The Signal-Coverage Matrix: Stratifying Type and Semantic Errors in Statement Autoformalization

Headline type-correctness (TC%) of LLM autoformalization has climbed from ~53% to ~76% in two years, yet this scalar conceals which errors each method resolves. We propose a signal-coverage matrix that crosses the Lean elaborator (pass/fail) with a semantic-equivalence judgment (equivalent/not), sorting every output into one of four cells: true success (TS), type-only (TO), semantic-only (SO), or both fail (BF). On ProofNet# and MiniF2F-test with DeepSeek V4-Pro across Vanilla, Lean-Retry, Sample-Filter, and Stratified Autoformalization (SAF): (1) the +34 to +36 TS gain across the three elab-feedback methods is ~64% type-stratum recovery, with SO flat on net (87.5% of original semantic errors rescued, 8 newly created). (2) The TO-to-TS rate is 23/61 for each method (Wilson 95% CI [26.6%, 50.3%]), and this stratum-level recovery rate predicts DeltaTS on held-out methods to within 2/186 and renders DeltaTC linear in the Vanilla elab-fail rate across six (model, dataset) cells (R2=0.96). (3) The two judges disagree by 26 to 37 pp on elab-feedback outputs (vs. 7 pp on Vanilla), with 30 to 56% of symbolic-judge false negatives traceable to elaborator-forced rewrites. The persistent residual reduces to two gold-formalization errors. TC% gains should be credited by which cell moved, not by the scalar alone.