Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T12:29:26.681271Z
Paper Citation Record · LEDGER
Epidemic dynamics in physical-information-social multilayer networks
As of 8 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2506.00104.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
47 of 47 outbound references displayed
- verified exact1
- verified fuzzy26
- unresolved20
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation f4d67b71-dd30-4d1f-841e-e8080e2dc6d1 · outbound
This paper cites Conversely, the SU state (a node in both S and U) retains the baseline infection probability: βU = β.
Epidemic dynamics in physical-information-social multilayer networks Conversely, the SU state (a node in both S and U) retains the baseline infection probability: βU = β
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:36.626933Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation fa96e5e4-9266-44b0-9f72-c68d2637b877 · outbound
This paper cites We define the observational metrics obs for the infection severity: obs = NEI N , where NEI is the total number of nodes in states E and I.
Epidemic dynamics in physical-information-social multilayer networks We define the observational metrics obs for the infection severity: obs = NEI N , where NEI is the total number of nodes in states E and I
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:36.363507Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 246ff364-91eb-45c6-bba5-c0740a10e0ce · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:36.199848Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation df6931f5-e61c-4272-9519-56c09fdd39b0 · outbound
This paper cites Near the epidemic threshold, the probability of infection for each individual approaches zero, so we have pSU i ≫ pEU i , pSA i ≫ pEA i + pIA i , g ≈ gl and λM ≈ km g gl.
Epidemic dynamics in physical-information-social multilayer networks Near the epidemic threshold, the probability of infection for each individual approaches zero, so we have pSU i ≫ pEU i , pSA i ≫ pEA i + pIA i , g ≈ gl and λM ≈ km g gl
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:36.043386Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation fb2f9fec-312d-4dac-8107-f7e03ec985e7 · outbound
This paper cites (2), we can derive the continuous microscopic mean-field equations.
Epidemic dynamics in physical-information-social multilayer networks (2), we can derive the continuous microscopic mean-field equations
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:35.861250Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation c8dedf78-8492-4bf0-8b78-23a9350e7dea · outbound
This paper cites Let F = P j βGaj1pEI j pSU 1 ...P j βGajN pEI j pSU NP j βGAaj1pEI j pSA 1 ...P j βGAajN pEI j pSA N 0.
Epidemic dynamics in physical-information-social multilayer networks Let F = P j βGaj1pEI j pSU 1 ...P j βGajN pEI j pSU NP j βGAaj1pEI j pSA 1 ...P j βGAajN pEI j pSA N 0
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:35.652241Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation efa63aa9-e9ea-4d6c-8d26-f3fb992048df · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:35.329291Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 124a752b-6f7d-4cca-9e75-569a5e6ead04 · outbound
This paper cites (B2), we can derive the continuous mesoscopic mean-field equations, also termed the heterogeneous mean-field equations.
Epidemic dynamics in physical-information-social multilayer networks (B2), we can derive the continuous mesoscopic mean-field equations, also termed the heterogeneous mean-field equations
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:35.008339Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 61554e8b-cb5b-447a-8be8-e93b8a74afd1 · outbound
This paper cites Near the epidemic threshold, the probability of infection for each individual approaches zero, so we have pSU k ≫ pEU k , pSA k ≫ pEA k + pIA k , g ≈ gl and λM ≈ km g gl.
Epidemic dynamics in physical-information-social multilayer networks Near the epidemic threshold, the probability of infection for each individual approaches zero, so we have pSU k ≫ pEU k , pSA k ≫ pEA k + pIA k , g ≈ gl and λM ≈ km g gl
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:34.714961Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 34434ad2-00da-445b-a95b-60fe70227e9a · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:34.424693Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 84ecd184-091d-4fdb-aaf1-f1d8d31811fa · outbound
This paper cites Malik, M.
Epidemic dynamics in physical-information-social multilayer networks Malik, M
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:34.112170Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 3b625135-0074-47fb-b4a1-b9d524378f42 · outbound
This paper cites Platto, T.
Epidemic dynamics in physical-information-social multilayer networks Platto, T
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:33.802615Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation dd6aba85-13f9-41b8-b43a-26f4e955c8bf · outbound
This paper cites Dietz and J.
Epidemic dynamics in physical-information-social multilayer networks Dietz and J
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:33.593721Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e10f8c38-13ed-496b-8204-229422da4648 · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:33.348614Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 033e742b-1bdc-45a6-8817-63cd686c3eda · outbound
This paper cites Albert, H.
Epidemic dynamics in physical-information-social multilayer networks Albert, H
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:33.127971Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b1df770d-637a-4c94-b987-e222d202904a · outbound
This paper cites Newman, Networks: An Introduction(Oxford University Press, 2010).
Epidemic dynamics in physical-information-social multilayer networks Newman, Networks: An Introduction(Oxford University Press, 2010)
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:32.877541Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e0e75fcc-9495-4b5c-96a5-bfa965d487e1 · outbound
This paper cites Pastor-Satorras and A.
