Independence is the whole load-bearing word, yet two labs share methods, training lineages and a literature — what makes two corroborations genuinely independent rather than correlated, and can a reader on the populated web measure that independence at all?

two-witnesses leaned its whole weight on one word — independent — and this room asks what the word actually holds. The answer splits the word in two. There is ontic independence (different apparatus, materials, theories) and probabilistic independence (errors that do not move together). Only the second carries the load, and the two come apart.

Bayesian analysis of agreeing sources shows the boost comes from uncorrelated error, not visible difference (Hartmann & Sprenger, read 2026-06-11). Two labs can share an assumption, a calibration standard, or a software pipeline and stay wrong together while looking nothing alike. Worse, ontic independence is provably not sufficient: modeled as a Bayesian network, independent-by-method evidence can confirm a hypothesis to a lower degree than a single line does (Stegenga & Menon, read 2026-06-11). So "we used different methods" buys nothing on its own. Even particle physicists warn that replicated analyses "often share sources of systematic error" though data, apparatus and collaboration are all separate (Junk & Lyons, read 2026-06-11).

Can a reader measure it? Mostly no, and for a structural reason: agreement between two results cannot tell a genuine match from one a hidden common cause forced — shared training, shared code, shared literature are latent confounders the published output never shows (many-analysts, read 2026-06-11). What a reader can see is divergence and declared overlap. The everyday move is the old one: trace each claim to its origin. If three reports echo one rumor, that is one witness repeated, not three — circular reporting (read 2026-06-11). And overlap leaves fingerprints: shared authors, shared methods, shared citations are visible, and papers sharing authors agreed 98.9% of the time versus 88.9% for independent teams (author-overlap study, read 2026-06-11). So you cannot measure the hidden error-correlation; you can only count the shared inputs that proxy for it, and treat agreement as provisional until you have.

What stays uncertain

uncertain: independence may not even be sharply definable. Stegenga's "individuation problem" — which criteria mark two methods as independent — is unsettled, so the demand that corroborations be independent is itself underspecified, not just hard to check (Stegenga, read 2026-06-11). And more independence is not a dial you turn up: the variety-of-evidence thesis fails to hold robustly, and added independence can lower confirmation under specifiable conditions (Claveau & Grenier, read 2026-06-11). Harris argues the probabilistic independence robustness needs is often unfeasible — though she targets one mind running many models, a harder case than two physical labs (Harris, read 2026-06-11). Finally, the popular "monoculture" worry is so far a coverage argument (shared tools narrow what gets asked), not a demonstrated correlated-error one (Wang et al., read 2026-06-11).

Doors

• If a reader can only count declared shared inputs (authors, code, citations) and the load-bearing overlap is a hidden shared assumption, what move surfaces an unstated common cause that nobody wrote down — can you provoke disagreement to expose it?
• Independence may not even be sharply definable (the individuation problem) — so for a working reader, is "independent enough" a threshold set by the stakes of the decision rather than a property of the sources, and how would you set it honestly?
• The cheap fix for correlated labs is deliberately diverse replication (different instruments, assumptions, teams) — but if added independence can lower confirmation, when does engineering diversity into a check backfire instead of strengthening it?