{"id":"3fee9d6a-55a1-4b07-8957-075f64721436","arxiv_id":"2507.06034","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A nine-language PageRank analysis of 237 philosophers shows culturally variable but Western-dominated rankings, and reduced-matrix analysis of 21 Presocratics surfaces hidden links, one later confirmed as a direct Wikipedia hyperlink.","lead":"This paper ranks 237 philosophers in nine Wikipedia languages using PageRank, finding that Aristotle and Plato lead in most editions while each language edition also favors its own cultural figures. It uses a reduced network method to uncover hidden links among 21 Presocratic philosophers, including connections that later appeared as direct Wikipedia hyperlinks.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 237-philosopher sample is drawn from a single French Wikipedia list and filtered by all-nine-edition presence, so the Western-dominance and reference-hub conclusions may reflect sample construction rather than Wikipedia's knowledge structure.","rationale":"The reader identified the same weakness: the dataset is built from a French Wikipedia list intersected across nine editions, making the all-nine-editions filter a likely source of Western bias. This is the most load-bearing concern because it affects the paper's primary comparative claims—the Western dominance in the Θ-score ranking and the broader claim that philosopher articles are reference hubs. The reduced Google matrix hidden-link analysis is also reliant on an unproven 'short indirect path' assumption, but that assumption is explicitly stated and partially validated by prospective examples (e.g., the later appearance of the Pythagoras–Empedocles link), whereas the sample-selection issue is unaddressed and undermines the multicultural framing of the entire paper. The reference-hub claim may also be partly tautological: selecting only internationally recognized philosophers with articles in all nine editions likely selects for highly cited, low-citing articles, making the hub conclusion an artifact of the sample. The proposed concrete test—rebuilding the sample from an independent, multilingual source—would settle whether the findings are robust. Since the reader's conditional verdict already requires addressing sample bias and data availability, no new verdict adjustment is needed.","tokens_in":16397,"tokens_out":8249,"duration_ms":95004,"concrete_test":"Construct an alternative list of philosophers from a source independent of the French Wikipedia list—e.g., the union of all articles categorized as philosophers in the nine editions, or Wikidata entries with occupation 'philosopher'—apply the same all-nine-editions filter, and recompute the Θ-score and the PageRank/CheiRank positions. Compare (i) the fraction of non-Western philosophers in the top 38 Θ-score positions and (ii) the (K,K*) distribution of the new set against the full-Wikipedia baseline. If the top 38 remain entirely Western and the set still lies above the bisectrix, the cultural and hub conclusions are robust; if not, they are artifacts of the French-list selection.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central cultural comparisons and the 'reference hub' conclusion rest on a sample that is not shown to be representative. Section 2 states that the 237 philosophers were extracted from a French Wikipedia list ('Liste de philosophes par année de naissance', ref. [20]) and then reduced to those with a dedicated article in all nine editions. Because the source list is French-language and the intersection removes any philosopher missing from one edition, the surviving set is enriched for figures already prominent in a Western/French encyclopedic tradition. The paper's headline result—that only Western philosophers occupy the first 38 Θ-score positions (Section 4)—and the statement that philosopher articles act as 'reference hubs' rather than 'foundational seeds' (Section 5) may therefore be properties of how the sample was assembled rather than of Wikipedia's cross-linguistic knowledge structure. The data availability section promises a DOI but provides no dataset or selection script, so the composition of the list cannot be independently audited. If the sample had been drawn differently, the Western-dominance and hub-versus-foundation findings could change; the paper does not test this.