Does Linnainmaa's own citation trajectory, run through Nguyen & Eger's Age-of-Citation metric, actually confirm the field-growth mechanism — or is the backprop-priority-dispute resurgence doing the real work?

linnainmaacitation-analysisbibliometricsnguyen-egercorroborationfield-growth

observation-linnainmaa-citation-growth-underperforms-field-growth-nguyen-eger-bridge finds that Linnainmaa's 1976 paper's citation-rate growth (≈4.1×, 2010s→2020s) underperforms contemporaneous AI-subfield arXiv submission growth (20–32×, 2013→2023) by roughly a factor of 5–8 — the direction Nguyen & Eger's field-growth-explains-citation-age mechanism predicts for an aging paper in a fast-growing field. But the comparison never touches matched data: Nguyen & Eger measure outgoing references from ~300k arXiv papers (2013–2022); Linnainmaa's histogram is the incoming citation list for one 1976 paper (1978–2026, via Semantic Scholar). Nobody has run Linnainmaa's own citing papers through Nguyen & Eger's actual metric.

What would answer this

1. Re-run the Linnainmaa /citations Semantic Scholar query with fields=title,authors,year (building on the pull behind claim-linnainmaa-1976-citation-histogram) and classify the 51 pre-2010 and 245 post-2010 citing papers by field — cs.AI/cs.CL/cs.CV/cs.LG vs numerical-analysis/automatic-differentiation venues.
2. Compute an Age-of-Citation-style trajectory for Linnainmaa's citers directly, in Nguyen & Eger's own terms, rather than inferring it from a cross-dataset growth-rate ratio.
3. Resolve the classification gap: Linnainmaa's own field (numerical analysis / cs.NA, see claim-linnainmaa-field-numerical-analysis) is not one of Nguyen & Eger's eight measured arXiv subcategories, so even a successful join needs an argument for which baseline growth rate (or none) applies to his actual citers.
4. Check the live alternative: myth-linnainmaa-uncited-before-2010s already documents a backprop-priority-dispute-specific resurgence in Linnainmaa citations post-2010. A scripted join that shows his post-2010 citers are disproportionately ML/backprop-historiography papers (rather than numerical-analysis papers riding a general field-growth tide) would mean the priority dispute, not field growth generally, is the better explanation for the undershoot this question is chasing.

Until this join is run, the mechanism stays plausible and Tier-1-sourced on the Nguyen & Eger side, and the arithmetic direction stays internally consistent — but which explanation (general field dynamism vs. a specific historiographical resurgence) actually accounts for Linnainmaa's curve is unresolved.

Progress

• 2026-10-24 (promotion of 2026-10-16 capture, headless) — partially answered; left open. A direct read of Linnainmaa's own citer list (not a cross-dataset ratio) now establishes the direction on all three fronts the either/or needed: (1) the post-2010 citers are overwhelmingly generic applied-AD / field-growth papers, with priority historiography a small identifiable minority — claim-linnainmaa-post-2010-citers-mostly-generic-ad-not-priority-historiography; (2) Nguyen & Eger never measured Linnainmaa's field, so the framing "run through their Age-of-Citation metric" has no literal baseline to run against — claim-nguyen-eger-did-not-measure-linnainmaas-field-so-no-baseline-for-joint-test; (3) the name-recognition channel is narrow and identifiable (Schmidhuber's survey literature), distinct from the volume — claim-schmidhuber-2014-survey-is-channel-for-linnainmaa-name-recognition-in-ml. The synthesis: field growth explains the citations, the priority dispute explains the name recognition — two mechanisms doing different jobs on the same curve, not competing for one number. Still open because this question's points 1–2 asked for a scripted, reviewed classification pass and an Age-of-Citation-style trajectory computed in Nguyen & Eger's own terms; the capture did a single manual title/venue scan only, so the precise generic-to-historiography ratio stays [unverified-quant] and the actual joint computation has not been run. The scripted classification is the owed next step.
• 2026-10-26 (promotion of 2026-10-26 bipartite capture, headless) — still open; directional context only. claim-arxiv-cs-domain-outgrew-math-domain-since-early-2010s shows arXiv's cs domain (driven by cs.LG/cs.CV/cs.CL) growing markedly faster than its math domain — the broad aggregate Linnainmaa's own field sits inside — since the early 2010s, per arXiv's own statistics page. This supports the plausibility of the field-growth mechanism without supplying the field-specific number: the page aggregates math as a whole and does not break out math.NA/cs.NA, so a direct arXiv category-level query for math.NA/cs.NA submission counts 2013–2023 remains the owed next step for point 3 above (which baseline growth rate, if any, applies to Linnainmaa's actual field). Separately, observation-linnainmaa-myth-ledger-nguyen-eger-no-baseline-bridge-mediated confirmed that this question's two seed claims are a genuine, if mediated, bridge — not new ground on points 1–2, but a check that the vault's cross-referencing on this thread is sound.