Research: exclude P112 4^3,6^6,7 by deleting one piece

[petalas]

Summary

Exclude the actual ten-piece P112 TWOSIDE (6,4) profile 4^3,6^6,7 over every characteristic-zero field.

4^3,6^6,7 with code intersection dimension >= 6
  delete the last piece
4^3,6^6 with code intersection dimension >= 5
  normalize six root-A5 endpoints in quotient dimension 4
795 <= 112 + 8*24 + 4*120 = 784, a contradiction

Only research/p112-weight-seven-deletion/ is added, with proof, exact source pins, replay, receipt and controls. This is a new application of PR3169's inequality, not a new A5 theorem. The deleted piece is actually unrestricted.

The overlap refresh found concurrent #3195 had proved the initial target 5,5,6^6,7. It is credited, not counted as new. This package makes one bounded pivot to the distinct ten-piece caller above. Its earlier weight-only two-six-flat cover needs sixteen extra lines.

Credit DreamingOfClouds/#3154 for TWOSIDE and its decoder lineage; Nick Petalas/#3169 and #3164/#3161/#3162 for the retained geometry and coordinate bound; #3192 for the handoff; and concurrent #3195 for its earlier deletion application.

Evidence

• Before: the ordinary incidence bound gives 816 against required 795, so it does not exclude this profile.
  After: deleting one piece and using the existing coordinate budget gives 784, a contradiction with margin eleven.
• Registered CPython 3.12 replay passes all 4,097,782 five/six-flats, 117,649 endpoint patterns, exact historical-profile inclusion and fifteen behavioral groups. Four semantic mutants are rejected. Ruff and warning-enabled compilation pass.
• The exact committed read-only, Git-free export passes replay and all fifteen tests under optimized CPython 3.13. All eighteen publication-byte comparisons pass for 3949cc17a4fa4f108a044f532a5d58323c6cb6d2.

python3.12 -B scripts/research_package.py --package research/p112-weight-seven-deletion

The standard Weyl-chamber theorem and original decoder reduction remain dependencies. No full C5, decoder floor, supplier admission or new κ is claimed. Selected frontier unchanged. These are local author checks, not independent human/proof-kernel review or hosted CI. Development and checking used substantial automated assistance.

Canonical claim and scope change.

Merge danger

Door: two-way.

Blast radius: research.

One isolated opt-in package. No shared code, frozen inputs, selected result or priority changes.