Paper Citation Record · LEDGER

Counting in Vieta graphs over $\mathbb{F}_p$

As of 22 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2608.03097.

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

pith.paper-citation-record.v1
2608.03097 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T14:57:54.403457Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

30 of 30 outbound references displayed

verified exact1
verified fuzzy19
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7cf304d1-98ec-43f1-8441-5ef506053028 · outbound

This paper cites Orderings of k-Markov Numbers.

Counting in Vieta graphs over $\mathbb{F}_p$ Orderings of k-Markov Numbers

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T14:57:54.281560Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d9baebb-55d2-4f9a-8084-1eea3f50bb2e · outbound

This paper cites Baragar:The Markoff equation and equations of Hurwitz, Ph.D.

Counting in Vieta graphs over $\mathbb{F}_p$ Baragar:The Markoff equation and equations of Hurwitz, Ph.D

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.921509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d6e025e0-dfd3-4830-98bf-3535336cb209 · outbound

This paper cites Baragar:Integral solutions of Markoff–Hurwitz equations, J.

Counting in Vieta graphs over $\mathbb{F}_p$ Baragar:Integral solutions of Markoff–Hurwitz equations, J

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.908770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e4dd8f76-73cc-4e30-91c8-d6f67a623532 · outbound

This paper cites Bourgain, A.

Counting in Vieta graphs over $\mathbb{F}_p$ Bourgain, A

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.895793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d20e0e5d-838a-4671-b5dc-efc3fd5b6a8a · outbound

This paper cites Bourgain, A.

Counting in Vieta graphs over $\mathbb{F}_p$ Bourgain, A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.883602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6f33e2c6-837b-4a3f-93ef-3edd4e3c69a8 · outbound

This paper cites Cantat:Bers and H´ enon, Painlev´ e and Schr¨ odinger, Duke Math.

Counting in Vieta graphs over $\mathbb{F}_p$ Cantat:Bers and H´ enon, Painlev´ e and Schr¨ odinger, Duke Math

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.870990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1ea8ed73-82e4-45ef-8c2f-96eb80f8c885 · outbound

This paper cites Cantat, F.

Counting in Vieta graphs over $\mathbb{F}_p$ Cantat, F

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.858416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3b942a80-7deb-403f-9a91-a75e3a1cb3ab · outbound

This paper cites Carlitz:Certain special equations in a finite field, Monatsh.

Counting in Vieta graphs over $\mathbb{F}_p$ Carlitz:Certain special equations in a finite field, Monatsh

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.845677Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 00a1c3ec-f49b-4ea3-9adf-7d65d06cc67c · outbound

This paper cites Carlitz:The number of solutions of some equations in a finite field, Portugal.

Counting in Vieta graphs over $\mathbb{F}_p$ Carlitz:The number of solutions of some equations in a finite field, Portugal

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.832912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 146b4bf3-601f-409b-9f03-25838f3eec50 · outbound

This paper cites Carlitz:The number of points on certain cubic surfaces over a finite field, Boll.

Counting in Vieta graphs over $\mathbb{F}_p$ Carlitz:The number of points on certain cubic surfaces over a finite field, Boll

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.820619Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ad4d1751-8091-459c-849e-2c06b5156f5f · outbound

This paper cites an unresolved cited work.

Counting in Vieta graphs over $\mathbb{F}_p$ Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:57:54.807983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cbf68e56-2246-4adf-857c-bf6eed847fbf · outbound

This paper cites de Courcy-Ireland:Non-planarity of Markoff graphs modp, Comment.

Counting in Vieta graphs over $\mathbb{F}_p$ de Courcy-Ireland:Non-planarity of Markoff graphs modp, Comment

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.795537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 74e5f3bb-82a2-4d07-8d0a-50392c905d8f · outbound

This paper cites de Courcy-Ireland, S.

Counting in Vieta graphs over $\mathbb{F}_p$ de Courcy-Ireland, S

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.782814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1293f760-6e02-4a39-aac5-93a4288044d9 · outbound

This paper cites Divisibility by $p$ for Markoff-like Surfaces.

