Paper Citation Record · LEDGER

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics

As of 7 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2606.05168.

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

pith.paper-citation-record.v1
2606.05168 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-12T21:23:44.468570Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

28 of 28 outbound references displayed

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unresolved28
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External citation measurements

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Outbound references

Observation e22355e9-879f-4ba0-a399-14676c306756 · outbound

This paper cites Self-Consuming Generative Models Go MAD.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Self-Consuming Generative Models Go MAD

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7e02c81a-3119-4d2b-855d-297cb07fd6f0 · outbound

This paper cites Dynamical Models of Tuberculosis and Their Applications.Mathematical Biosciences and Engineering, volume 1, pp.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Dynamical Models of Tuberculosis and Their Applications.Mathematical Biosciences and Engineering, volume 1, pp

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 618d6c32-e002-49db-b616-b0ab1887e9be · outbound

This paper cites an unresolved cited work.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation c65e37d2-737d-45c3-b5f3-213b3dff9a4d · outbound

This paper cites Strong Model Collapse.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Strong Model Collapse

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 73141138-8704-469f-b00a-6d3bed9e3ebe · outbound

This paper cites Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation cb9b4774-9833-46a9-8aa3-a57f506a1ef7 · outbound

This paper cites The Mathematics of Infectious Diseases.SIAM Review, volume 42, pp.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics The Mathematics of Infectious Diseases.SIAM Review, volume 42, pp

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation a8cb3eb6-c4f9-4679-8e2d-3b5f8f356f85 · outbound

This paper cites Epidemiologi- cal Modeling of News and Rumors on Twitter.Proceedings of the Workshop on Social Network Mining and Analysis, pp.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Epidemiologi- cal Modeling of News and Rumors on Twitter.Proceedings of the Workshop on Social Network Mining and Analysis, pp

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 2c1dbe3d-466a-41d0-8071-1c3ca24a0415 · outbound

This paper cites Measuring and Modeling Computer Virus Prevalence.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Measuring and Modeling Computer Virus Prevalence

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 16bc07e2-de9f-4780-bacb-a96fe7bd81ea · outbound

This paper cites A Contribution to the Mathematical Theory of Epidemics.Proceedings of the Royal Society of London.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics A Contribution to the Mathematical Theory of Epidemics.Proceedings of the Royal Society of London

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 632a5ec0-f95b-4225-b8fb-887856c81e54 · outbound

This paper cites A Watermark for Large Language Models.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics A Watermark for Large Language Models

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation bc750028-1782-4fd2-b6c4-b7219a74ae6a · outbound

This paper cites Monitoring AI- Modified Content at Scale.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Monitoring AI- Modified Content at Scale

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 190cbd97-1d64-49a7-b860-948616d5b451 · outbound

This paper cites A Pretrainer's Guide to Training Data: Measuring the Effects of Data Age, Domain Coverage, Quality, & Toxicity.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics A Pretrainer's Guide to Training Data: Measuring the Effects of Data Age, Domain Coverage, Quality, & Toxicity

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 54862341-d493-4ef7-aa6b-274597f84022 · outbound

This paper cites Pointer Sentinel Mixture Models.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Pointer Sentinel Mixture Models

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation dc515572-43e5-4e1d-a02d-f6adcfcc3486 · outbound

This paper cites Model Cards for Model Reporting.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Model Cards for Model Reporting

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation ab75398d-4194-47b8-8dbd-4b4b2daa3f3d · outbound

This paper cites Epidemic Processes in Complex Networks.Reviews of Modern Physics, volume 87, pp.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Epidemic Processes in Complex Networks.Reviews of Modern Physics, volume 87, pp

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 667124e1-f1a7-49ed-8256-96dcbb701cbc · outbound

This paper cites an unresolved cited work.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 1450a001-d7ab-4a64-b82c-77e47e3a0ff5 · outbound

This paper cites Language Models are Unsupervised Multitask Learners.OpenAI Blog, 2019.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Language Models are Unsupervised Multitask Learners.OpenAI Blog, 2019

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation fb9d8010-3c75-4840-82a2-65f0be2e77fe · outbound

This paper cites Variance Based Sensitivity Analysis of Model Output.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Variance Based Sensitivity Analysis of Model Output

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation be72ae39-e5e5-4674-94d4-df177db1afdd · outbound

This paper cites How Bad is Training on Synthetic Data? A Statistical Analysis.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics How Bad is Training on Synthetic Data? A Statistical Analysis

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 655447cc-815b-4133-a45a-72c4a67f459f · outbound

This paper cites AI models collapse when trained on recursively generated data.Nature, volume 631, pp.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics AI models collapse when trained on recursively generated data.Nature, volume 631, pp

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 63a3f436-394a-4684-b263-7fbe20f27f16 · outbound

This paper cites The Science of Detecting LLM-Generated Text.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics The Science of Detecting LLM-Generated Text

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 92120aa8-aa04-459d-a944-21d0b1aa39f9 · outbound

This paper cites AI-Generated Content Prevalence in Web Corpora.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics AI-Generated Content Prevalence in Web Corpora

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 7ca09481-2e47-438e-a150-a4badfe250f0 · outbound

This paper cites Reproduction Numbers and Sub-threshold Endemic Equilibria for Compartmental Models of Disease Transmission.Mathematical Bio- sciences, volume 180, pp.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Reproduction Numbers and Sub-threshold Endemic Equilibria for Compartmental Models of Disease Transmission.Mathematical Bio- sciences, volume 180, pp

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation c7b418f3-43a6-4b51-b20e-3a7ea867939e · outbound

This paper cites The Spread of True and False News Online.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics The Spread of True and False News Online

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 96067dd7-092d-4a81-b39d-4ac2e472fc70 · outbound

This paper cites Infection occurs with probabilityp(Bernoulli trial).

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Infection occurs with probabilityp(Bernoulli trial)

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 49dd3c83-7b8a-41b5-961c-0c527d83e410 · outbound

This paper cites 3.Recovery: Each infected node recovers with probabilityγ i per step.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics 3.Recovery: Each infected node recovers with probabilityγ i per step

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 6dfbde08-ff32-4e66-8d0d-1b3ef0e60525 · outbound

This paper cites an unresolved cited work.

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Observation 10b608e1-6fb6-44fd-af06-02006342a180 · outbound

This paper cites 20 realizations are run per configuration for 50 time steps (default).

Epidemiology of Model Collapse: Modeling Synthetic Data Contamination via Bilayer SIR Dynamics 20 realizations are run per configuration for 50 time steps (default)

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-12T21:23:44.468570Z

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Pith citing papers

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