A Sharp Finite-Window No-Free-Lunch for Coverage-Sufficient Dependence: Exact Block-Conformal Coverage under Structural Envelopes

A finite score window cannot identify the dependence functional needed by the block-conformal coverage bound, even over stationary ergodic binary processes. For every window length n, two processes can have the same observed n-window law while their two-block joint-to-product total variation differs by 1/2. Over the stationary ergodic binary class with known uniform marginal, the resulting exact minimax absolute estimation risk is (1-2^-B)/2. A second construction gives identical complete calibration laws but rank-miss probabilities on opposite sides of the nominal release level, forcing any pointwise-valid rule to refuse on a benign member; the construction extends to every conformal rank. The complete score law can identify score dependence but still need not identify full-process mixing. We therefore target the weaker score-block discrepancy that is sufficient for coverage: miscoverage is bounded by the exact conformal rank term plus this discrepancy, itself at most B beta_S(h) for a stationary score process. Because one finite trajectory cannot supply that envelope without additional assumptions, we give a conservative structural route based on an observed finite-state Markov state, fixed emissions, independent transition evidence, and Dobrushin contraction. Controlled experiments test that premise-matched route; named-data diagnostics are not dependence certificates, and all estimated methods still refuse at h=27.