[pinterbanget]

Independent recomputation of intqwq's #4610 raw crossing. This closes the item my #4614 left open. It agrees. No new κ.

research/pr4610-crossing-recompute/verify.py uses the standard library only and runs in under 1 s.

Method

• Histograms. Target and paid histograms are rebuilt from main's pinned joint-helper-lattice/CONTROLLER.json, covering 18 calls, 15 shears, 15 idles and the diagonal terms. They combine Pnew with the unchanged helper list.
• Root. The crossing is found by bisection in 50-digit Decimal arithmetic. This engine differs from Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610's Fraction intervals, and nothing is imported from Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610.

Results

• Pnew root: 0.00302155511144…, inside Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610's (0.0030215551, 0.0030215552).
• Control: Pold reproduces PR4535's 0.00302016597701….
• Counts: paid calls 64,404 vs 64,620; rank-mass surplus 752.
• κ selection: κ = ⌊root·10⁸⌋ − 3 = 0.00302152.
• Failure control: dropping the idle charges moves the root far above the bracket.

Not covered

• the 54 outer-ledger checks;
• native phase lowering;
• the Lean certificates;
• contract admissibility.

Credit: intqwq (#4610) and Cinna Davis (#4470). Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance.

Head: 29e1120

🤖 Generated with Claude Code