[aliromman]

The new fee-region tool prices two paid fee patterns together against a complete invoice change. Exact hinge inequalities and rational polygon clipping return the full feasible tradeoff region, binding ranks, and an optional whole-fee budget with a next-count rejection witness. This can guide route/restoration choices before a full caller replay.

Six tests pass normally and under -O on Python 3.12. They compare 30 random regions to independent pairwise line intersections and 1,080 direct integer-grid tariff checks, then cover fractional vertices, zero slack, mismatched or credited fees, large counts, limits, and isolated CLI input hashes.

The guide proves sufficiency/completeness for the stated increasing-concave tariff class and explains why it is stronger than an all-power test. Physical fee completeness, source maps and κ admission remain open obligations. Current main/priorities/overlap rechecked. Coordination: Discussion #5752.

Base: de5ec2e7a6074068452f45b1a191b5c72832df4a. Verified head: dc75e2175b09e9c270ff10ecb61075ed1411b414.

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.