Paper Citation Record · LEDGER

Pierce-Birkhoff conjecture is true for splines

As of 12 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2507.07976.

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

pith.paper-citation-record.v1
2507.07976 v2

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:42:42.403930Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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 fuzzy18
unresolved15
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 00a735a9-bab6-437c-a10d-5abb08ba71a3 · outbound

This paper cites Aguiar and S.

Pierce-Birkhoff conjecture is true for splines Aguiar and S

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:50.491919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2faa1535-7acd-48b4-8c38-9b41f0354230 · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:50.184932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4f9523e0-7863-4c02-81ec-46bf2f93f6b8 · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:49.902819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 732e0b7e-384e-4b54-8e36-b8a918be6ea5 · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:49.656188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f87a1f88-b421-49ac-9826-f63b72d04b9d · outbound

This paper cites Birkhoff and R.

Pierce-Birkhoff conjecture is true for splines Birkhoff and R

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:49.378225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ced247f4-88a6-4e63-8fa0-e5cd9980b209 · outbound

This paper cites Bochnak, M.

Pierce-Birkhoff conjecture is true for splines Bochnak, M

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:49.124901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ab64fb0b-cc11-4d5b-8177-74e8dd0524a7 · outbound

This paper cites Br¨ ocker.

Pierce-Birkhoff conjecture is true for splines Br¨ ocker

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:48.819352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation da56465b-eb8b-4a7a-88b1-10cac802c6bd · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:48.597170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0aafaf6e-1091-4ae9-ab5a-82bbbb79a2c8 · outbound

This paper cites de Boor, K.

Pierce-Birkhoff conjecture is true for splines de Boor, K

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:48.364545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 774f0d07-5b12-468b-9065-cd1ef12a1b25 · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:48.125393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 52ca786a-1550-4b52-83ac-af43a0ff1084 · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:47.894759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 22cd0220-3b31-4911-a907-3c029507d3e0 · outbound

This paper cites DiPasquale and F.

Pierce-Birkhoff conjecture is true for splines DiPasquale and F

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:47.672182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation eeca06ed-6b06-4654-8bb9-ec0f26e5bdb7 · outbound

This paper cites DiPasquale, F.

Pierce-Birkhoff conjecture is true for splines DiPasquale, F

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:47.429137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 14ab59cd-d173-4980-8efe-321cafe32525 · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T18:42:38.968475Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3af33cbf-d29f-4117-8f45-0b022fb9363e · outbound

This paper cites Henriksen and J.

Pierce-Birkhoff conjecture is true for splines Henriksen and J

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:47.168161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 9de59516-b918-4115-a5a7-27bf8645423e · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:46.860026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3ecffe69-52db-4b94-b579-a19911882c7e · outbound

This paper cites Attention is a smoothed cubic spline.

Pierce-Birkhoff conjecture is true for splines Attention is a smoothed cubic spline

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T18:42:39.402921Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8a2e491-1c1c-407b-b832-e4ccdb009b53 · outbound

This paper cites Lapenta and I.

Pierce-Birkhoff conjecture is true for splines Lapenta and I

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:46.618343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation cba0478e-815f-4ff1-b13d-cd659688a3b6 · outbound

This paper cites Lucas, J.

Pierce-Birkhoff conjecture is true for splines Lucas, J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:46.361640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1f1ed511-49f8-41da-b1db-fc4768ee33b3 · outbound

This paper cites Lucas, J.

Pierce-Birkhoff conjecture is true for splines Lucas, J

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:46.142853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e69e85f1-96ad-44a6-921c-9eae101131f1 · outbound

This paper cites Lucas, D.

Pierce-Birkhoff conjecture is true for splines Lucas, D

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:45.858136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ea39ad45-63f0-4139-b200-f03d3ea0f69b · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:45.589392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e5688b59-599a-4da8-ba17-0753ad47ead1 · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:45.319893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a180833a-429a-4e21-8279-1bbdfb03fa59 · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:45.065158Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c4e299c8-242f-4d72-9f8d-927555de84f3 · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:44.801141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 946f6128-14c0-4789-a39e-7dfaabad34b5 · outbound

This paper cites Marshall.

Pierce-Birkhoff conjecture is true for splines Marshall

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:44.477524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 41a0355e-e79d-47eb-ae02-5e6068f6ad54 · outbound

This paper cites Matouˇ sek.Lectures on discrete geometry, volume 212 of Graduate Texts in Mathematics.

Pierce-Birkhoff conjecture is true for splines Matouˇ sek.Lectures on discrete geometry, volume 212 of Graduate Texts in Mathematics

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:44.229360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1d0c13cf-a4ae-4179-a746-d4581ba84d2d · outbound

This paper cites Ovchinnikov.

Pierce-Birkhoff conjecture is true for splines Ovchinnikov

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:43.900467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2349e566-c49f-4070-b7e7-0ec4c7be133c · outbound

This paper cites Plaumann.

Pierce-Birkhoff conjecture is true for splines Plaumann

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:43.579291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 06b43c92-ce9a-45f0-8641-18dc657a459c · outbound

This paper cites Shekhtman and T.

Pierce-Birkhoff conjecture is true for splines Shekhtman and T

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:43.378097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation db2333ba-57dd-45fd-b051-051ffb98381b · outbound

This paper cites Stoer and C.

Pierce-Birkhoff conjecture is true for splines Stoer and C

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:42:43.145484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 77de3c02-4bd1-474b-bd91-b24167cb5459 · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:42.912160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 27b4a8b6-f545-44b6-91ac-40e47411b38f · outbound

This paper cites an unresolved cited work.

Pierce-Birkhoff conjecture is true for splines Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:42:42.667138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

No inbound Pith citation observations are available.