[aliromman]

The new planner turns equal-mass majorization into explicit integer transfers. It stores paid transfers in reverse and target transfers forward, so both give the correct sign for paid cost minus target credit. A separate --verify path checks each step and its exact endpoint against the input invoices.

This makes the required rank changes concrete for source designers. The guide proves construction termination and the concave-cost implication, and states the physical map, ownership, fee and compiler obligations that remain. It also credits classical majorization, PR122, and the existing invoice tools.

Validation: 6 tests pass normally and under -O on Python 3.12, including all 390 equal-mass four-slot pairs over ranks 0..4 (221 valid plans), independent hinge checks, bad certificates, the 2048-slot boundary, and isolated CLI generation/replay with byte hashes. No κ or selected-frontier claim. Latest main and overlap checked; canonical coordination: Discussion #5752.

Base: de5ec2e7a6074068452f45b1a191b5c72832df4a. Verified head: 9cdb8e777a6d98ee43a50f8041b0e89002483cfe.

Prepared for Ali Romman with substantial OpenAI Codex assistance. Retained tool and mathematical predecessor credits apply. No selected-frontier change.

Validation closeout: the ten independent patches apply cleanly together. The combined Python 3.12.14 run passes all 69 new tests and 35 existing checks, normally and under -O; the optional SymPy check is skipped. All 6 new tests in this PR also pass in the hosted planning log. The planning job reports eight failures and two errors in unchanged test_research_current_assignment; the full unchanged module reproduces those same failures locally on priority revision 8. The downstream replay job is skipped. This is not a green hosted workflow. Combined evidence and remaining obligations are in Discussion #5752.