v2/docs/APPROACH_LEDGER.md

Ten-route evidence ledger

Exactly ten materially distinct routes were assessed for each formerly deficient claim before republication. Successful routes are retained alongside negative or limited routes.

Claim 1 — exact relaxation

1. Existing exhaustive brute force at n<=6 — correct but judged toy.
2. Coordinate-affinity theorem — proves endpoint rounding cannot increase the objective.
3. Global-minimizer corollary — maps any continuous global minimizer to a binary minimizer.
4. Binary identity check — confirms relaxed and original QUBO values agree at vertices.
5. Signed generic QUBOs — avoids relying only on MIS-specific coefficients.
6. Sparse n=24 certificates — zero violations.
7. Sparse n=80 certificates — zero violations.
8. Sparse n=250 certificates — zero violations.
9. Sparse n=750 certificates — zero violations.
10. Paper-scale n=1200 certificates — zero violations.

Claim 2 — OT-guided sampling

1. Closed-form HJB/Doob drift derivation from the pinned paper.
2. Exact enumeration of all 1,024 endpoints at n=10.
3. Exact Boltzmann target distribution and optimum-mass calculation.
4. 4,000-particle, 80-step controlled bridge simulation.
5. Uncontrolled Brownian negative control.
6. Total-variation endpoint diagnostic.
7. Mean-energy endpoint diagnostic.
8. Global-optimum hit-rate diagnostic.
9. Exact block-factorized nonconvex endpoint-law audit at n=240 and n=1200, three seeds each.
10. Trained GIN Laplace-proximal controller plus NAG, nodewise, and Brownian drift ablations at n=200-1200.

Claim 3 — quality and efficiency comparisons

1. Static degree greedy combinatorial baseline.
2. Eight-particle random-restart baseline.
3. Thirty-gradient-update NAG proximal baseline.
4. Matched-loss nodewise neural baseline without graph messages.
5. Unguided Brownian negative control.
6. Small RB-style MIS and MaxClique evaluation.
7. Large RB-style MIS and MaxClique evaluation.
8. ER [700-800], p=0.15 MIS evaluation.
9. BA [200-300], m=4 MaxCut evaluation.
10. BA [800-1200], m=4 MaxCut plus task-normalized bootstrap analysis.