Theorem · cross-length sewing

FPRD-QA-RA-T01

Adjacent-chart seam matching

Exact statement

Every cross-length profile fibre has at most two points and lies in the two adjacent charts determined by the output length.

StatusProved and exhaustively regressed
External reviewNo documented external or specialist review of this Quotient Arsenal result is recorded.

Context

The fixed-length mirror quotient extends across adjacent length charts with one seam bit, but complete growth responses require infinitely many states and separated-flank inverse limits contain non-realizable ghosts.

Proof or evidence

The length law gives the two-chart bound; 1,208,130 profiles corroborate it.

Verification notes

The mirror-profile charts, output-length bound, one-bit receipt, and raw-fibre sum were reconstructed. An independent implementation checked 1,208,130 admissible profiles, 310 overlap outputs, and a sharp collision in every base from two through twelve. Missing Stage 6 archival payloads remain separate at L1.

Limitations

  • The theorem concerns profile states, not the full raw-source fibre.

Open work

Carry only the chart choice across the seam.