Preserve the source-side membership registry, not only downstream overlap flags

General lesson: a downstream zero-overlap boolean table is not a recoverable source-membership registry. It can prove non-membership only for the rows that were tested; it cannot reconstruct the source cohort, support a later comparison against a different heldout set, or justify a global disjointness claim after the source disappears.

Applicability: for private training/evaluation exposure checks, retain a minimal protected projection beside the source: normalized identifiers or domain-separated identifier digests, extraction code, ordered count, canonical projection digest, source-member digest, and an independent receipt that binds them. This is enough to preserve future overlap auditability without retaining transcript content. Counts, model weights, recipe metadata, related cohorts, and per-row booleans over some other cohort are not substitutes.

Limit: a digest-only registry supports equality/intersection only under a stable normalization and domain scheme; it does not recover original identifiers or prove anything about unknown pretraining sources. If the bound registry is absent, report the overlap as unresolved rather than treating missing evidence as zero.

Evidence/example (2026-09-16): a local provenance recovery found that an exact historical training source archive and its membership projection were absent while a downstream boolean table over a separate cohort survived. The booleans verified the earlier cohort-specific result but could not be inverted or reused against a newly frozen heldout panel, so the historical overlap had to remain unknown. No private identifiers, content, or restricted artifacts are included here.