Corollary · quantitative lower bound

QA-RA-S6-C11.5

Linear finite-horizon class lower bound

Exact statement

The horizon-hh growth quotient has at least ⌊(h+2)/6⌋−1\lfloor(h+2)/6\rfloor-1 realized classes; a fixed-parity fibre retains an order-h/12h/12 bound.

StatusProved
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

Pairwise first-divergence positions in the explicit family give the count.

Verification notes

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

Limitations

  • No matching upper bound is known.

Open work

Search for a sharper family or an upper-bound presentation.