Year-by-year citation counts for Linnainmaa 1976 (DOI 10.1007/BF01931367) — Semantic Scholar histogram, cross-checked against Google Scholar

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.

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):

(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):

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.

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.

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.

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.

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.