Paper Citation Record · LEDGER

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research

As of 23 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 2 inbound Pith citation observations for arXiv:2506.22946.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.22946 v1

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:01:23.496406Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-18T10:31:36.556121Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-18T10:32:33.980113Z

Reference resolution

45 of 45 outbound references displayed

verified exact12
verified fuzzy4
unresolved25
parse uncertain0
malformed identifier1
metadata mismatch3

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 90bc79d2-a778-4436-8f84-ce14e2517204 · outbound

This paper cites Emergence of scaling in random networks.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Emergence of scaling in random networks

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:19.902522Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6b0e649f-5daf-4c47-97c7-486886fdbec6 · outbound

This paper cites Models of core/periphery structures.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Models of core/periphery structures

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:20.001050Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0675ee26-806f-4325-9997-138c987befd3 · outbound

This paper cites an unresolved cited work.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Unresolved cited work

Reference 3

Resolution: verified exact; doi, observed 2026-08-06T22:01:24.820140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5c1c0b7d-bcc0-462c-9e06-62c0b06f7786 · outbound

This paper cites an unresolved cited work.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:01:25.243205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation de015123-9c39-4651-bb35-d7205bbbf07b · outbound

This paper cites Structural holes and good ideas.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Structural holes and good ideas

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:20.425656Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9669fc59-4f0b-46ae-8be8-bf185d865989 · outbound

This paper cites A supervised and distributed framework for cold-start author disambiguation in large-scale publications.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research A supervised and distributed framework for cold-start author disambiguation in large-scale publications

Reference 6

Resolution: verified exact; doi, observed 2026-08-06T22:01:24.547704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 955b60a7-9b8d-4e63-8237-b4bf761db577 · outbound

This paper cites On the Use of ArXiv as a Dataset.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research On the Use of ArXiv as a Dataset

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:20.714838Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36281acd-83be-4d6c-94c2-202d1b2a343a · outbound

This paper cites Dominance statistics: Ordinal analyses to answer ordinal questions.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Dominance statistics: Ordinal analyses to answer ordinal questions

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:20.806763Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6eeb06b6-b139-4d5e-ab04-6a373725805c · outbound

This paper cites Invisible Colleges; Diffusion of Knowledge in Scientific Communities.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Invisible Colleges; Diffusion of Knowledge in Scientific Communities

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:25.228147Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d33dff60-691e-4d5c-a438-65b18131c509 · outbound

This paper cites de Solla Price and Donald deB.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research de Solla Price and Donald deB

Reference 10

Resolution: verified exact; doi, observed 2026-08-06T22:01:24.314366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c0ac6780-6af4-4450-a1d1-b604cd05cc9e · outbound

This paper cites BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:21.128608Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a3a76ad2-018d-4c89-b1a8-82d667e162d5 · outbound

This paper cites Unpacking burt's constraint measure.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Unpacking burt's constraint measure

Reference 12

Resolution: verified exact; doi, observed 2026-08-06T22:01:24.023024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 30860092-35dc-47f8-9c0c-38dc7b3ed1fc · outbound

This paper cites Community detection in graphs.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Community detection in graphs

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:21.353374Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a3acc9fb-570d-4abf-8975-0953f232130d · outbound

This paper cites an unresolved cited work.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:21.517174Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f575e30-15ac-4d4e-9a13-a9fb97801cab · outbound

This paper cites The strength of weak ties.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research The strength of weak ties

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:25.211910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a904f9f1-74d8-4bfb-87c1-420fd02cc3a3 · outbound

This paper cites BERTopic: Neural topic modeling with a class-based TF-IDF procedure.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research BERTopic: Neural topic modeling with a class-based TF-IDF procedure

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:21.752791Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a48862ab-baa4-49dd-8a88-b38e990a2f07 · outbound

This paper cites Hagberg, Pieter J.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Hagberg, Pieter J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:25.197230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 0c0a62b5-250f-472a-a64f-51aff181c8d1 · outbound

This paper cites A strategic model of social and economic networks.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research A strategic model of social and economic networks

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:22.035976Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 25cc0f4a-6073-40ea-bb15-23783378bbb6 · outbound

This paper cites The homophily principle in social network analysis: A survey.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research The homophily principle in social network analysis: A survey

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:22.180783Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9445f309-d38f-4600-83b7-ea984bf05008 · outbound

This paper cites Degree assortativity in collaboration networks and invention performance.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Degree assortativity in collaboration networks and invention performance

Reference 20

Resolution: verified exact; doi, observed 2026-08-06T22:01:23.784618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 451c50f7-e011-49a3-a483-58a524b697d8 · outbound

This paper cites Scale‐free collaboration networks: An author name disambiguation perspective.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Scale‐free collaboration networks: An author name disambiguation perspective

Reference 21

Resolution: verified exact; doi, observed 2026-08-06T22:01:23.769542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation bdc74393-d2d9-4292-bfae-2d2991f3b5a5 · outbound

This paper cites Factors influencing the research impact in cancer research: a collaboration and knowledge network analysis.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Factors influencing the research impact in cancer research: a collaboration and knowledge network analysis

Reference 22

Resolution: verified exact; doi, observed 2026-08-06T22:01:23.753644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8af7bf57-444a-426d-acb9-00555e3fab92 · outbound

This paper cites an unresolved cited work.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:22.753872Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f35be207-4eb7-4929-b550-03d9e45eb243 · outbound

This paper cites The role of citation networks to explain academic promotions: an empirical analysis of the italian national scientific qualification.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research The role of citation networks to explain academic promotions: an empirical analysis of the italian national scientific qualification