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper analyzes Wikipedia's knowledge network by computing PageRank and CheiRank for 237 philosopher articles across nine language editions (Arabic, Chinese, English, French, German, Japanese, Portuguese, Russian, Spanish) using May 2017 snapshots, aggregates the rankings with a Theta-score, compares the results with the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy, and applies the reduced Google matrix to a subnetwork of 21 Presocratic philosophers in the English edition to uncover hidden links. The main findings are that Aristotle and Plato occupy the top positions in most editions, that Western philosophers dominate the top of the combined ranking, that philosopher articles act more as reference hubs than as foundational seeds, and that hidden links such as [Melissus of Samos → Xenophanes] and [Leucippus → Parmenides] can be interpreted as intellectual relationships. The paper also reports an out-of-sample validation in which a predicted hidden link [Pythagoras → Empedocles] later became a direct hyperlink.","tokens_in":16551,"tokens_out":7722,"duration_ms":78626,"significance":"If the results hold, the paper provides a scalable method for quantifying cultural influence in Wikipedia across languages and demonstrates that the reduced Google matrix can reveal latent historical connections in a knowledge network. The strengths include the use of standard Google matrix methods, an explicit definition of the Theta-score, a clear presentation of the PageRank-CheiRank plane, and a concrete out-of-sample validation of one hidden link. The novelty lies in applying these techniques to philosophers and the Presocratic subnetwork, and the work connects network analysis with the history of philosophy. However, the significance is currently limited by concerns about sample selection and reproducibility, which need to be addressed before the conclusions can be fully accepted.","major_comments":[{"comment":"The construction of the 237-philosopher sample from a single French Wikipedia list intersected with the requirement of dedicated articles in all nine editions introduces a selection bias that is not addressed. This filter enriches for figures already prominent in a Western/French encyclopedic tradition, so the claims that only Western philosophers occupy the first 38 Theta-score positions and that philosophers are \"reference hubs\" rather than \"foundational seeds\" may reflect sample construction rather than properties of the Wikipedia knowledge network. The paper should demonstrate robustness by using an independent source list or by testing the sensitivity of the Western-dominance and hub-versus-foundation conclusions to the inclusion criterion.","section":"Section 2 / Section 4 (Table 2)"},{"comment":"The data availability statement promises a DOI and a repository but provides no actual dataset, selection script, or reduced Google matrix code. Because the central results depend on the exact list of 237 philosophers and the 2017 Wikipedia dumps, the absence of these materials prevents independent replication and verification of the selection procedure. The paper should either provide the data and scripts or clearly state where they will be made available before publication.","section":"Declarations (Availability of data and material)"},{"comment":"The interpretation of Gqr hidden links relies on an unvalidated assumption that a direct link present in one similar subnetwork but absent in another should appear as a short indirect path in the latter. The two supporting examples ([Leucippus → Parmenides] and [Pythagoras → Empedocles]) are anecdotal; the paper does not systematically test this assumption by comparing Gqr values across the nine editions or against a null model. Without such a test, the claim that hidden links correspond to intellectual relationships remains speculative. A systematic validation would strengthen the paper considerably.","section":"Section 4 (The Presocratics in Wikipedia)"},{"comment":"The analysis uses the standard damping factor alpha = 0.85, but no sensitivity test is reported. Since the reduced Google matrix decomposition and the rank positions may depend on alpha, the paper should show that the main conclusions (e.g., the top 10 lists and the dominant hidden links) are stable for other reasonable values of alpha, such as alpha = 0.5 or alpha = 0.9.","section":"Section 3, Eq. (1)"}],"minor_comments":[{"comment":"Table 2 contains repeated rank numbers (e.g., two entries at rank 86 and two at rank 126) with no explicit tie-breaking rule; please state whether ties are allowed and how they affect the \"first 38 positions\" count.","section":"Table 2"},{"comment":"The text says the sum is performed over the N(N-1)/2 pairs of items, but the formula's normalization and the statement that each term equals 2 on disagreement imply a sum over unordered pairs; the description should be clarified to avoid confusion.","section":"Section 3, Eq. (7)"},{"comment":"The sentence \"Aristotle ranks first, followed by Plato, with the exceptions of the Russian and Chinese editions\" is imprecise; Aristotle is first in all editions, and it is Plato's second-place position that varies. Please rephrase for clarity.","section":"Section 4, first paragraph"},{"comment":"The SEP and IEP data were accessed in November 2019, while