[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. Exact conditional κ change 0%. This package checks all 897 adjacent nested chart pairs used by a paid MOVE on the retained BIT word. Within one pair, both operands at any shared ADD can change chart together while scalar order, logical lifetimes, public endpoint charts and the caller stay fixed. The bound grants free incremental ordinary work, phase, routing, ownership, restoration, precision and tape. Every flow certificate equals its cut. All 897 cases are resolved.

Each certified minimizing witness uses the original labels. The complete 36-copy signed invoice has a savings upper below 6.7×10⁻⁴⁶ raw units, including directed rounding. At κ = 0.0040075385047236 the best net upper remains approximately −60.10389921914735. The strongest independently reproduced comparable benchmark remains #7277 at κ = 0.003645669928698.

Task and overlap

The changed bit-helper-contract scope is recorded in TASK.json. Canonical base is e545235. #7289 bounds balanced ingress retargeting at fixed clocks. #7293 tests the original destination library with fixed charts. This package couples shared contacts over the complete fixed order. It inherits the two exact #7257 CI prerequisite commits for navigation and historical replay and adds one scientific package.

Validation

From a clean checkout with CPython 3.12 and assertions enabled:

python3.12 -B scripts/research_package.py --package research/bit-coupled-chart-bound
python3.12 -B scripts/check_research_commit.py --package research/bit-coupled-chart-bound --check-modes --check-source-history
python3.12 -B -m unittest discover -s tests -p test_research_current_status.py

The independent verifier authenticates both retained inputs, reconstructs 62,474 contact edges and the full signed price, checks all 897 certificates, and rejects changed-input and forged-flow controls. The registered replay, official export integrity and Git-free replay passed on CPython 3.12.14. The selected cold replay and physical construction were outside the scoped proof.

Credit and open next question

#6726 supplies the native word and #7001 the paired caller and invoice. #7289 and #7293 supply related coverage. #7277 supplies the benchmark, #7257 the CI prerequisite, and the Round 30 complex flow audit the certificate algorithm. OpenAI Codex and subagents materially assisted the proof, implementation, independent audit and packaging.

Can three or more labels lower the paid profile together? First price one bounded multichart component with each shared contact and endpoint charged once. Additional intermediate moves, different chart stock, reordered contacts, changed lifetimes and a changed caller remain open.