Reference 24

Resolution: verified exact; doi, observed 2026-08-06T22:01:23.728344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 71e50ad3-b968-49fd-b07e-2cb046c0df8b · outbound

This paper cites hdbscan: Hierarchical density based clustering.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research hdbscan: Hierarchical density based clustering

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:22.963602Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3d3a0334-26fc-466b-8748-dba42822e72f · outbound

This paper cites Umap: Uniform manifold approximation and projection.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Umap: Uniform manifold approximation and projection

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:23.078634Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7052793-f862-4b04-b505-d6109b1f834e · outbound

This paper cites Birds of a feather: Homophily in social networks.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Birds of a feather: Homophily in social networks

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:23.195545Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 281ff643-81b3-40ca-bebf-0ecd21cf6f3a · outbound

This paper cites The matthew effect in science.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research The matthew effect in science

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:23.317373Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4534be60-e32d-4460-ae80-2920937645af · outbound

This paper cites The structure of scientific collaboration networks.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research The structure of scientific collaboration networks

Reference 29

Resolution: verified exact; doi, observed 2026-08-06T22:01:23.668841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9329c151-1154-4a21-80d0-1ad561876b14 · outbound

This paper cites Assortative mixing in networks.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Assortative mixing in networks

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:23.418696Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41c5281f-393d-4610-8504-62233f09cede · outbound

This paper cites Coauthorship networks and patterns of scientific collaboration.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Coauthorship networks and patterns of scientific collaboration

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:23.423004Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 891906d7-f4d8-463e-87cc-d3fd79fa3ad9 · outbound

This paper cites Power laws, pareto distributions and zipf's law.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Power laws, pareto distributions and zipf's law

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:23.427751Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95f56a66-0e88-43bb-b47f-a25836841182 · outbound

This paper cites Modularity and community structure in networks.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Modularity and community structure in networks

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:23.433240Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f84e231f-b38e-4d84-b300-8e305c8d19c0 · outbound

This paper cites Mapping collaborations and partnerships in sdg research.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Mapping collaborations and partnerships in sdg research

Reference 34

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T22:01:25.074897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7da7a263-e2a7-460b-ad52-20ffc7e29d6b · outbound

This paper cites Quantifying the impact of weak, strong, and super ties in scientific careers.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Quantifying the impact of weak, strong, and super ties in scientific careers

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:23.443560Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac664db6-f3a8-45af-ba05-c399d260ced4 · outbound

This paper cites A causal test of the strength of weak ties.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research A causal test of the strength of weak ties

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:23.448739Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2801d3f2-7190-493e-8ee3-341af8056e7a · outbound

This paper cites A supervised machine learning approach to author disambiguation in the web of science.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research A supervised machine learning approach to author disambiguation in the web of science

Reference 37

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T22:01:24.995843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ff8efc64-d8a8-492d-a674-d234aacf7637 · outbound

This paper cites Romano, J.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Romano, J

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:01:25.171303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b7d52cfb-a99a-49df-824a-97efd0600408 · outbound

This paper cites an unresolved cited work.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:23.463580Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2f961ec4-d265-4360-b41f-335d97d58dd7 · outbound

This paper cites Special values of L-functions of one-motives over function fields.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Special values of L-functions of one-motives over function fields

Reference 40

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T22:01:24.863918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5e66d53c-5eb8-4ee0-9f7a-908c0baf662f · outbound

This paper cites The role of endogenous and exogenous mechanisms in the formation of r & d networks.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research The role of endogenous and exogenous mechanisms in the formation of r & d networks

Reference 41

Resolution: verified exact; doi, observed 2026-08-06T22:01:23.592934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 73764cab-773f-46e2-b8b6-8cfd6e14e6fa · outbound

This paper cites Collective dynamics of ‘small-world’ networks.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Collective dynamics of ‘small-world’ networks

Reference 42

Resolution: malformed identifier; no resolver link, observed 2026-08-06T22:01:23.479838Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e2ffedb6-897a-4e7e-9834-f9850f889dde · outbound

This paper cites The increasing dominance of teams in production of knowledge.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research The increasing dominance of teams in production of knowledge

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-06T22:01:23.486311Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 96a14d75-328e-4fcc-98a9-cd4417892b91 · outbound

This paper cites Higher-order structures of local collaboration networks are associated with individual scientific productivity.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Higher-order structures of local collaboration networks are associated with individual scientific productivity

Reference 44

Resolution: verified exact; doi, observed 2026-08-06T22:01:23.553699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c2a86b65-6afa-44cd-9640-dee66fef315b · outbound

This paper cites an unresolved cited work.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research Unresolved cited work

Reference 45

Resolution: verified exact; doi, observed 2026-08-06T22:01:23.535239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

Observation 5bba0948-d77e-4e51-8c3b-1817a304cf49 · inbound

You Have Been LaTeXpOsEd: A Systematic Analysis of Information Leakage in Preprint Archives Using Large Language Models cites this paper.

You Have Been LaTeXpOsEd: A Systematic Analysis of Information Leakage in Preprint Archives Using Large Language Models Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-18T10:32:33.982964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6946bac1-9516-4472-92d1-f4c897da98cc · inbound

Hidden Secrets in the arXiv: Discovering, Analyzing, and Preventing Unintentional Information Disclosure in Source Files of Scientific Preprints cites this paper.

Hidden Secrets in the arXiv: Discovering, Analyzing, and Preventing Unintentional Information Disclosure in Source Files of Scientific Preprints Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-05-10T00:54:49.105555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.