Research: execute the A13 native climb with 209,920 fewer CNOTs

[petalas]

Summary

Implement the reached forward A13 source83 warp, target126 rank-one climb and half-ADD in both pinned PR3076 providers using reversible Boolean gates.

- Materialize two HALF and two DOUBLE operations per Gaussian C pair
+ Read aligned half-sources through shifted wire controls

At 69 bits, the complete local boundary saves 209,920 CNOTs against the constructed physical-shift control, with the same 996,672 Toffolis. Both counts charge native permutation SWAPs, phase signs and the final half-ADD. The implementation uses no component scratch and returns its 68 clean carries.

The proof covers the quarter grid and P+5 signed bits for P=3..128, conditional on PR3086's exact physical entrance. The package retains the reproducible generator, exact source pins, proof, controls and evidence. Credit PR3086's native-format boundary, PR3094's scalar circuits, PR3080's shifted adder and the retained supplier lineage.

Evidence

• Before: physical-shift control at 69 bits: 2,126,656 CNOTs and 996,672 Toffolis.
  After: direct native boundary: 1,916,736 CNOTs and 996,672 Toffolis.
• Registered Python 3.12 cold replay passed, including both fresh native bindings, 279,616 parity-matched truth columns per sign/implementation and literal inverses, 18 complete native fixtures, and a complete 69-bit control/inverse.
• Nine optimized behavioral groups, Ruff E/F/B/SIM/UP and formatting passed. Publication-byte check passed all 38 package/input files at e5c265f.
• Reproduce with uv run --python 3.12 --no-project python -B scripts/research_package.py --package research/rank7-reversible-native-climb. The README gives external-output commands and exact coverage.

Merge Danger

Door: two-way

Blast Radius: package

This is a conditional local construction. The producer/residual adapters, clean-stock production, physical routing/access, later consumers and complete supplier bill remain open. Gate counts use unit-cost arbitrary-wire Boolean operations. No circuit optimum, new kappa or selected-frontier change is claimed. Hosted CI is separate from the recorded local checks.