Counting in Vieta graphs over $\mathbb{F}_p$ Divisibility by $p$ for Markoff-like Surfaces

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T14:57:54.338392Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d392becf-ac28-41b3-9c8e-69dbed2ddb67 · outbound

This paper cites an unresolved cited work.

Counting in Vieta graphs over $\mathbb{F}_p$ Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:57:54.769727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 612c7ec0-9c3f-4487-b859-30b12816b4ea · outbound

This paper cites Fuchs, M.

Counting in Vieta graphs over $\mathbb{F}_p$ Fuchs, M

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.757559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 87dae90e-ce3b-476c-9ad6-1f0a1e69184a · outbound

This paper cites Gamburd:Arithmetic and dynamics on varieties of Markoff type, ICM—International Congress of Mathematicians 2022, Vol.

Counting in Vieta graphs over $\mathbb{F}_p$ Gamburd:Arithmetic and dynamics on varieties of Markoff type, ICM—International Congress of Mathematicians 2022, Vol

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.745264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dee00422-7668-4efa-bc49-a3f70fb7b011 · outbound

This paper cites Ghosh, P.

Counting in Vieta graphs over $\mathbb{F}_p$ Ghosh, P

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.731812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ede82c50-77ce-41f5-84b7-6903f658ce8e · outbound

This paper cites an unresolved cited work.

Counting in Vieta graphs over $\mathbb{F}_p$ Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:57:54.719182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 987f28e2-9d71-4c62-b6b7-6baf0aa93721 · outbound

This paper cites Uniqueness theorem of generalized Markov numbers that are prime powers.

Counting in Vieta graphs over $\mathbb{F}_p$ Uniqueness theorem of generalized Markov numbers that are prime powers

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T14:57:54.362798Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce8ab713-1edc-4c75-95da-c5ddc6ddc0c5 · outbound

This paper cites SL(2,Z)-matrixizations of generalized Markov numbers.

Counting in Vieta graphs over $\mathbb{F}_p$ SL(2,Z)-matrixizations of generalized Markov numbers

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T14:57:54.367423Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af17b819-87cf-4845-8e89-f74f9af85079 · outbound

This paper cites Gyoda, K.

Counting in Vieta graphs over $\mathbb{F}_p$ Gyoda, K

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.706125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6bcc09f6-e039-4707-838c-085ab8df85d2 · outbound

This paper cites Kiritchenko, M.

Counting in Vieta graphs over $\mathbb{F}_p$ Kiritchenko, M

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.693232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9b7ea281-1f82-4907-92b8-04b3e7b6e5ee · outbound

This paper cites an unresolved cited work.

Counting in Vieta graphs over $\mathbb{F}_p$ Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:57:54.680082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 30304e28-54f9-490f-a869-d215fde93d2e · outbound

This paper cites an unresolved cited work.

Counting in Vieta graphs over $\mathbb{F}_p$ Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:57:54.665634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 35c6a5bc-c4b5-461f-8aef-dde9d5dbcd36 · outbound

This paper cites Nica:Jacobsthal Sums, Monogr.

Counting in Vieta graphs over $\mathbb{F}_p$ Nica:Jacobsthal Sums, Monogr

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.652662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ece25833-1093-494f-b732-a11c23b700ee · outbound

This paper cites Rebelo, R.

Counting in Vieta graphs over $\mathbb{F}_p$ Rebelo, R

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.639508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 748740e8-c4ad-4659-8e94-e3c6d319f206 · outbound

This paper cites Silverman:The Markoff equation: past, present, future, Notices Amer.

Counting in Vieta graphs over $\mathbb{F}_p$ Silverman:The Markoff equation: past, present, future, Notices Amer

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:57:54.625095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6af80272-a90d-4e49-add6-fe77054585f8 · outbound

This paper cites Satake, Y.

Counting in Vieta graphs over $\mathbb{F}_p$ Satake, Y

Reference 29

Resolution: verified exact; raw_fallback, observed 2026-08-15T14:57:54.543821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9eb5ad28-8049-4b4b-9f5e-d555611fcdb6 · outbound

This paper cites an unresolved cited work.

Counting in Vieta graphs over $\mathbb{F}_p$ Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:57:54.611046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.