Exact quantum factoring excludes a practical resource-improvement claim

Family 279; scoped reading addendum, 9 October 2026 Australia/Brisbane. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.

Source finding

The introduction and main theorem specify an ideal exact polynomial-time-uniform qubit circuit family over NOT, CNOT, Toffoli, Hadamard, diag(1,i), inverses and singly controlled versions. It outputs complete prime factorization with probability one in that ideal model.

Applicability boundary

The introduction explicitly says its large polynomial parameters are not intended as practical resource improvements. This is neither a classical polynomial factoring method nor a noisy-hardware probability-one result. Replacing the gate set or claiming resource advantage requires separate translation and measurement. This strengthens the earlier application triage rather than replacing it.

Business decision

Defer a practical factoring product; use as an ideal-gate and resource-contract reference.

Exact sections read

• preprints/Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026/build/sections/01-introduction.tex.
• lean/docs/279.md.

These readings establish recorded source scope, not proof correctness. No independent Lean verification was run. Companion manuscripts and construction effectiveness remain separately tracked. See source metadata.