bundle/v0/APPENDIX_ROUTES_REVIEW_RECEIPT.md

Appendix routes scientific review receipt

Outcome: three missing formulations locally validated; all claims HOLD

The independent backend now implements Appendix A.2.1's empirical W1 portfolio route, Appendix A.3.1's W1 absolute-regression route, and Appendix A.3.2's W2 squared-regression route. Each lower-level value derivative, empirical OT derivative, and active-coverage total derivative was checked against central differences at a nonzero transport point.

Last hardened bounded evidence (historical after source freeze)

• Canary: appendix-routes-bounded-v4; one deterministic task per route; two outer steps; 1.3502885 seconds externally.
• Empirical W1 portfolio: OT/conic/combined relative gradient errors 1.93984457134682e-11, 3.3112261505737953e-6, 6.045940024069482e-6; maximum conic/OT-optimality residuals 2.2470190510991542e-11 / 4.218847493575595e-15.
• Absolute regression: OT/conic/combined relative gradient errors 1.0968022561153782e-11, 7.337391946191968e-8, 2.834630958624701e-6; maximum conic/OT-optimality residuals 1.6667875968323642e-9 / 2.1316282072803006e-13.
• Squared regression: OT/conic/combined relative gradient errors 1.0479655422729093e-11, 2.0242615265999206e-6, 1.2198092636906306e-6; maximum conic/OT-optimality residuals 9.079005991452505e-9 / 2.205524651799351e-11.
• Squared-route terminal root objective 47.03610807379594 is squared after solve to 2212.3954627298112; its value gradient uses the same chain rule.
• Bundle receipt SHA-256: f7cff4d083b73ddcbb9d7675a92fda685d9e49ea38011fde8f075a50e72013f5.

The subsequent clean-snapshot enforcement changed the live source tree, so the v4 validator now correctly rejects this receipt as stale. Config appendix_canary_v5.json is frozen and unexecuted; it must run once after the exact paper lane is committed and clean.

Audit assumptions

• The empirical portfolio formulation removes Appendix A.2.1's redundant sample epigraph variables after algebraic reduction under full support Xi=R^k, uniform empirical weights, and linear loss. The retained SOCP has the same robust value and portfolio decision.
• W1/W2 finite-support distances are solved exactly with uniform empirical marginals. The reported metric derivative is an envelope subgradient for the returned optimal coupling; nonzero deterministic instances are used for finite-difference validation.
• Exact-zero handling is triggered only by an exact zero transport value/cost. Scale-dependent dead zones were removed, and tiny distinct shifts remain nonzero.
• The absolute route solves mean(abs(y-Xw)) + epsilon*||L^-1[-w;1]||_2.
• The squared route solves the nonnegative root expression from Appendix A.3.2, then squares the value after solve. It is not silently treated as an absolute-loss estimand.
• All three routes use the paper's plain constant-step metric update, clipping, eigenvalue projection, and Cholesky refactorization. These numerical modifications are outside the ideal recurrence audited for C2.
• The canonical validator binds the manifest, receipt, selected config, live source/input tree, plan, route/task/order/implementation, regenerated datasets, complete trace continuity, and terminal states. Each conic row retains dual/slack/q data and a seven-part KKT residual certificate; the checked OT solve retains coupling and dual potentials with marginal, dual-feasibility, complementarity, and gap checks.

Why claims remain HOLD

• Each route has only one deterministic dataset and two outer iterations; no result estimates a paper-scale mean or uncertainty.
• Discrete and GMM suites share the empirical W1 formulation but only the discrete task was exercised here.
• No converged run, clean Linux rerun, out-of-sample evaluation, coverage ablation, or paper-scale raw matrix exists.
• The C2 theorem audit is HOLD / inconclusive: finite stationarity behavior cannot verify the infinite-horizon theorem or logically falsify its conditional form.

No presentation, remote compute, paid service, inference provider, push, publication, or submission action was taken.