[pinterbanget]

Summary

This adds research/pr4416-invoice-rebuild/. It rebuilds #4416's p7 invoice from its literal controller word, answering the open question of my #4420.

#4420 certified #4416's moment inequalities on its recorded invoice. There α clears its requirement by only 5.6·10⁻⁹, while one rank-one paid call moves α by about 7.6·10⁻⁶, so the invoice is the weak link.

Claim type: an independent exact replay and assembly. No new κ.

Result

The invoice is rebuilt exactly.

1. Laurent identity. All 70 physical events of P7-FACTOR.json are replayed as an exact Laurent matrix over Q, D0..D14, under Conditional κ = 0.00268647 via paid target padding after native composition #4416's stated native contract. The left and right scalar programs replay to the stored matrices. left · M · right equals the 14 stated diagonal monomials, and every coefficient matrix matches the stored one.
2. Main targets. Rank 1 + 8·#D per role, over the 112 port recipes on main: {25:448, 41:448, 57:448, 121:224}.
3. Paid idles. The 12 retained windows are exactly the literal IDLE events, and keep mask 232127 selects them. Each pays rank 8·|stages| on both roles at every port: {8:1344, 16:448, 32:448, 48:448}.
4. Supplier. The THREE-base helper widths and unsplit paid profile, over the 15 native calls.
5. Total. T and P equal Conditional κ = 0.00268647 via paid target padding after native composition #4416's invoice exactly (rank-one 131,723 and 131,115).

Control. Flipping one reversed native call breaks the identity.

Evidence

• Standard library only; runs in under a second.
• Imports nothing from Conditional κ = 0.00268647 via paid target padding after native composition #4416. The three inputs are the files whose SHA256 values Conditional κ = 0.00268647 via paid target padding after native composition #4416's RESULT.json records, vendored byte-identically. The port recipes are on main.

python3.12 -B scripts/research_package.py --package research/pr4416-invoice-rebuild --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/pr4416-invoice-rebuild
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4416-invoice-rebuild outcome=completed

Head: 6f918e2658c727007611d98ffb8d3c7336e2290c.

Not covered

• The supplier's own numbers. Its paid profile alone contributes 15·2487 rank-one calls, and re-deriving it from its native certificate is the open next question.
• The rest: the native local contract, the physical 121-axis admission, and the tensor and outer arguments.

Task and overlap

• Card: independent-moment, refined, priority revision 7.
• Base: canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244.
• Claimed in Handoffs and requests for independent checks #1166 before starting (comment 19103903).

Credit

The controller and invoice are 1337isnot1337's (#4416, with OpenAI Codex assistance), building on zxv's #4359. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. Apache-2.0.

🤖 Generated with Claude Code