complexity excludes richer invariants.