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Paper Citation Record · LEDGER

A counterexample for the polar conjecture of Spencer-Brown

As of 11 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2607.22398.

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

pith.paper-citation-record.v1
2607.22398 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T04:55:10.806509Z

measured 18 of 18 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

18 of 18 outbound references displayed

  • verified exact0
  • verified fuzzy0
  • unresolved17
  • parse uncertain0
  • malformed identifier1
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b3560cc8-2995-4b6b-bb7a-5313d7a493e4 · outbound

This paper cites Appel and W.

A counterexample for the polar conjecture of Spencer-Brown Appel and W

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.734834Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.734834Z digest=sha256:0b7941d0a084f7d5135d5a607eb2675e004bc546ad4c5e3bcfa83a3f58afae7a

Observation 9cc70f98-47a5-481e-806b-0435175df44b · outbound

This paper cites Appel, W.

A counterexample for the polar conjecture of Spencer-Brown Appel, W

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.740278Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.740278Z digest=sha256:af5c174157db17dd147fc2c43c5861387cd279c1fd23369e87f62898cf430709

Observation 5db53d36-82d8-4c56-aca2-f4d63430292a · outbound

This paper cites Baldridge, L.

A counterexample for the polar conjecture of Spencer-Brown Baldridge, L

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.744566Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.744566Z digest=sha256:432939cd49779bc767b770f3c9ace8c8cc9f71fc6716158bd2e7d075b584f30b

Observation fd035756-c77f-4cc8-854e-d48d5ff52aae · outbound

This paper cites The 2-Factor Polynomial Detects Even Perfect Matchings.

A counterexample for the polar conjecture of Spencer-Brown The 2-Factor Polynomial Detects Even Perfect Matchings

Reference 4

Resolution
malformed identifier
no resolver link, observed 2026-08-01T04:55:10.748888Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.748888Z digest=sha256:d93bbeb6ff92bbeb6a43b204a49f735054621c8d493e8ad274a9c2bcfd2825f5

Observation a03a4caf-76ef-4661-a5e1-7bffe32b021b · outbound

This paper cites A topological quantum field theory approach to graph coloring.

A counterexample for the polar conjecture of Spencer-Brown A topological quantum field theory approach to graph coloring

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.754036Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.754036Z digest=sha256:14d51debe8988a9a3c881a2fbcc3c60a42e11e0a60d46773bb347cb3c8c2ef1a

Observation 59da4f89-b811-4687-9536-1bfe5ba65fde · outbound

This paper cites A new way to prove configuration reducibility using gauge theory.

A counterexample for the polar conjecture of Spencer-Brown A new way to prove configuration reducibility using gauge theory

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.758925Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.758925Z digest=sha256:26e338202f4de9d810ffdee346e51b10ca3428b08ce5d6aacfb7ecb5efa1c07f

Observation 148e15e2-d21c-4c62-8efb-0f8d56d851b8 · outbound

This paper cites Baldridge and B.

A counterexample for the polar conjecture of Spencer-Brown Baldridge and B

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.763310Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.763310Z digest=sha256:ea002b084315d6895daa13a8d5c4d44beb447399f85109ba9ac9423bd44957cf

Observation 1a4879eb-c456-4564-9918-9d3d29c272c2 · outbound

This paper cites Baldridge, L.

A counterexample for the polar conjecture of Spencer-Brown Baldridge, L

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.767090Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.767090Z digest=sha256:5ac4b229c113e963e100937cf6f67b97eae6010df5b09684a3bcfcd819db4bc6

Observation 2f893e51-e7aa-4bc6-8230-f20fd0be0d4a · outbound

This paper cites an unresolved cited work.

A counterexample for the polar conjecture of Spencer-Brown Unresolved cited work

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.770992Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.770992Z digest=sha256:2228702eae25dadb8719c4e57cae07513e892f4ad906afa87fd01964f9d40087

Observation cf4f2226-c6ea-4647-99c0-c2fd81e14cdb · outbound

This paper cites H.,A state calculus for graph coloring, Illinois Journal of Mathematics, Volume 60, Number 1, Spring 2016, pp 251-271 S 0019-2082 (Special Issue celebrating Wolfgang Haken).

A counterexample for the polar conjecture of Spencer-Brown H.,A state calculus for graph coloring, Illinois Journal of Mathematics, Volume 60, Number 1, Spring 2016, pp 251-271 S 0019-2082 (Special Issue celebrating Wolfgang Haken)

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.775156Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.775156Z digest=sha256:4870822c24f93ce339f34be55bbf74e3e0d6ed9daf890bab62642ff2116fbd48

Observation 07141c76-3acd-4a26-9ec3-2149ba18ce8c · outbound

This paper cites H.Map coloring and the vector cross product, J.

A counterexample for the polar conjecture of Spencer-Brown H.Map coloring and the vector cross product, J

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.779064Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.779064Z digest=sha256:ee567758cf02d4a5bd7a7da0d3090f0e01d6de2af4a4259895d86c07e13f41f9

Observation 34800331-e5e4-44a8-9684-a1fc1680efe1 · outbound

This paper cites Map Reformulation,.

A counterexample for the polar conjecture of Spencer-Brown Map Reformulation,

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.783127Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.783127Z digest=sha256:965b8132bc169248a7cff6b2652346c4ca681a7e17eb0e10a93d629d6d527a54

Observation 353c218b-d746-4739-ba66-4a087865a334 · outbound

This paper cites Reformulating the Map Color Theorem.

A counterexample for the polar conjecture of Spencer-Brown Reformulating the Map Color Theorem

Reference 13

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.787000Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.787000Z digest=sha256:9a872809c4f42fd58400a79270856bc024bf302ffc805e3b339ff7b9d0651b1a

Observation 18d629f1-0c57-44d9-a742-f0c043306293 · outbound

This paper cites A group of operations on a partially colored map, Bull.

A counterexample for the polar conjecture of Spencer-Brown A group of operations on a partially colored map, Bull

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.791158Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.791158Z digest=sha256:1fddc4d06f5efc634f523060d656df5aeef7037c811b7ccd8e062ccc7f473777

Observation 31f953d4-9415-410c-89c7-67916d5a221f · outbound

This paper cites an unresolved cited work.

A counterexample for the polar conjecture of Spencer-Brown Unresolved cited work

Reference 15

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.795401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.795401Z digest=sha256:b98603f5e5f44a6aa5ac9d2a08dfc83dfe395696a928f6bffacd67a36e217b5b

Observation 4eb118b0-d542-48d1-bd32-153ca812d1e4 · outbound

This paper cites an unresolved cited work.

A counterexample for the polar conjecture of Spencer-Brown Unresolved cited work

Reference 16

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.799287Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.799287Z digest=sha256:a8a123e73140abb83614ea6274267e2f469320fa2fc328723be6bac93ca40b93

Observation 2027c8cd-2741-417a-bbf6-22981f5ffeaf · outbound

This paper cites an unresolved cited work.

A counterexample for the polar conjecture of Spencer-Brown Unresolved cited work

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.803023Z

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.803023Z digest=sha256:db2bf8b9f70dd653478e41db3e8e1e75c036a8e828f9fe6ae72e57db21ecd500

Observation f64cee93-4c34-4aee-b9fc-fb0d13ff10f3 · outbound

This paper cites an unresolved cited work.

A counterexample for the polar conjecture of Spencer-Brown Unresolved cited work

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-01T04:55:10.806509Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T04:55:10.806509Z digest=sha256:a07a63f50244feca133deb302dfbf866279b136fb5edfd89446350a206c8e959

Pith citing papers

No inbound Pith citation observations are available.