[petalas]

Summary

Add research/p104-clean-dual-precision/, an exact all-cut precision and private-erasure audit of the complete zero-restored corrected P104 dual.

exact signs: P = 127/2, A = 4761/4, K = 6039/4
permitted return defect: collector = 1/1024 immediately before erase

A sufficient 17-bit state-relative guard follows only with residual-tolerant disposal. Ideal zero restoration does not admit rounded strict-zero erasure automatically. Allowing sign defects has separately checked coefficients in the receipt. This is an interface audit, not a new corrected word or a supplier.

Card p104-side-correction, priority revision 4, explicitly changed to the precision/lifecycle obligation left open by the completed word. Scientific base is 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.

Credit ywz65 / #2497 at 7f2cf129d42030d3eb3975b7d1b07392c6d32a1b for the exact 4982-event word and #2503 at 6ea94fa4e547a2038deb3aa2064f6d4e4caa5bf5 for the different original-dual precision precedent; Adam Gall / #2096 at f22626f334a06f6e842766e4a6647419e6821d2d for the Hilbert-defect method; and #2458 plus the retained P104 lineage. The source word is preserved byte-for-byte, with exact pins and full credit in the package.

Tested artifact

Evidence

• Before: all eight ideal private erasures are zero, which does not establish a rounded erasure contract.
  After: with D31 initially a unit vector, a permitted rank-seven return defect at event 1825 leaves a nonzero collector at the erase boundary. This does not contradict the predecessor's exact theorem.
• Signed forward rows and separately implemented reverse functionals agree on all endpoints and attaining rows, including 70231 nonzero input/error coefficients. Literal executions attain the independent-defect maxima; an additional run injects rational defects at all 4966 sites. The registered replay and six behavioral groups pass, including cleanup/chart/sign, source/receipt and state-relative counterexample controls.

python3.12 -Werror -I -B scripts/research_package.py \
  --package research/p104-clean-dual-precision

Checked with CPython 3.12.15 on Linux x86_64 / WSL2. Native unitary correctness is inherited from the pinned realization. No actual rounded child, strict-zero physical disposal, global invoice, remaining 102 corrections, all-size compiler, full selected cold replay, supplier or new kappa is supplied. The guard is sufficient, not a precision lower bound.

Merge Danger

Door: two-way

Blast Radius: research

Only this opt-in audit package is added. Selected records and frozen source inputs are unchanged. Residual-tolerant disposal must remain beside the feedback bound; deleting that premise would overstate the result.