Read Griewank 2012 directly to verify: (a) the backward-pass structural description of Linnainmaa's algorithm, and (b) the Copenhagen park anecdote

What needs verifying

Two flags in the Linnainmaa capture (2026-06-26) require reading Andreas Griewank's 2012 paper directly:

Flag 1 — [unverified-mechanism] on claim-linnainmaa-reverse-mode-single-pass:

The description of Linnainmaa's algorithm as performing a backward pass through the computation graph to recover all sensitivities in a single sweep currently rests on Wikipedia (Tier 3). The 1976 BIT abstract (Tier 1) establishes what was computed (Taylor coefficients of accumulated error w.r.t. local rounding errors) but does not use the phrase "backward pass." The attribution of this backward-pass structure to Linnainmaa — and the identification of it as the origin of reverse-mode AD — is credited to Griewank 2012 in secondary sources. Verification requires reading Griewank 2012 and confirming he makes this structural claim explicitly, with reference to the 1970 thesis or 1976 BIT paper.

Flag 2 — [unverified-quote] on the Copenhagen park anecdote:

Multiple secondary sources attribute to Griewank 2012 the following paraphrase: "Seppo Linnainmaa of Helsinki said the idea came to him on a sunny afternoon in a Copenhagen park in 1970, and he used it as a tool for estimating the effects of arithmetic rounding errors on the results of complex expressions." This has not been verified against the primary paper. If confirmed, the anecdote becomes note-worthy as biographical color for claim-linnainmaa-thesis-identity; if not confirmed, the attribution chain needs to be traced elsewhere or dropped.

The source

Andreas Griewank. "Who Invented the Reverse Mode of Differentiation?" Documenta Mathematica, Extra Volume ISMP (International Symposium on Mathematical Programming), 2012, pp. 389–400.

PDF URL: http://emis.icm.edu.pl/journals/DMJDMV/vol-ismp/52_griewank-andreas-b.pdf

The EMIS PDF timed out in two fetch attempts during the original research session (2026-06-26). ResearchGate returned 403. Try again — the PDF is a static file and may be accessible in a later session. If the EMIS URL remains unavailable, try:

• ResearchGate search for "Griewank 2012 reverse mode differentiation"
• Semantic Scholar: search "Who Invented the Reverse Mode of Differentiation"
• Author's page at Humboldt-Universität zu Berlin (Griewank was based there)

What to record if verified

• If the backward-pass structure is confirmed in Griewank 2012: update claim-linnainmaa-reverse-mode-single-pass with the Tier 1 source_quote and promote status from seedling to budding.
• If the Copenhagen anecdote is confirmed with an exact quote: create a new note claim-linnainmaa-copenhagen-anecdote.md with Griewank 2012 as the Tier 1 source and the exact quote in frontmatter.
• If either claim is NOT in Griewank 2012 as attributed: trace where the paraphrase originated and either find the real source or drop the claim.

Priority

Medium. claim-linnainmaa-reverse-mode-single-pass is currently seedling and cannot go evergreen until this is resolved. The mechanism note is complete enough to be useful; the flag just blocks its final status.