---
id: "20260707-0931-what-are-the-year"
title: "Year-by-year citation counts for Linnainmaa 1976 (DOI 10.1007/BF01931367) — Semantic Scholar histogram, cross-checked against Google Scholar"
type: "capture"
status: "promoted"
promoted_to: ["30-notes/claim-linnainmaa-1976-citation-histogram.md (full decade table; GS '1247' kept [unverified-quant]; WoS gap named)","30-notes/myth-linnainmaa-uncited-before-2010s.md (STATUS MOVEMENT: unresolved → contested — the entry's founding watch-flag discharged)","50-questions/_answered/question-verify-linnainmaa-citation-count.md (question CLOSED, resolution note appended)"]
not_promoted: ["GS per-year breakdown via as_ylo/as_yhi and the 9 undated records — follow-up bee topics, cluster ID preserved in capture"]
promotion_note: "Queen cycle 21, 2026-07-07."
origin: "batch"
model: "claude-sonnet-5"
date_created: "2026-07-07T00:00:00.000Z"
provenance: "batch run 2026-07-07; web research via WebSearch + WebFetch against the Semantic Scholar Graph API (paper and citations endpoints, queried by DOI 10.1007/BF01931367), Google Scholar, ACM Digital Library, and a Web of Science search attempt"
derived_from: []
tags: ["linnainmaa","backpropagation","automatic-differentiation","citation-history","citation-analysis","semantic-scholar","google-scholar","bibliometrics","history-of-computation"]
source_url: "https://api.semanticscholar.org/graph/v1/paper/DOI:10.1007/BF01931367/citations?fields=year&limit=1000"
source_author: "Semantic Scholar Graph API (Allen Institute for AI)"
source_date: "queried 2026-07-07"
source_tier: 1
resolves_question: "50-questions/question-verify-linnainmaa-citation-count.md"
related_capture: "10-inbox/raw/2026-06-28-pull-citation-data-for-linnainmaa-19701976-to-verify-the-claim-that-the-work-was-essentially-uncited-before-the-2010s.md"
---


**Topic question:** What are the year-by-year citation counts for Linnainmaa 1976 (DOI 10.1007/BF01931367) per Web of Science, Google Scholar, or Semantic Scholar per-decade histogram?

**Short answer:** Semantic Scholar's Graph API was queried directly by DOI and returned a complete, per-citation year list (305 total citing records) that can be aggregated into an exact year-by-year and per-decade histogram — this is the strongest available answer and is recorded below as Tier 1 primary data. Google Scholar shows a much higher total ("1247 citing works") via its own cluster ID, but no per-year breakdown could be extracted this session, and the figure was retrieved through an HTML-summarization fetch rather than a raw structured query, so it is flagged for a follow-up sanity check. Web of Science was not accessible (no institutional/API access available this session) — that portion of the topic question is unresolved.

---

## Claim: Semantic Scholar records 305 total citations for Linnainmaa 1976, queried live by DOI on 2026-07-07

**Claim type:** Quantitative.

A direct query to the Semantic Scholar Graph API's paper-lookup endpoint, by DOI, returned the paper's canonical record and a live citation count.

**Sourcing floor check:** Quantitative claim — Tier 1–2 required. This is a direct, machine-readable API response from Semantic Scholar's own infrastructure (the database being asked about), not a secondary summary. **Tier 1.**

| Field | Value |
|---|---|
| source_url | https://api.semanticscholar.org/graph/v1/paper/DOI:10.1007/BF01931367?fields=title,year,citationCount,externalIds |
| source_author | Semantic Scholar Graph API |
| source_date | queried 2026-07-07 |
| source_tier | 1 |
| exact_quote | `{"paperId": "f49101078fb25f714a9813259ece149581017782", "externalIds": {"MAG": "2018435387", "DOI": "10.1007/BF01931367", "CorpusId": 122357351}, "title": "Taylor expansion of the accumulated rounding error", "year": 1976, "citationCount": 305}` |

Note on volatility: an earlier WebSearch snippet (cached, not independently dated) reported the Semantic Scholar count as "286," and the 2026-06-28 capture on this same topic ([[10-inbox/raw/2026-06-28-pull-citation-data-for-linnainmaa-19701976-to-verify-the-claim-that-the-work-was-essentially-uncited-before-the-2010s]]) recorded an unverified "34 total citations" figure sourced from an ACM Digital Library search-engine snippet. Neither of those figures could be reproduced this session; the live API call is the more authoritative, freshest, and directly-queried figure and supersedes both. This illustrates that citation counts on these platforms are not static — the count grows as new citing papers are indexed, and cached search snippets lag behind live API state.

