[petalas]

Summary

F0 output error epsF + B_1_2 output error epsB
  -> fixed zero-retention decoder
  -> original-array error <= 49 epsF + 1923 epsB + decoder error

Adds only research/qq16-producer-defect-transfer/. This supplies the approximate-producer stability implication left open by #2959. The F0 inverse constant 49 is sharp for arbitrary completed-output errors; 1923 is a conservative endpoint bound for the full decoder. Different chart routes remain ordered.

A sufficient original-input budget is epsF <= H*2^(-beta-8), epsB <= H*2^(-beta-13) and decoder error at most H*2^(-beta-1). The resulting coefficient is exactly 7587/8192 < 1. A separate actual-input norm bound permits the inherited completed-relative decoder parameter u <= 2^(-beta-38).

Canonical claim and handoff. Scientific base 318ba71b8, priority revision 5. Refreshed canonical main 0614abaef has unchanged relevant guidance, selected record and all five inputs. Final complete overlap covers 238 open PRs, 2,413 closed/merged bodies and 1,657 Discussion records; search omissions remain possible.

Evidence

• Before: the exact-producer entry contract explicitly excludes approximate F0/B1 errors. After: an ordered two-stage fault identity and source-bound sensitivities price them separately.
• Literal word replay and an independently implemented derivation from the ordered inverse equations agree on all 448 polynomial row summaries, including 286,376 full-decoder terms. No predecessor executable is imported.
• Registered CPython 3.12.15 replay and six behavioral groups pass. Optimized CPython 3.14.8 tests also pass, including noncommuting toy owner actions, coherent faults, the sharp 49 witness, scalar mutation, dirty scratch, source/typed-receipt corruption, Git-free replay and exclusive receipt creation.
• Ruff, warning-as-error compilation, metadata/source pins and the exact 13-file committed-byte preflight pass. Independent internal mathematical review found no substantive flags. Hosted CI is separate.

python3.12 -Werror -I -B scripts/research_package.py \
  --package research/qq16-producer-defect-transfer

Credit Ali Romman and the joint-query team; Arham Tahir/#2681; ywz65/#2707/#2540; Nick Petalas/#2736/#2959; and the retained native/geometry lineage detailed in the package. Substantial automated assistance was used; no independent human or formal-kernel review is claimed.

Merge Danger

Door: two-way

Blast Radius: isolated

One opt-in research package. Ideal native/chart semantics and the completed-decoder error theorem remain inherited. This does not implement producer interiors, bound dirty-helper magnitudes, supply finite grids/overflow guarantees, or price physical hosting, movement, storage, cleanup and consumption. No supplier, new kappa or frontier change; selected cold replay is unrun. Next work needs one pinned finite producer meeting the stated completed-stage tolerances. Family decision is narrow and stop at this lemma.