the Wikipedia snapshots are from May 2017; please state whether this temporal mismatch could affect the comparisons and whether the lists of philosophers were adjusted accordingly.","section":"Section 2"},{"comment":"The legend for the Presocratic philosophers uses colored markers that may be difficult to distinguish in grayscale; consider using distinct symbols instead of colors alone.","section":"Figure 3"}],"recommendation":"major_revision","confidential_remarks":"The main concern for the editor is sample selection bias, which requires either a robustness analysis or a clear acknowledgment as a limitation. The reproducibility issue is also important given the journal's standards for data availability. The paper is otherwise methodologically sound, but the central claims about Western dominance and reference hubs need to be supported by additional tests."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a competent application of the reduced Google matrix to a new topic, with one genuinely nice prospective finding, but the headline cultural claims are weaker than the analysis because the sample is built from a French Wikipedia list intersected across nine editions. If the authors publish the selection scripts and re-run on a more balanced sample, the empirical core would be credible.\n\nWhat's new: the nine-edition rankings, the Theta-score aggregation, the SEP/IEP comparisons, and the hidden-link table for 21 Presocratics. None of these appear in the cited references. The methods are standard and correctly applied; the reduced Google matrix derivation is fine. The Pythagoras-to-Empedocles hidden link that later became a direct Wikipedia hyperlink is real supporting evidence, and the Xenophanes-Gorgias link via the pseudo-Aristotelian text is a nice interpretive touch.\n\nThe soft spot is the sample construction. Section 2 says the list came from a French Wikipedia page 'Liste de philosophes par année de naissance,' then filtered to those with articles in all nine editions. That intersection is not a representative sample of philosophical importance across languages; it is a set of figures who are already prominent enough to have articles everywhere, and the source list is French. So the finding that only Western philosophers occupy the first 38 Theta-score positions is likely an artifact of selection, not a discovery about Wikipedia's cultural structure. The same concern applies to the 'reference hubs, not foundational seeds' conclusion: the 237 selected thinkers are not a random or stratified sample of philosophers, so their position in the (K,K*) plane may not generalize. The paper does not test this.\n\nThe other issues are minor but real: no dataset or scripts available despite the promised DOI, damping factor fixed at 0.85 with no sensitivity check, and the 'short indirect path' assumption behind hidden links is asserted rather than demonstrated. The Gorgias recomputation is a good partial validation, but it is one case.\n\nWho is this for? Digital humanists and wiki-curation researchers will get value from the quantitative rankings and the hidden-link case. It deserves a serious referee, but the revision must include data/code, sensitivity tests, and a re-analysis with a less biased sample. I would not accept the cultural claims as they stand.","headline":"Solid application of reduced Google matrix to philosophers, but the Western-dominance and reference-hub claims rest on a biased sample and need re-analysis.","tokens_in":17105,"tokens_out":2730,"would_cite":false,"duration_ms":29806,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Wikipedia treats philosophers as reference hubs rather than foundational sources, and hidden network structure exposes unstated links among Presocratics.","keywords":["Wikipedia","PageRank","CheiRank","reduced Google matrix","Presocratic philosophy","knowledge networks","cultural analysis","philosopher rankings"],"falsifier":"Rebuild the rankings from seed lists drawn independently for each language edition and check whether the all-Western top 38 of the $\\Theta$-score survives; if it dissolves, that result is a selection artifact. Separately, recompute the $G_{qr}$ hidden links for the Presocratics using $\\alpha = 0.5$ and using a later English Wikipedia snapshot; the Leucippus–Parmenides and Melissus–Xenophanes links should persist if they reflect stable structural relationships rather than one snapshot's particular hyperlink choices.","tokens_in":16132,"feed_emoji":"🌐","tokens_out":10953,"duration_ms":110402,"temperature":0.7,"pith_summary":"The paper follows 237 philosophers, each with an article in all nine Wikipedia language editions, and ranks them with PageRank and CheiRank. It finds that these articles are cited more often than they cite other articles: philosophers function as reference hubs inside Wikipedia's knowledge network