Linnainmaa's 1976 BIT paper itself contains the reverse-mode structure — Algorithm T sweeps backward through recorded operations accumulating partial derivatives

Until now the vault's evidence that Linnainmaa's work contains what is now called reverse-mode AD rested on Griewank's attributions (2012 read directly; 2014's Table 5 paragraph). The 1976 primary has now been read page-by-page, and the structure is in Linnainmaa's own text:

• Eq. 10 (p. 149): "each coefficient c_{i,p} is the partial derivative of u_i with respect to u_p" — the Taylor coefficients of accumulated rounding error are partial derivatives.
• §4, Algorithm T (pp. 151–152): "When the value u_n has been computed, its Taylor coefficients can be determined using Algorithm T, which utilizes the contents of the previously mentioned tables in reverse order." The recursion (eq. 24) runs cycles i = n, n−1, …, 1 and accumulates chain-rule contributions (c_j^{[i−1]} ← c_j^{[i]} + c_i^{[i]}·d_{i,j}) — the accumulation-of-adjoints structure of the modern backward pass, applied to rounding-error sensitivity rather than learning.

So the mechanism claim in claim-linnainmaa-reverse-mode-single-pass is confirmed in the primary itself, not only in Griewank's retellings.

Bibliographic correction, upstream-applied. The paper's masthead reads "BIT 16 (1976), 146—160"; its title is "Taylor expansion of the accumulated rounding error." The venue "Annales Academiae Scientiarum Fennicae," which entered the vault via a 2026-06-28 further-leads guess at the "(Lin76)" citation key, does not exist as a Linnainmaa venue — no source (the paper's own reference list, Springer's DOI record, dblp, Scholar) places any Linnainmaa work there. The paper's ref [2] also confirms the 1970 Helsinki thesis lineage (claim-linnainmaa-thesis-identity). Freely accessible at the baulab mirror; Springer full text is auth-walled.

Cluster: claim-linnainmaa-rounding-error-problem, claim-linnainmaa-field-numerical-analysis, claim-reverse-mode-multiple-independent-discovery, backpropagation-gap, moc-backpropagation-origins.