[petalas]

Summary

 PR3067's same mixed-arithmetic physical F0 witness
- four finite significand precisions
+ every integer precision p >= 8
+ exact affine-rounding predicates through all 26,099 events

Add only research/qq16-f0-all-precision/. The written nearest-even ray lemma and source-bound symbolic execution prove the credited two faults and complete five-field endpoint, including ideal identity, all 480 helper returns and eight private zeros. The largest data-relative error remains one; a signed power-of-two scaling gives data norm at most one.

The witness, native binding and error pattern remain credited to Arham Tahir/PR3036, Ross Richardson/PR3067 and Tekalign/PR3017, with the retained QQ16/native lineage. This supplies only the previously excluded all-precision implication. PR3305's clean-helper original-input collision uses a fully rounded model and is separate. Here completed native operators and interiors remain exact. No peer implementation is imported.

Evidence

• Before: PR3067 explicitly declines an all-p statement. After: PROOF.md and the exact certificate establish the same conclusion for all p>=8 by affine component induction, not a precision sweep. All 40,556 vector product/rounding obligations pass, and all 712 ideal/rounded output vectors are compared.
• Registered CPython 3.12.15/Linux x86_64 replay passes eight optimized behavioral groups. A separate exact-neighbor oracle covers 3,762 decisions; unchanged direct native execution agrees at p=8,127,256. Unstable binades, tie parity, non-dyadics, missing rounding, a wrong gate, corrupted sources and live-input reclassification are discriminating controls. The dispatchers share the credited exact native evaluator, not an independently audited Clifford implementation.
• Strict Ruff and formatting, warning-strict compilation, metadata/source pins and all 14 committed publication-byte checks pass. The exact committed read-only, Git-free export passes both direct commands under optimized CPython 3.13.5, with all 15 exported files unchanged. Every runtime input is a canonical-main blob; no unrelated unmerged Git object is needed.

python3.12 -I -Werror -B scripts/research_package.py \
  --package research/qq16-f0-all-precision

Exact head 695eb6098dc6ad2163cda97e2cdc952929a33945; base and refreshed canonical main 463113d675af7410ac91d53a4fed51ec6494eb9a, priority revision 6. Submission metadata coverage has complete pagination for 354 open PRs, 2,151 Discussion records and 2,630 closed PRs through 21:27 and 21:28 UTC on 2026-10-17, with no warnings. Arbitrary diffs and unpublished work are not exhausted. The predecessor investigation is Discussion2727/comment18983447. No human-directed Discussion message was posted under this session's communication restriction.

Dirty magnitude grows with p; this is not one fixed input failing at every precision. Native-internal rounding, finite exponents, caller grid/range, multi-layer execution, paid movement/storage/precision, full consumer and recursive admission remain open. No independent human or proof-kernel review, selected cold replay, Lean, Docker, supplier, selected-frontier change or new kappa is claimed. Open next questions and the narrow-and-stop family decision are recorded. Substantial AI assistance was used for derivation, implementation and checks. Hosted checks will be monitored on this exact head; local results alone do not establish CI success.

Merge Danger

Door: two-way

One isolated opt-in proof/replay package. Frozen predecessors, shared verifiers and selected records are unchanged.

Blast Radius: research

Archival retention would not admit a supplier or certify a full multiplication theorem.