Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T13:32:21.809205Z
Paper Citation Record · LEDGER
On discrete loop signatures and Markov loops topology
As of 21 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:1908.05187.
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 2026-08-20T06:33:59.587034+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
19 of 19 outbound references displayed
- verified exact2
- verified fuzzy13
- unresolved4
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation c759a831-7ef8-438d-86f2-f906143ecf12 · outbound
This paper cites Some relations between the spectra of simple and non-backtracking random walks.
On discrete loop signatures and Markov loops topology Some relations between the spectra of simple and non-backtracking random walks
Reference 1
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T13:32:21.854469Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ab6f95d2-1ad7-494b-8ac1-cf510f268dfb · outbound
This paper cites an unresolved cited work.
On discrete loop signatures and Markov loops topology Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:32:22.012476Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b0955a59-634e-4eb5-9137-bbc6edc1afcd · outbound
This paper cites an unresolved cited work.
On discrete loop signatures and Markov loops topology Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:32:22.003046Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d3c810d4-dcb8-44e7-ad3a-ebeef256f513 · outbound
This paper cites Zeta functions of finite grap hs.
On discrete loop signatures and Markov loops topology Zeta functions of finite grap hs
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.993362Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6afc5ba8-c5d1-45cb-aaa3-11a4c63b18bc · outbound
This paper cites Jacobian Tori Associated wit h a Finite Graph and Its Abelian Covering Graphs.
On discrete loop signatures and Markov loops topology Jacobian Tori Associated wit h a Finite Graph and Its Abelian Covering Graphs
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.983806Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a4503c8b-d1a0-48e5-aff4-f35f5e07e951 · outbound
This paper cites The Brownian loop soup.
On discrete loop signatures and Markov loops topology The Brownian loop soup
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.975048Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ef18c8e2-0397-403b-98cf-45450855464f · outbound
This paper cites Markov paths, loops and fields.
On discrete loop signatures and Markov loops topology Markov paths, loops and fields
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.966047Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0a5d3aa4-a283-4c0b-bbe6-2b99f1d995eb · outbound
This paper cites Random flows defined by Markov loops.
On discrete loop signatures and Markov loops topology Random flows defined by Markov loops
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.956545Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 5d39215b-cfc7-4ced-9464-245859295cd9 · outbound
This paper cites Markov loops, complex free field and Eulerian circuits.
On discrete loop signatures and Markov loops topology Markov loops, complex free field and Eulerian circuits
Reference 9
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T13:32:21.841281Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 14cc1c61-c04a-4bc3-a302-16e90be4581c · outbound
This paper cites an unresolved cited work.
On discrete loop signatures and Markov loops topology Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:32:21.947522Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8edca245-58f7-42fe-9559-550761cf34c3 · outbound
This paper cites Markov loops, Coverings and Fields.
On discrete loop signatures and Markov loops topology Markov loops, Coverings and Fields
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.938536Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation fdfc4223-0f81-4e3b-a324-35ad37d00d9f · outbound
This paper cites Discrete Path Integral Approach to the Selber g Trace For- mula for Regular Graphs.
On discrete loop signatures and Markov loops topology Discrete Path Integral Approach to the Selber g Trace For- mula for Regular Graphs
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.929596Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4a46762e-6770-4a82-8fc8-0c0428a3f7a8 · outbound
This paper cites Massey, Algebraic Topology: An Introduction Springer (1967).
On discrete loop signatures and Markov loops topology Massey, Algebraic Topology: An Introduction Springer (1967)
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.920741Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4ff0b992-f69a-4811-9e33-5a7c9329d15d · outbound
This paper cites Lie elements and an algebra associated with shuffles.
On discrete loop signatures and Markov loops topology Lie elements and an algebra associated with shuffles
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.911705Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0cd6e577-6ee9-4746-b484-3e52b9172473 · outbound
This paper cites Free Lie algebras.
On discrete loop signatures and Markov loops topology Free Lie algebras
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.902271Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation df2008f7-cc6b-4f45-aaf3-1859e73f36ec · outbound
This paper cites Stark, Audrey A.
On discrete loop signatures and Markov loops topology Stark, Audrey A
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.892990Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 25face47-d3e1-47f1-9f7d-6ed7ae1db3ce · outbound
This paper cites Scuola intenazio nale di Fisica ”Enrico Fermi”.
On discrete loop signatures and Markov loops topology Scuola intenazio nale di Fisica ”Enrico Fermi”
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.883439Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 466819a7-322d-42ce-a1c7-cf7feeda96cb · outbound
This paper cites an unresolved cited work.
On discrete loop signatures and Markov loops topology Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:32:21.874297Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ace7850e-9a95-4957-a781-8edba14262b7 · outbound
This paper cites Appendix in Graphs on Surfaces and their Application s, by S.K.
On discrete loop signatures and Markov loops topology Appendix in Graphs on Surfaces and their Application s, by S.K
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:32:21.864388Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Pith citing papers
No inbound Pith citation observations are available.