[petalas]

Summary

 mixed inverse-generator Q8 targets; positive i/j calls; arbitrary restored dirt
- n >= 2t; balanced 2/2 four-target eight-call boundary still open
+ 2n+n_i >= 6t-t_i and 2n+n_j >= 6t-t_j, hence 5n >= 11t
+ balanced 2/2 eight calls excluded; four-target minimum is ten or twelve

The author-written proof charges each actual target-product rank and uses both inherited cubic orientations. It closes the remaining balanced handoff from #3570/#3578. The homogeneous 5t/2 result remains stronger in its own domain. Ten-call existence, sharpness, independent human/formal acceptance, physical supplier and kappa remain unclaimed.

Evidence

• Before: the balanced counts (t_i,t_j,n_i,n_j)=(2,2,4,4) pass the predecessor cubic count bound.
  After: they violate the new boundary-rank inequalities. The proof permits any finite restored dirty workspace.
• At d269b2981edbc3e1989c1de7435a33ba90c37302, registered CPython 3.12 science/metadata/pins, eight optimized behavioral controls, committed-byte/source-history checks and Ruff 0.14.0 E/F/B/UP pass. Actual committed Git-free normal science, optimized science and optimized controls all pass. Fourteen exclusive regular export copies, 81,750 bytes, retain identical source/export hashes before and after execution.
• Finite corroboration includes both full algebra bases, 216 generic words on 6,048 dirty columns, 4,452 boundary-rank pairs, 578 cubic fixtures and 42 direct endpoints. These support the universal proof; they are not a word-length census.
• All four actual inherited proof premises are retained unchanged with origin commit/path/blob/SHA256 and predecessor credit. Scientific replay needs no pending branch, foreign Git object or network.

python3.12 -Werror -B scripts/research_package.py --package research/q8-mixed-boundary-rank
python3.12 -B scripts/check_research_commit.py --package research/q8-mixed-boundary-rank --check-source-history

Canonical claim, finding and limitations. The selected full cold replay, Lean, Docker and physical caller/invoice are unrun.

Merge Danger

Door: two-way

Blast Radius: isolated

Adds one self-contained research package. The selected frontier and shared runtime code are unchanged.