Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T20:58:56.748397Z
Paper Citation Record · LEDGER
Branching Ratios of Input Trees for Directed Multigraphs
As of 16 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2501.06812.
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 2026-08-16T06:30:59.297886+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
33 of 33 outbound references displayed
- verified exact0
- verified fuzzy19
- unresolved14
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 30e6aa30-3e1b-4cd7-83cd-b90bd60a65b4 · outbound
This paper cites Abdi and N.
Branching Ratios of Input Trees for Directed Multigraphs Abdi and N
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:57.200332Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 60e604d5-065c-4d9e-9a00-2b93af3e032d · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:57.187527Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c23e5872-31df-42c0-b03e-d3cb9af0dde8 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:57.175375Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ea22d32e-d689-492e-a8c2-40f15cff4fc7 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:57.163934Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2456a952-b9be-4e3a-934e-bea92bb918d0 · outbound
This paper cites Boldi, S.
Branching Ratios of Input Trees for Directed Multigraphs Boldi, S
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:57.151525Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d95e6d9c-2dab-4e8a-9dc3-c9a620b959f7 · outbound
This paper cites Boldi and S.
Branching Ratios of Input Trees for Directed Multigraphs Boldi and S
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:57.139498Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 419061c3-8abd-4af3-ad3a-40f5d6263ed3 · outbound
This paper cites Boldi and S.
Branching Ratios of Input Trees for Directed Multigraphs Boldi and S
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:57.127663Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 65edd161-72ac-49fb-9f3e-5492a31fd823 · outbound
This paper cites Boldi and S.
Branching Ratios of Input Trees for Directed Multigraphs Boldi and S
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:57.115204Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6cc315f3-ac72-4102-890d-1cca39433e2b · outbound
This paper cites Boreviˇ c and I.R.ˇSafareviˇ c.Number Theory, Academic Press, New York 1966.
Branching Ratios of Input Trees for Directed Multigraphs Boreviˇ c and I.R.ˇSafareviˇ c.Number Theory, Academic Press, New York 1966
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:57.103092Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 468390f0-1693-499f-a9e6-b4f96e8f1172 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:57.091193Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 08fb0857-8092-4200-a066-5859bb6e02a6 · outbound
This paper cites Brualdi and H.J.
Branching Ratios of Input Trees for Directed Multigraphs Brualdi and H.J
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:57.078877Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3611786b-75d3-434a-8ac0-93ffb8bf6a48 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:57.065928Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 44f983f2-d582-4e78-8da3-7a3151447829 · outbound
This paper cites Buckley and F.
Branching Ratios of Input Trees for Directed Multigraphs Buckley and F
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:57.053604Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 55cfbda2-0fa5-4daa-a755-c16ef58689a8 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:57.040505Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cc603e71-4dcd-4f24-8926-c74ef417cd36 · outbound
This paper cites Frobenius.
Branching Ratios of Input Trees for Directed Multigraphs Frobenius
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:57.027610Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 60cbdde5-9802-4081-a146-06ac33d94d01 · outbound
This paper cites Gantmacher.
Branching Ratios of Input Trees for Directed Multigraphs Gantmacher
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:57.014371Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5a8e5368-99b7-4a4b-b785-6f5de01f606e · outbound
This paper cites Godsil and G.F.
Branching Ratios of Input Trees for Directed Multigraphs Godsil and G.F
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:57.000740Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 97c49619-bcc3-4a4a-98ca-9be8fcbca72a · outbound
This paper cites Golubitsky and I.
Branching Ratios of Input Trees for Directed Multigraphs Golubitsky and I
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:56.985310Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1c2a2f12-8a84-4b77-a6a6-f255e1f824f3 · outbound
This paper cites Humphreys.
Branching Ratios of Input Trees for Directed Multigraphs Humphreys
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:56.972290Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 705b0f3b-b787-427b-9981-19cd8a3f040a · outbound
This paper cites Kitchens.
Branching Ratios of Input Trees for Directed Multigraphs Kitchens
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:56.958539Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ac72c630-07b2-44c1-8cac-d1937b7329b2 · outbound
This paper cites Lancaster and M.
Branching Ratios of Input Trees for Directed Multigraphs Lancaster and M
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:56.945157Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6a78a37b-aab6-411d-92ed-416c22fa3883 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:56.932611Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 85c81719-75d1-4dcd-919a-917c772fd813 · outbound
This paper cites Leifer, F.
Branching Ratios of Input Trees for Directed Multigraphs Leifer, F
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:56.919182Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation df5ccff4-cad3-43b4-8d75-cf8cf08dec02 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:56.904494Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation dec60c77-5c44-4987-82ad-715b426f410d · outbound
This paper cites Makse, P.
Branching Ratios of Input Trees for Directed Multigraphs Makse, P
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:56.892478Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 35da7207-d716-46f7-8e45-d4eeef6df667 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:56.880051Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f4494bb3-d114-48e4-b4f1-61711250ba95 · outbound
This paper cites Morone, I.
Branching Ratios of Input Trees for Directed Multigraphs Morone, I
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:56.864998Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0d3d7ea5-8070-4a4c-8ca2-830cb9422fc0 · outbound
This paper cites Morone and H.A.
Branching Ratios of Input Trees for Directed Multigraphs Morone and H.A
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-08-10T20:58:56.726700Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f5029d5d-fca7-4340-88c7-5e10db76ce07 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:56.849443Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 96ece847-cdbf-4409-b1ff-602552e2e516 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:56.835710Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2fdc6644-6871-4c6e-93da-97e7c071de55 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:56.820340Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4aca1a99-6298-4d9d-a6ca-ca291dd5ac95 · outbound
This paper cites an unresolved cited work.
Branching Ratios of Input Trees for Directed Multigraphs Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:58:56.806063Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 32126619-a475-4f3e-91a9-d528718ccd5d · outbound
This paper cites en.wikipedia.org/wiki/Perron-Frobenius theorem (7 June 2024).
Branching Ratios of Input Trees for Directed Multigraphs en.wikipedia.org/wiki/Perron-Frobenius theorem (7 June 2024)
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:58:56.792743Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.