[ToikY]

Change and mathematical scope

For two independent equal-mask BIT fields, at most two proper-rank rational projector children with physical-address-preserving ordinary work cannot save paid volume, even with varying cover labels. Both children need at least two original field volumes asymptotically. The proof sums simultaneous rank cuts at common physical addresses, counting each bank cell once.

The exact #7001 caller has 1,776 distinct same-mask pair placements after 243 disjoint-role exchanges. The best aggregate paid credit is zero, even with free new routing, setup, ownership, restoration, precision and tape. The full raw BIT deficit remains approximately 60.10389921914735 at target κ = 0.0040075385047236. NO VERIFIED GAIN in κ. Exact #7161 remains the independently replayed comparable witness at 0.003644890067940.

Task and overlap

Canonical base e545235. Changes the bit-new-register-model card to the retained #7001 idle contract. #7190 assumes each ordinary adapter preserves the tracked normalized grades. This proof allows those grades to change by fixed right routing and imposes the separate at-most-two-child scope. #7200 studies cached strict-chart donors. The separate navigation commit reuses the already replayed #7161 CI documentation.

Validation

From a clean checkout using CPython 3.12 with assertions:

python3.12 -B scripts/research_package.py --package research/bit-full-cover-volume-cut

The verifier authenticates four canonical #7001 inputs by exact path, Git blob and SHA-256. It recounts every pair, checks the simultaneous formal reorder on all 1,444 coefficients, encloses the full directed price and exercises three exact two-cover controls. An independent replay verifies the adjoint, all 36 native namespaces and unchanged invoice. Bad source and changed receipt controls reject. Local registered replay, 11 committed-byte/mode/source-history checks and six navigation tests passed. Hosted checks pending at submission.

Credit

CubeJerry #7001 supplies the retained caller and tariff. Credit #6726/#6834/#6980 and the delayed-cover authors for the physical projector and whole-fibre routing contract, #7163/#7190 for related rank bounds, and Round 16 of #7111 for the port-1 and local two-cover controls. Clear1nsight #7161 supplies the comparable complete benchmark. OpenAI Codex and subagents materially assisted.

Open next questions

With three paid positions, the middle bank can receive several distinct physical address maps. Bound its charged volume and the aggregate compatible stock before selecting a site. A changed physical supplier, ordinary addressing, compiler and fixed tape remain outside this result.