Remark. The two-epsilon theorem is a decision bound [ftip-007I]
✍️source

The bound in Theorem [ftip-007H] follows directly from the uniform approximation condition. It compares two maximizers on one fixed finite candidate set. It does not describe how either score was learned or how a policy changes when that score becomes a training objective.

The result is useful because its transfer assumption is visible. To apply it after an update or a larger search, the uniform bound must hold on the outcomes that the new procedure can actually select. The verifier evidence of Definition [ftip-0047] can support such an audit, but reproducible evidence alone does not establish the bound.

Remark. The two-epsilon theorem is a decision bound [ftip-007I]
✍️source

Proxy reward and verifier fidelity [ftip-007F]

Definition. Uniform proxy approximation [ftip-007G]

Theorem. Uniform proxy error gives two-epsilon selection regret [ftip-007H]

Proof.

Remark. The two-epsilon theorem is a decision bound [ftip-007I]
✍️source

Example. Counterexample: Small average proxy error fails after distribution shift [ftip-007J]

Definition. Repeated verifier audit [ftip-007K]

Theorem. Independent false accepts amplify with candidate count [ftip-007L]

Proof.

Theorem. A false-accept union bound without independence [ftip-007M]

Proof.

Example. Weight updates and candidate selection are different proxy operators [ftip-007N]

Remark. What verifier error rates do not identify [ftip-007O]

Theorem. Uniform proxy error gives two-epsilon selection regret [ftip-007H]

Proof.

Definition. Verifier evidence [ftip-0047]