---
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.