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Corollary · state lower bound

QA-RA-S6-C11.3

Any complete-response quotient is infinite

Exact statement

Every quotient from which the full binary growth response can be decoded has infinitely many states.

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

Distinct complete responses must occupy distinct quotient fibres.

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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

  • Infinite state does not forbid finite symbolic descriptions.

Open work

Separate cardinality lower bounds from description complexity.