# 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](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026/build/sections/01-introduction.tex).
- [lean/docs/279.md](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/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](source.json).