[petalas]

Summary

 P112, three residual binary support ranks <=5,5,6
- sufficient common-cut allowance: 37
+ sufficient common-cut allowance: 38
 root-code intersection dimension <=1 over characteristic zero

Add only research/p112-mixed-support38/. The proof closes PR3260's D6 boundary. Equality would require a rank-six piece on 20 singleton coordinates in one live projective fiber; all 896 relevant axis fibers have rank-six capacity 18. The E6 branch uses the rechecked joint A2 incidence bound, with allowance 76 versus required 80.

This is a sufficient theorem, with no sharpness, new historical profile exclusion, full C5, supplier or kappa claim. Global support capacities 12/20 and the Weyl-chamber theorem remain inherited dependencies. Exact PR3260/3262 proof and receipt bytes are retained and authenticated; direct exported replay needs no pending Git objects. Credit Nick Petalas's predecessor work, DreamingOfClouds/PR3154 and the retained E8/P112 lineage including joaqcoo. The concurrent uniform rank-five support46 result has a different predicate and is not a premise.

Canonical investigation and scope. Baseline is canonical main 463113d675af7410ac91d53a4fed51ec6494eb9a, priority revision 6. Selected science is unchanged.

Evidence

• Before, PR3260 explicitly stopped at support38's 30-root parabolic case. After, all 3,780 orthogonal planes and 896 live-axis fiber censuses, each with 10,795 six-spaces, support the D6 contradiction. A separate ambient-space enumeration checks all 788,035 six-spaces, reconstructs 16 full-axis support20 sets and excludes their survival under all 120 orthogonal four-root punctures.
• Registered CPython 3.12 replay, seven optimized control groups, Ruff and metadata/source-pin checks pass. A designated read-only peer check found no blocking issue after a prose clarification restricting singleton sites to the codeword union outside the cut. Exact hashes, evidence and unrun obligations are in REVIEW.json and CHECKS.json.
• All 19 final committed package/input byte comparisons pass. The exact committed read-only Git-free export passes all three direct commands under optimized CPython 3.13.16. Historical global capacity suites, Lean, Docker and selected cold replay are unrun.

python3.12 -W error -B scripts/research_package.py --package research/p112-mixed-support38

Merge Danger

Door: two-way

Blast Radius: isolated

Only this research package is added. Shared tooling, frozen predecessors and the selected result are unchanged.