rather than as the foundational seed articles from which the network grows. Rankings differ across editions in culturally telling ways, and the first 38 positions of the combined nine-edition ranking are all Western thinkers. Compared with two specialized philosophy encyclopedias, the Wikipedia rankings are only weakly correlated, which the paper reads as the difference between a figure's societal presence and their scholarly canonization. On the English edition, a reduced Google matrix over 21 Presocratics uncovers hidden links, such as Melissus of Samos to Xenophanes and Leucippus to Parmenides, that do not exist as direct hyperlinks but are historically interpretable.","feed_headline":"Philosophers anchor Wikipedia as hubs, not foundations","feed_subtitle":"Nine language editions show 237 thinkers cited more than they cite; hidden links tie Leucippus to Parmenides.","key_machinery":"The carrying mechanism is the Google matrix $G = \\alpha S + (1-\\alpha)/N$ of a directed Wikipedia edition, with $\\alpha = 0.85$, together with its PageRank eigenvector $P$ and the CheiRank eigenvector $P^*$ computed on the reversed link network. PageRank measures how much an article is pointed to by influential pages; CheiRank measures how much an article points toward influential pages. For the 21 Presocratics, the paper uses the reduced Google matrix $G_R = G_{rr} + G_{pr} + G_{qr}$, where $G_{rr}$ contains direct transitions among the selected nodes, $G_{pr}$ reproduces the already-known reduced PageRank distribution, and $G_{qr}$ collects transitions that travel through the rest of Wikipedia before returning to the selected set. The $G_{qr}$ component is the instrument that exposes hidden links, and the $\\Theta$-score aggregates per-edition PageRank ranks into one cross-cultural list.","core_discovery":"The central claim is that Wikipedia's philosopher subnetwork is a landscape of influential reference points rather than a genealogy of foundational sources. In the PageRank–CheiRank plane, the 237 philosopher articles sit mostly above the diagonal, the region of nodes that receive many links from the rest of the encyclopedia while sending few links outward. Aristotle and Plato lead almost every edition, but each language inserts its own local figures, and the aggregated $\\Theta$-score places only Western philosophers in the top 38 positions. Rankings from two specialized philosophical encyclopedias differ by Kendall distances of about 0.36 to 0.41 from the Wikipedia rankings, and the paper attributes this gap to Wikipedia encoding broad societal influence while specialized encyclopedias encode academic standing. For the 21 Presocratics in the English edition, the reduced Google matrix is split into direct transitions, a trivial PageRank term, and a hidden-transition part $G_{qr}$, and the largest elements of $G_{qr}$ identify relationships absent from the adjacency matrix, including one pair that later became a direct hyperlink after the snapshot date.","pith_inferences":["One step beyond the paper: the Western-only top 38 should be tested against language-specific seed lists before being read as a fact about philosophical importance, because the all-nine-editions filter may itself select for Western canonization.","The hidden links are network facts, not historical proofs; they become historical claims only when paired with external evidence such as the pseudo-Aristotelian treatise or teacher–student traditions.","The same $G_{qr}$ pipeline could be applied to non-Western philosophical traditions or to scientists and artists, with the existing results providing a baseline for whether hidden links reproduce known intellectual lineages.","A natural robustness test is to recompute $G_{qr}$ with a different damping factor or a later Wikipedia dump; stable hidden links would strengthen the case that they reflect structure rather than one snapshot's accidents."],"forward_implications":["If the central claim holds, Wikipedia's philosophical knowledge is organized around thinkers as citation targets, not around doctrines as starting points.","Language-specific top-ten lists imply that each Wikipedia edition encodes a distinct cultural memory of philosophy, with figures like Marx in Russian, Confucius in Chinese, and Avicenna in Arabic rising locally.","The weak correlation with specialized encyclopedias means that societal influence and scholarly canon are genuinely different ranking principles, not noisy versions of one another.","Reduced Google matrix analysis can surface candidate missing links in knowledge networks, as in the Melissus–Xenophanes and Leucippus–Parmenides cases in the English edition.","The later appearance of a direct Pythagoras-to-Empedocles hyperlink suggests such hidden links can anticipate connections that editors subsequently add."],"supporting_citations":[{"why":"It defines