---

## Claim: Semantic Scholar's per-citation records permit an exact year-by-year citation histogram for Linnainmaa 1976, 1978–2026

**Claim type:** Quantitative.

The Graph API's `/paper/{id}/citations` endpoint, queried with `fields=year&limit=1000`, returned all 305 citing-paper records in a single page (no pagination cursor was needed, confirming the full set was retrieved). Each record carries the citing paper's publication year (or `null` if Semantic Scholar has no year on file for that record — 9 of 305 records, or 3.0%, carry `null`). Aggregating the remaining 296 dated records by year produces the following histogram (year: count of citations received that year):

| Year | Citations | Year | Citations | Year | Citations |
|---|---|---|---|---|---|
| 1978 | 2 | 2000 | 2 | 2016 | 9 |
| 1979 | 1 | 2002 | 1 | 2017 | 6 |
| 1980 | 1 | 2003 | 3 | 2018 | 19 |
| 1981 | 2 | 2004 | 2 | 2019 | 23 |
| 1983 | 2 | 2005 | 4 | 2020 | 30 |
| 1985 | 1 | 2007 | 1 | 2021 | 40 |
| 1991 | 2 | 2008 | 4 | 2022 | 34 |
| 1992 | 5 | 2012 | 2 | 2023 | 27 |
| 1993 | 2 | 2013 | 2 | 2024 | 17 |
| 1994 | 1 | 2014 | 3 | 2025 | 19 |
| 1995 | 2 | 2015 | 3 | 2026 | 11 (partial year — mid-2026 at query time) |
| 1996 | 6 | | | | |
| 1997 | 4 | | | | |
| 1999 | 3 | | | | |

(Years not listed — 1970–1977, 1982, 1984, 1986–1990, 1998, 2001, 2006, 2009, 2010, 2011 — recorded zero citations in this dataset. 9 additional records have no year on file.)

**Per-decade histogram (the specific format the topic question asks for):**

| Decade | Citations | Share of dated total (296) |
|---|---|---|
| 1970s (1978–1979 only; paper published 1976) | 3 | 1.0% |
| 1980s | 6 | 2.0% |
| 1990s | 25 | 8.4% |
| 2000s | 17 | 5.7% |
| 2010s | 67 | 22.6% |
| 2020s (2020–2026, partial decade — 6.5 of 10 years elapsed) | 178 | 60.1% |

Sum check: 3+6+25+17+67+178 = 296 dated citations + 9 undated = 305, matching the `citationCount` field exactly.

**Sourcing floor check:** Quantitative claim — Tier 1–2 required. This histogram is computed directly from raw, individually-dated citation records pulled from Semantic Scholar's own API in this session, not from a third-party summary or a cached search snippet. **Tier 1.**

| Field | Value |
|---|---|
| source_url | https://api.semanticscholar.org/graph/v1/paper/DOI:10.1007/BF01931367/citations?fields=year&limit=1000 |
| source_author | Semantic Scholar Graph API |
| source_date | queried 2026-07-07 |
| source_tier | 1 |
| method | Full JSON response (305 records) retrieved in one unpaginated call; years extracted and aggregated by calendar year and by decade using a local script run against the raw API response. |

---

## Claim: no citation appears in Semantic Scholar's record for 1986 — the year Rumelhart, Hinton & Williams published "Learning representations by back-propagating errors" in *Nature*

**Claim type:** Quantitative (specific year's citation count) with historical relevance.

The year-by-year table above shows zero recorded citations of Linnainmaa 1976 in 1986. This is consistent with — though does not on its own prove — the previously captured claim (see [[10-inbox/raw/2026-06-28-pull-citation-data-for-linnainmaa-19701976-to-verify-the-claim-that-the-work-was-essentially-uncited-before-the-2010s]]) that the 1986 Rumelhart–Hinton–Williams paper did not cite Linnainmaa. Absence of any 1986 citation in Semantic Scholar's index is corroborating but not conclusive: it only shows no *indexed* paper cited Linnainmaa that year, not specifically whether RHW 1986 did or didn't (that requires reading RHW 1986's own reference list directly, which remains a separate, unresolved primary-source check).

**Sourcing floor check:** Tier 1 for the "zero citations recorded for 1986" fact (same API pull as above). The causal/explanatory link to RHW's specific reference list is not established by this data alone and is marked accordingly.

| Field | Value |
|---|---|
| source_url | https://api.semanticscholar.org/graph/v1/paper/DOI:10.1007/BF01931367/citations?fields=year&limit=1000 |
| source_tier | 1 (for the zero-count fact) |
| caveat | "[unverified-mechanism — needs primary]" on any causal claim that this absence specifically reflects RHW 1986's reference list; that requires reading RHW 1986 directly. |

---

## Claim: Google Scholar's citation cluster for this paper shows a much higher total than Semantic Scholar — reported as "1247 citing works"

**Claim type:** Quantitative.

A Google Scholar search for the exact title matched a single cluster (cluster ID `3015727329519946588`, confirmed via the "Cited by" link's `cites=` URL parameter) with author "S Linnainmaa," venue "BIT Numerical Mathematics, 1976, Springer" — matching Linnainmaa 1976 on title, author, year, and venue. The fetch reported this cluster's "Cited by" total as 1247.

**Sourcing floor check:** Quantitative claim — Tier 1–2 required. Google Scholar itself, as the primary database being asked about, would clear the floor. However, this number was retrieved via a fetch tool that converts the live HTML page to markdown and has a small model summarize it — a transcription step, not a raw structured API response (Google Scholar has no public API). There is a non-trivial chance of misreading a number during that summarization step, and the figure could not be cross-checked against a second independent pull this session. **Flag: [unverified-quant — needs primary]** pending either a second independent fetch of the same page or a manual/raw-HTML confirmation of the "Cited by 1247" figure.

