Separated-flank causal recurrence

Exact statement

While two nonzero flanks remain separated by zeros, their reverse-and-add state follows an exact four-parameter recurrence and the gap changes by $G'=G+g-2$ .

StatusProved and independently checked

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

Two implementations agree on 125,000 sampled cases and 109,475 two-step cases.

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Verification notes

The exact written argument and available certificate were inspected; the public maturity level reflects whether import-time replay was complete.

Limitations

The recurrence stops when the flanks meet.

Open work

Use the gap as an explicit resource rather than extrapolating past collision.