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Theorem · sharp receipt

FPRD-QA-RA-T02

One growth bit is the sharp seam receipt

Exact statement

The bit ε=M−m\varepsilon=M-m suffices to recover the source chart from the post-step value, and one bit is necessary in every base.

StatusProved in every base
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

Universal collision families supply necessity, including the base-two boundary.

Reverse-and-add cross-length atlas review and independent audit →

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 bit recovers the profile chart, not the original digit word.

Open work

Combine it with the within-chart source-fibre receipt when raw reconstruction is required.