[pinterbanget]

Scoped independent check of intqwq's #4610 (head 4b4c75bc), which claims conditional κ 0.00302152 via changed warp maps. The parts checked all hold. No new κ.

research/pr4610-endpoint-profile-check/verify.py uses the standard library only and takes about 2 s. #4610's emitted ACTUAL-WORD.json.gz is vendored (blob 79dad65b, SHA256-pinned), and its canonical payload hash equals #4610's frozen 4409d2d9….

Endpoint frames

This is the test #4596 failed (#4604).

• Frames. All 632 start and final frames equal PR4470's as subspaces of F₂⁹. PR4470's frames come from main's pinned constructor.
• Interfaces. Ports, v and h are unchanged, while the warps do change.
• Contrast with Conditional κ = 0.0034 (BIT-limited, +12.58%): complex supplier to 0.011417749 via the ambient quotient by span{511} #4596. Unlike the span{511} quotient, the substituted generators keep every output chart.

Profile arithmetic

• Profile. The emitted local profile is exactly Pnew.
• Difference. Pold − Pnew = 12(3H1 − 2H2 − H3 + H4).
• Totals. Rank mass is unchanged at 5,327, with 12 fewer jobs per call. Over the controller that gives 64,620 → 64,404.

Moment positivity (written proof)

With x = 2^a and c = log₂3, the difference is 3 − 2·2^a − 3^a + 4^a = (x−1)² + 2 − x^c.

• Convex: this function is convex on [1, 2], because c < 2 (3 < 4).
• Decreasing: its derivative at x = 2 is negative, because c > 4/3 (27 > 16).
• Conclusion: its value at x = 2 is 0. So the difference is positive for every 0 < t < 1.

Not covered

• native phase lowering;
• the Lean certificates;
• the outer crossing interval;
• whether substituting generators of the free-group identity is admissible under the supplier contract. That is the maintainers' call.

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

Head: b14d286

🤖 Generated with Claude Code