---
title: "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?"
type: "question"
status: "open"
date_raised: "2026-10-13T00:00:00.000Z"
tags: ["linnainmaa","citation-analysis","bibliometrics","nguyen-eger","corroboration","field-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.