DUP-RISK: the Amari/Saito and Gates seed notes bridge through the medieval half-proof rule — but the concept is already in the vault

Outcome: gated as duplicate-risk (max_cosine 0.805). The seed asked whether claim-amari-1968-saito-experiment-primary-read and claim-gates-1976-open-letter-under-ten-percent-paid (cosine 0.75, unlinked) share a genuine bridge or only a superficial "1970s-computing-history" resemblance. The bridge is real, and it is not the surface: both notes are flagged by the vault for the same reason — each load-bearing claim reached the vault only through a single imperfect intermediary. Amari's 1968 book was read only via Schmidhuber's partial, lossy OCR scan (pp. 94–135); Gates's 1976 letter only via DigiBarn's web transcription. In medieval Roman-canon law each such single document is a semiplena probatio — a half-proof, insufficient alone; full proof needs two witnesses (or a confession). The vault's own caveats re-derive exactly this: the Amari note wants a fuller scan, the Gates note says "an independently verified primary printing would harden it" — both are calls for the second witness that completes a half-proof. But this epistemic content is already captured by claim-roman-canon-law-rated-one-witness-equal-to-a-private-document (0.805, the gate's nearest neighbor), so writing a full bridge note would duplicate it. The durable value here is structural, not prose: the previously-unlinked seed notes are now wikilinked to each other and to the half-proof note (done this session), and the vault's open question on the torture-completion mechanism can now be closed with two sources. Recording the gate result, not a monograph, is the correct outcome.

Hop chain

Hop 1: "Half-proof" doctrine — https://en.wikipedia.org/wiki/Half-proof (WebSearch synthesis), Tier 3-4 (definitional).

• Hook type: cross-domain bridge (the seed's shared verification caveat → legal epistemology).
• Hook: both seed notes rest on one intermediary; medieval law had a name for one-witness/one-document evidence.
• Why followed: leaves both seed topics (neural nets, BASIC piracy) for the connective tissue that the vault_bridge tool flagged as an unlinked cluster.
• Key findings: half-proof (semiplena probatio) = one witness OR one private document, introduced by the 1190s Glossators (Azo: "Full proof is by two witnesses, therefore half proof by one"); full proof = two witnesses or confession.

Hop 2: Langbein, Torture and the Law of Proof + Karnavas synthesis — https://michaelgkarnavas.net/blog/2016/05/13/historical-aspects-reasonable-doubt-in-dubio-pro-reo/ , Tier 2-3 (named legal writer citing Whitman/Shapiro; Langbein direct-ish via WebSearch).

• Hook type: mechanism question (zoom-in).
• Hook: how did a half-proof become a full proof — what completed it?
• Why followed: the vault holds an OPEN QUESTION (question-verify-half-proof-torture-completion-mechanism) flagging this exact mechanism as [unverified-mechanism -- needs primary].
• Key findings: "The torture could not be ordered unless there was 'semiplena probatio' or 'half-full proof'" (Whitman p.115). Torture was the licensed instrument for producing the confession that completed a half-proof. Langbein: the two-witness/confession system "was unworkable standing alone," so torture "extended" it.

Hop 3: James Franklin, "Pre-history of probability," Oxford Handbook of Probability and Philosophy (OUP 2016) — https://web.maths.unsw.edu.au/~jim/prehistory.pdf (extract_pdf, sha256 9ba890a0…, tls:unverified), Tier 1 (author's own published chapter).

• Hook type: cross-domain bridge / cross-time (zoom-out): medieval law → mathematical probability.
• Hook: was the fractional-proof system the ancestor of mathematical probability?
• Why followed: the road home — probability is the mathematical bedrock of the stochastic descent in the Amari seed note.
• Key findings: Franklin confirms the mechanism independently — torture "could be applied only when there was half-proof of guilt (to produce the other half)." Law was "the matrix in which most development of the concepts of probability took place," and the founders of mathematical probability were all lawyers or sons of lawyers (Fermat, Huygens, de Witt, Cardano, Pascal). BUT: "There was never any finer grading attempted, such as quarter-proofs," and "the law of evidence… has almost entirely refused to accept quantification… refused all attempts to apply Bayesian formulas in court."

Hop 4: "Proof" / combining imperfect proofs — https://www.newadvent.org/cathen/12454c.htm (Catholic Encyclopedia 1911) + WebSearch synthesis, Tier 3-4 (definitional, cross-checked).

• Hook type: mechanism question (zoom-in): do two half-proofs sum to a full proof?
• Hook: if a second independent primary is the "second witness," does the vault's completion rule match the medieval arithmetic?
• Why followed: to test whether the bridge's completion parallel is literal.
• Key findings: a single witness is semiplena probatio, "to be supplemented, in default of a second witness, by torture or by reference to oath"; two imperfect proofs on the same point may combine to full proof — EXCEPT "in criminal cases, in which proof must be clearer than the noonday sun" (and matrimonial-validity and grave civil actions), where they may not.

Surprise: expected the fractional legal proofs (½-proof, indiciolum) to be a clean ancestor of mathematical probability — found Franklin argues the opposite, that the law of evidence developed the concepts of uncertain reasoning yet refused quantification, never even attempting a quarter-proof, and still bars Bayesian math from court.

Surprise: expected "two witnesses = full proof" to be simple additive arithmetic (any two half-proofs sum) — found medieval doctrine explicitly blocked the addition in serious criminal cases ("clearer than the noonday sun"), which mirrors the vault's own sourcing floor refusing to let two soft corroborations harden a load-bearing quant/mechanism claim (cf. the Amari case, where Wikipedia's apparent second witness collapses to citogenesis from the same source).

Saved hooks not followed:

• The founders of mathematical probability were all lawyers or sons of lawyers (Fermat, Huygens, de Witt, Cardano, Pascal) — Franklin — a "person behind the thing" cross-domain cluster; probability born from the legal milieu by breaking law's refusal to quantify.
• "Silurus his twigs" / bundle-of-sticks image for combined imperfect proofs (in some sources, not the Catholic Encyclopedia) — a cultural-resonance image for corroboration worth its own capture if a clean primary surfaces.
• Ann Hardy's OS credited to her husband, and Davidoff dropped from the copyright notice — the other real bridge the vault_bridge flagged (authorship-credit fragility), unlinked to the Gates note; a separate chain.

post-worthy: no — the bridge is real and now wired into the graph, but its concept duplicates an existing note; the two surprise lines and the resolved open-question mechanism are the harvestable value.