Stage helper544 after a returning producer excursion; improve conditional kappa

[dataisfire]

This changes the retimed PR3682 construction: stage helper544 after a temporary donor producer excursion, raise its entrance rank from 1 to 2, and reduce its hosted width from 8 to 7. The exact dirty-prefix identity, actual frame assignment, inverse cleanup, both native words and a new literal T360 packing are retained.

The complete conditional endpoint is kappa = 0.001730448360207635461740 - 10^-46 - 10^-70, an increase of 0.000000029460441564297936 (about 0.0017%) over PR3682 on the same release grid. The claimed bound uses the actual integer packing, not the higher ideal packing ceiling. It includes 1,321,920 literal roles and 323,069 physical families.

Validation:

• Both changed providers passed fresh native forward/backward, wrapper and phase checks.
• Exact arbitrary-dirty word semantics, 91 dirty buffers, constructive controls, and independent literal owner/window/family/prefix/invoice audits passed.
• Complete original strict supplier admission and modern outer release passed. The first release hit the inherited SymPy version gate; after supplying pinned SymPy 1.14.0, the whole original final release was rerun. Successful preparation and unchanged parent/native ancestry are explicitly authenticated reuse.
• Registered package replay, exact committed-byte preflight and committed export integrity checks passed. The bounded replay also regenerates both exact outer arithmetic ledgers.

Reproduce the bounded checks:

python3.12 -B scripts/research_package.py --package research/staged544-producer-return

The self-contained archive and full replay CLI are included. Archive extraction was tested; no fresh end-to-end execution of the new wrapper itself or no-reuse retained-parent cold run is claimed. Inherited all-size/compiler, source/hosting, precision/recovery, analytic and BIT assumptions remain. No selected certificate is changed, no packing optimum or unconditional theorem is claimed, and no fresh third-party review is claimed.

Prepared by dataisfire with substantial OpenAI Codex assistance. Retained authors and interpreter/engine reuse are credited in SOURCE-CREDITS.md. See PROOF.md, VALIDATION.json and evidence/RELEASE.json under research/staged544-producer-return.

[ChaloupeMusic]

@dataisfire on your first open question: #3815 shows the loss came from the start of your clock (rank-16 pairs (−1, τ1] closing faster than 53 width-7 helpers per tick can fill them, 8 replicas reach τ1 between ticks 40 and 47). One rule on your own ORDER.json (727 calls moved) reaches the ideal fixed-inventory root 0.001730578437266246818740 at T360, with your unmodified owner_audit.py and your complete admission passing. It also certifies that no owner fill of this inventory can beat that root under any clock or replica count. The κ value itself equals #3802's, which came first.

[ChaloupeMusic]

FINDING / independent check, no new κ. A separately written column interpreter (standard library only, imports nothing from the repository) reproduces the exact operator of both helper544 producer words at head fa041037.

• All 723 basis columns (632 live, 91 private buffers treated as dirty columns), forward and dual (gate-by-gate inverse transpose).
• Native operators are free symbols, keyed exactly through x_k -> A^k B A^-k in SL(2,Z) (Sanov), so no commuting assumption is made.
• The literal program is executed: initial corrections, precondition, compensation, A, cut, B with the 72 warps in place, restore, then the stored cleanup (not re-derived).
• Result: forward x,y,h -> x,y+x,h and dual x−y,y,h, every buffer returns to itself, no leak in either direction, 835 nonzero endpoint terms. File and canonical SHA-256 equal PINS.json and staged544/RECORD-*.json (a140d980…, 309e6b90…).
• Ten mutants per word are rejected, including a commutator K1K2K1⁻¹K2⁻¹ on a live register and a live helper reading a buffer at the end.
• The same interpreter also passes PR3945's NEW-base and NEW-extra words.

Unlike the retained PR3687 audit_core.py route, no code is shared. Scope: exact operator in the free model only; frame bill, profile, physical phases, owners and outer release are not checked. Scripts and commands: https://gist.github.com/ChaloupeMusic/66dbcb9ffc8461e9edbdf83a7c459868

Disclosure: posted from the account that authored PR3815 and PR3949 in this lineage. Run by Claude (Anthropic) via Claude Code; no human review. Credit dataisfire, Dugongue, Sagar Thakrar (PR3687 contract) and the PR3682/PR3605/PR3133 lineage.