the Google matrix and damping factor used to build the ranking matrices for each Wikipedia edition.","marker":"[8]"},{"why":"It defines PageRank as the steady-state centrality measure behind every philosopher ranking.","marker":"[9]"},{"why":"It supplies the $\\Theta$-score formula used to merge the nine per-edition PageRank rankings into one list.","marker":"[10]"},{"why":"It defines CheiRank on the reversed network, the measure of how much philosopher articles diffuse rather than attract links.","marker":"[26]"},{"why":"It introduces the reduced Google matrix decomposition into direct, PageRank, and hidden transition parts.","marker":"[27]"},{"why":"It shows hidden-link inference with reduced Google matrices on biological networks, supporting the interpretation of the Gqr links.","marker":"[28]"},{"why":"It applies reduced Google matrix to hidden links between political leaders in Wikipedia, the direct precedent for the Presocratic analysis.","marker":"[11]"},{"why":"It supplies the French Wikipedia list of philosophers by birth year from which the 237 names are drawn.","marker":"[20]"},{"why":"They provide the two books used to select the 21 Presocratics and their four traditional schools.","marker":"[21, 22]"}],"fun_headline_variants":["Wikipedia philosopher hubs out-cite their own sources","237 thinkers cited more than they cite across 9 Wikipedias","Presocratic hidden links mapped via reduced Google matrix","Aristotle and Plato lead Wikipedia influence rankings worldwide"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The rankings assume that the 237 philosophers chosen from a French Wikipedia list, and then filtered to those with articles in all nine editions, fairly represent philosophical importance in each language; if that selection favors Western figures, the Western dominance and several cross-edition comparisons are artifacts of selection rather than properties of Wikipedia's knowledge network.","fun_headline_variants_meta":{"raw":{"variants":["Wikipedia philosopher hubs out-cite their own sources","237 thinkers cited more than they cite across 9 Wikipedias","Presocratic hidden links mapped via reduced Google matrix","Aristotle and Plato lead Wikipedia influence rankings worldwide"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000305,"raw_usage":{"total_tokens":1739,"prompt_tokens":924,"completion_tokens":815,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":540,"completion_tokens_details":{"reasoning_tokens":752}},"tokens_in":540,"tokens_out":815,"duration_ms":7694,"temperature":1.0,"reasoning_tokens":752,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T19:13:13.398436+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Rebuild the rankings from seed lists drawn independently for each language edition and check whether the all-Western top 38 of the $\\Theta$-score survives; if it dissolves, that result is a selection artifact. Separately, recompute the $G_{qr}$ hidden links for the Presocratics using $\\alpha = 0.5$ and using a later English Wikipedia snapshot; the Leucippus–Parmenides and Melissus–Xenophanes links should persist if they reflect stable structural relationships rather than one snapshot's particular hyperlink choices.","supporting_citations":[{"cited_title":"Princeton University Press, Princeton and Oxford (2012)","cited_arxiv_id":null,"evidence_quote":"It defines the Google matrix and damping factor used to build the ranking matrices for each Wikipedia edition."},{"cited_title":"Computer Networks and ISDN Systems30(1), 107–117 (1998) https://doi.org/10","cited_arxiv_id":null,"evidence_quote":"It defines PageRank as the steady-state centrality measure behind every philosopher ranking."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It defines CheiRank on the reversed network, the measure of how much philosopher articles diffuse rather than attract links."},{"cited_title":"Reduced Google matrix","cited_arxiv_id":"1602.02394","evidence_quote":"It introduces the reduced Google matrix decomposition into direct, PageRank, and hidden transition parts."},{"cited_title":"PloS one 13(1) (2018) https://doi.org/10.1371/journal.pone.0190812","cited_arxiv_id":null,"evidence_quote":"It shows hidden-link inference with reduced Google matrices on biological networks, supporting the interpretation of the Gqr links."},{"cited_title":"The European Physical Journal B 89(12), 269 (2016) https://doi.org/10.1140/epjb/e2016-70526-3 21","cited_arxiv_id":null,"evidence_quote":"It applies reduced Google matrix to hidden links between political leaders in Wikipedia, the direct precedent for the Presocratic analysis."},{"cited_title":"[En ligne; Page disponible le 21-d´ ecembre-2018] (2018)","cited_arxiv_id":null,"evidence_quote":"It supplies the French Wikipedia list of philosophers by birth year from which the 237 names are drawn."}],"review_version":1}