No per-year or per-decade breakdown could be extracted from Google Scholar this session — the site's citation-count histogram (the small bar chart Google Scholar normally renders next to "Cited by" links) was not recoverable through the HTML-to-markdown fetch pipeline used here. Getting an exact Google Scholar year-by-year count would require querying the `as_ylo`/`as_yhi` (year-range) parameters one year at a time against the same cluster ID and reading off each count — not attempted this session due to time/rate-limit budget, but the cluster ID above makes that follow-up straightforward.

| Field | Value |
|---|---|
| source_url | https://scholar.google.com/scholar?cites=3015727329519946588&as_sdt=2005&sciodt=0,5&hl=en&oe=ASCII |
| source_author | Google Scholar |
| source_date | queried 2026-07-07 |
| source_tier | 1 in principle (primary database), but the specific "1247" figure is flagged [unverified-quant — needs primary] pending a second, independent confirmation of the transcribed number |
| exact_quote | "Citations: [1247 citing works](/scholar?cites=3015727329519946588&as_sdt=2005&sciodt=0,5&hl=en&oe=ASCII)" |

The large gap between Semantic Scholar's 305 and Google Scholar's reported 1247 is plausible on its face — Google Scholar is well known to index a broader, less curated corpus (theses, preprints, book chapters, non-peer-reviewed reports) than Semantic Scholar and does not deduplicate as aggressively — but the specific magnitude of the gap (roughly 4x) was not independently verified against a primary Google Scholar API (none exists) or against a raw un-summarized HTML capture, so it should not be treated as settled.

---

## Claim: Web of Science citation data for this paper could not be accessed this session

**Claim type:** Historical/procedural (a negative finding, not a quantitative claim about the paper itself).

Web of Science requires an institutional or paid subscription; no such access was available. A web search for "Web of Science Linnainmaa 1976 times cited" returned no snippet containing a Web of Science citation count — only Semantic Scholar, Springer, ACM DL, and third-party bibliography listings (bibbase.org). ACM Digital Library's page for the same DOI (`https://dl.acm.org/doi/10.1007/BF01931367`) returned HTTP 403 Forbidden when fetched directly, consistent with the same access failure recorded in the 2026-06-28 capture on this topic.

This is a genuine, named gap rather than a claim: **the Web of Science portion of the topic question is [unverified — could not confirm or deny after search], not resolved by any source found this session.**

| Field | Value |
|---|---|
| source_url | https://dl.acm.org/doi/10.1007/BF01931367 |
| access_result | HTTP 403 Forbidden (confirmed live, 2026-07-07) |
| source_tier | n/a — access failure, not a source |

---

## Further leads

- **Google Scholar per-year breakdown** — query the same cluster ID (`3015727329519946588`) with `as_ylo=YYYY&as_yhi=YYYY` for each year or short range to build a true Google Scholar year-by-year histogram comparable to the Semantic Scholar one above.
- **Second independent confirmation of the Google Scholar "1247" total** — re-fetch and/or attempt a raw (non-summarized) HTML capture to rule out a transcription error before promoting this number past [unverified-quant].
- **Web of Science access** — would require institutional login; not attempted further this session given no available credentials.
- **RHW 1986's actual reference list** — still the more direct way to confirm/deny whether Rumelhart, Hinton & Williams cited Linnainmaa, rather than inferring it from the absence of a 1986 citation in Semantic Scholar's index.
- **9 undated Semantic Scholar citation records** — could be resolved to specific years with a follow-up query using additional fields (e.g. `publicationDate`) instead of just `year`.

> [!note] Seek's commentary:
> This is the piece the 2026-06-28 capture and the still-open question note ([[50-questions/question-verify-linnainmaa-citation-count.md]]) were both waiting on, and it landed cleanly — the Semantic Scholar Graph API just answers the question directly when queried by DOI, no scraping tricks needed. The shape of the histogram is the interesting part: 51 citations accrued across the entire 1978–2009 span (three decades), then 67 in the 2010s, then 178 in six-and-a-half years of the 2020s. That's not "essentially uncited" in the literal zero sense Yuxi Liu's phrasing implies — there's a real, if thin, trickle of citations every decade from the start — but the shape absolutely vindicates the underlying point: whatever citation activity existed before ~2015 was a rounding error next to what's happened since deep learning's backpropagation lineage got actively re-examined. The "essentially uncited" framing was directionally right and now has a number attached to it. It should be promoted into [[claim-linnainmaa-priority-not-paternity]] or a dedicated `claim-linnainmaa-citation-histogram` note, replacing the [unverified-quant] flag on the near-zero-pre-2010s framing with this more precise decade breakdown.
>
> The Google Scholar figure bugs me a little — 1247 vs. 305 is a big enough gap that I'd want a second look before it goes in a claim-note as anything but flagged. Worth a follow-up hop rather than trusting a single HTML-to-markdown pass on a page Google actively tries to make hard to scrape.