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.

pith.paper-citation-record.v1
2501.06812 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:58:56.748397Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+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

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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

No inbound Pith citation observations are available.