Epidemic dynamics in physical-information-social multilayer networks Pastor-Satorras and A
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:32.685126Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 02f6f7da-ca85-42a9-b267-08c35fdfee79 · outbound
This paper cites Pastor-Satorras, C.
Epidemic dynamics in physical-information-social multilayer networks Pastor-Satorras, C
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:32.522827Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7c27e90a-ed96-44a1-ad12-4e13a449aa06 · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:32.373545Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 6f81e051-98fb-43ee-9fb1-ee63645800ff · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:32.233968Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 3c8bf239-69de-496e-bb01-92b058ea58ed · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:32.045843Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 66b653c6-df80-4f1f-a825-4994e14af8a7 · outbound
This paper cites Samanta, S.
Epidemic dynamics in physical-information-social multilayer networks Samanta, S
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:31.811741Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation dffd3157-a181-4b75-bef1-80758a4bbd13 · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:31.631772Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 3b51c880-259b-4c1b-8ea5-ddbbf2de2627 · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:31.483635Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7648d8b6-043e-47ce-8720-0a748e054587 · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:31.328167Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 696fde8b-f216-4714-959e-e207a48155ec · outbound
This paper cites Granell, S.
Epidemic dynamics in physical-information-social multilayer networks Granell, S
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:31.116274Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation a7f66152-e3d3-47e6-97ea-9c5140f9c1c5 · outbound
This paper cites Granell, S.
Epidemic dynamics in physical-information-social multilayer networks Granell, S
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:30.939863Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 1d25c934-f577-4fa3-aed4-4db2f5446973 · outbound
This paper cites Huang, J.
Epidemic dynamics in physical-information-social multilayer networks Huang, J
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:30.827868Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 353ae034-2cd5-440a-a7f0-bfd875de1ec4 · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:30.682391Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation cb5378a7-97d8-4716-8824-5fa0c662d4ca · outbound
This paper cites Pan and Z.
Epidemic dynamics in physical-information-social multilayer networks Pan and Z
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:30.364672Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 34fecc27-661c-4524-8c2b-74709254ab5d · outbound
This paper cites Zheng, C.
Epidemic dynamics in physical-information-social multilayer networks Zheng, C
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:30.117285Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 41ec4400-5776-48b9-be7f-556a41ee1aeb · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:29.928849Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 827ff596-797b-4ac0-904b-cd88011d2230 · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:29.650146Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7c3fd2d9-eda9-4fd5-ba1e-a00dc7e45a55 · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:29.371200Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7cc48ad0-a822-492b-89bd-b437d4b9e00a · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:29.181064Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 458a55a7-119c-4548-8dfd-37f3e07cffbd · outbound
This paper cites He and L.
Epidemic dynamics in physical-information-social multilayer networks He and L
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:28.916880Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e93c7e04-c07d-4013-b0e2-17ee9c955fa5 · outbound
This paper cites Yu and L.
Epidemic dynamics in physical-information-social multilayer networks Yu and L
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:28.755619Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 1e92a069-52aa-42ce-8b35-f0c21f298abe · outbound
This paper cites Yu and L.
Epidemic dynamics in physical-information-social multilayer networks Yu and L
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:28.616571Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 3300ed8e-e123-457c-872a-f76cddecad1b · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 39
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:28.398411Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 2fd4afe4-16d0-4d9c-b553-3cfaa300bbda · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 40
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:28.291608Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d51a15c5-2085-4d58-b984-ef30dec2ed8c · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 41
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:28.149150Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 59d59175-6993-4625-b00f-4f5b08da1c40 · outbound
This paper cites Van Den Driessche and J.
Epidemic dynamics in physical-information-social multilayer networks Van Den Driessche and J
Reference 42
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:27.942825Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ef571721-bea4-4ae0-8e47-c7c589ec2e33 · outbound
This paper cites Chang, C.-R.
Epidemic dynamics in physical-information-social multilayer networks Chang, C.-R
Reference 43
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:27.746226Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0827eac8-8ae2-4f90-98e5-637fd537ea7d · outbound
This paper cites Pastor-Satorras and A.
Epidemic dynamics in physical-information-social multilayer networks Pastor-Satorras and A
Reference 44
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:29:27.486543Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation eac030b7-05d9-4dc8-9b40-1c00116d6aa5 · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 45
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:27.345054Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ddefbc0f-d9df-4a2b-bc9f-bd0519a4f8be · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 46
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:29:27.149353Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 9b1d26d0-11ef-48ea-924a-673e6132b749 · outbound
This paper cites an unresolved cited work.
Epidemic dynamics in physical-information-social multilayer networks Unresolved cited work
Reference 47
- Resolution
- verified exact
- doi, observed 2026-08-07T12:29:26.970954Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Pith citing papers
No inbound Pith citation observations are available.