Two half-proofs on the same point could combine into full proof — except in grave criminal cases, where proof had to be 'clearer than the noonday sun'

The Roman-canon fractional-proof system did permit some addition. Per the 1911 Catholic Encyclopedia entry on "Proof," "imperfect or semi-proof is derived from the testimony of one witness only, or of several singular witnesses," and two imperfect proofs bearing on the same point may combine into full proof. But the arithmetic was not universal. The combination was blocked in the most serious matters — "in criminal cases, in which proof must be clearer than the noonday sun," and likewise in questions of matrimonial validity and grave civil actions. [unverified -- needs primary]

The exception is the interesting part, and it inverts a naive reading of the half-proof system as simple additive bookkeeping (any two halves make a whole). Where the stakes were highest, medieval doctrine explicitly refused to let two soft, imperfect proofs sum into a hard conviction, demanding instead a proof "clearer than the noonday sun" (luce clarior). This is structurally the same instinct the vault encodes in its sourcing floor: a load-bearing quantitative or mechanism claim may not be hardened by piling up two weak corroborations. The Amari case is the sharp instance — claim-amari-1968-saito-experiment-primary-read and its citogenesis counterpart show apparent second witnesses collapsing back into a single source, exactly the addition the criminal-case rule would forbid; the same shape recurs in claim-gates-1976-open-letter-under-ten-percent-paid, which still asks for its independently verified primary printing. See also the combination rule's darker completion device, torture, at claim-medieval-judicial-torture-required-a-half-proof-and-produced-the-completing-confession, and the broader taxonomy at claim-roman-canon-law-rated-one-witness-equal-to-a-private-document.

Because this note asserts a surprising doctrinal rule on a Tier-3/4 encyclopedia source, its verification is routed to question-verify-half-proof-combination-rule-criminal-exception-primary.