Classify c4 h7 first-exhaustion Tq forks

[lieoric]

Scope

Classify the first-exhaustion Tq sibling fork family for balanced c=4, k=2, h=7.

• rebuild the 418 canonical bridge parents / 429 bridge edges;
• isolate the 412 sibling parents / 423 sibling edges;
• enumerate the exact 1,256,148 committed next-run decorations;
• enforce Hall/exact-run feasibility and count the 6,131,033,832 residual words symbolically;
• reduce the surviving geometry to low-energy unique-source Tq corners and D2 configurations;
• independently rebuild every census and reject any claim of residual-word, entry-family, or full-layout coverage.

Claim boundary

A successful workflow establishes only NEXT_RUN_CENSUS_COMPLETE. It does not enumerate all residual words, eliminate this entry family, or prove the full c4/k2/h7 boundary.

Local checks

• MSVC /W4 /WX build
• focused CTest smoke
• independent 257-decoration differential
• strict report validator
• Python compile, actionlint, and whitespace checks

The complete census is intentionally left to GitHub Actions.

GitHub result

Formal run: https://github.com/lieoric/water-sort-counterexample/actions/runs/31425456795

• NEXT_RUN_CENSUS_COMPLETE, verified=true
• 1,256,148 / 1,256,148 decorations checked
• 406,528 nonnegative; 403,685 Hall-feasible
• residual-word weight 6,131,033,832 (counted exactly, not iterated)
• refined split: 101,922 direct; 11,226 N>=3; 223,321 low-energy noncorner; 67,206 D2; 10 Tq corners
• independent rebuild, report replay, strict claim-boundary checks, and artifact hashes passed

The remaining mathematical core is therefore the D2 reduction plus the ten low-energy Tq corner decorations; this PR does not claim those families are solved.