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Paper Citation Record · LEDGER

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$

As of 20 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 1 inbound Pith citation observation for arXiv:2606.11301.

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

pith.paper-citation-record.v1
2606.11301 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-27T10:46:11.287420Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-12T14:00:26.551941Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

14 of 14 outbound references displayed

  • verified exact3
  • verified fuzzy0
  • unresolved11
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cc5a1252-1c81-4ebc-972f-03e6fdf98e75 · outbound

This paper cites Alexander Polynomials of closed alternating braids.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Alexander Polynomials of closed alternating braids

Reference 1

Resolution
verified exact
arxiv_id, observed 2026-07-03T08:17:46.027366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:2e67103dd02761d3a83e9e750bdb14d562920f870ca3b481a721d310db227775

Observation 8d0b5a03-567f-4253-9912-2bb3f4b1004c · outbound

This paper cites On Fox's trapezoidal conjecture.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ On Fox's trapezoidal conjecture

Reference 2

Resolution
verified exact
arxiv_id, observed 2026-07-03T08:17:46.019718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:1a2a61bb84f5073ab4d1ce9af50b8e3fdb5aa094508635b9bd3a829a69872344

Observation 5047d22c-32e8-4d13-bd28-e9705376c826 · outbound

This paper cites an unresolved cited work.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Unresolved cited work

Reference 3

Resolution
unresolved
no resolver link, observed 2026-06-27T10:46:11.287420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:049f345ea95785a4167717a1afb12222c793cb360b759c54e045e959b6959a1c

Observation d2552792-b7da-4a3a-b9ec-c9d9e02a8464 · outbound

This paper cites Burau, ¨Uber zopfgruppen und gleichsinnig verdrillte verkettungen, Abhandlungen aus dem Mathematischen Seminar der Universit¨ at Hamburg11(1936), 179–186.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Burau, ¨Uber zopfgruppen und gleichsinnig verdrillte verkettungen, Abhandlungen aus dem Mathematischen Seminar der Universit¨ at Hamburg11(1936), 179–186

Reference 4

Resolution
unresolved
no resolver link, observed 2026-06-27T10:46:11.287420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:eb8294cb275e2f8f2a7d05cdad95b19d86cc7317c3a4c4890625be5bf2fad3cd

Observation a5ed1527-9029-452d-aabe-c327f2172bc4 · outbound

This paper cites an unresolved cited work.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Unresolved cited work

Reference 5

Resolution
verified exact
arxiv_id, observed 2026-07-03T08:17:46.023361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:6d938611d50ed332b7a29a2d3b35021526eaa697e96a24cfe991dd429fa4c628

Observation ba120c43-ec99-4463-8b0b-e1e42eedaa62 · outbound

This paper cites Kawauchi,A survey of knot theory, Birkh¨ auser, Basel, 1996.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Kawauchi,A survey of knot theory, Birkh¨ auser, Basel, 1996

Reference 6

Resolution
unresolved
no resolver link, observed 2026-06-27T10:46:11.287420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:1b68513460303fc2702c7c5c658efa91bcb2c4b9de113cde6953b556c8ba37bb

Observation 6d06f77a-4632-4739-b2ab-adfdec78470f · outbound

This paper cites Keilson and H.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Keilson and H

Reference 7

Resolution
unresolved
no resolver link, observed 2026-06-27T10:46:11.287420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:eed01e0d0ecfd9b5885d2d4e75f466f1794e94aecf52269c527b04b09b2c0ef2

Observation af46fecd-b761-4f51-be4d-b10cc3cc1dc1 · outbound

This paper cites an unresolved cited work.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Unresolved cited work

Reference 8

Resolution
unresolved
no resolver link, observed 2026-06-27T10:46:11.287420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:8df5c2aadf5a63d6ac52cf0bd805453b4b5dd90acde6d08d2092004c5426ed0a

Observation df64f6f5-e4dd-42e2-b1ee-b2138308f4aa · outbound

This paper cites an unresolved cited work.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Unresolved cited work

Reference 9

Resolution
unresolved
no resolver link, observed 2026-06-27T10:46:11.287420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:cfdb94a57d40b3adc1003e6995b6fa3de788353e9cc34f9fccfe4f99fce60070

Observation 59b066e5-740d-4cea-a2f9-8ecc2515fddf · outbound

This paper cites Murasugi,On the alexander polynomial of the alternating knot, Osaka Mathematical Journal10(1958), no.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Murasugi,On the alexander polynomial of the alternating knot, Osaka Mathematical Journal10(1958), no

Reference 10

Resolution
unresolved
no resolver link, observed 2026-06-27T10:46:11.287420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:f2f0170bf529518514192e8616e0cc2475547eb45640721885d28df8674f2260

Observation 628c8dce-b283-4477-bf0d-48cfd5c133dd · outbound

This paper cites Petkovˇ sek, H.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Petkovˇ sek, H

Reference 11

Resolution
unresolved
no resolver link, observed 2026-06-27T10:46:11.287420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:f5fedeb58c7c803bc5142ad676393b1d38028e10250fb5508df9bcdc1f8584e0

Observation b9a462c5-b3dc-4fbc-a947-1a8cff61e5f6 · outbound

This paper cites Rolfsen,Knots and links, Publish or Perish, Berkeley, CA, 1976.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Rolfsen,Knots and links, Publish or Perish, Berkeley, CA, 1976

Reference 12

Resolution
unresolved
no resolver link, observed 2026-06-27T10:46:11.287420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:1a907a563a9fcb57b57ffc605b2b9d25172e61e65dae60c4aaf6cc3e5d3bbf80

Observation 3f51f89d-089c-472e-9337-f4c91d4571be · outbound

This paper cites an unresolved cited work.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Unresolved cited work

Reference 13

Resolution
unresolved
no resolver link, observed 2026-06-27T10:46:11.287420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:31b05b16b1a350810f69a057c7f56565f908a883dd1364845540b5fb6fab4148

Observation a8321f24-c349-431e-94a7-c05518853537 · outbound

This paper cites Takemura,Relations among alexander-conway polynomials of turk’s head links, Tech.

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$ Takemura,Relations among alexander-conway polynomials of turk’s head links, Tech

Reference 14

Resolution
unresolved
no resolver link, observed 2026-06-27T10:46:11.287420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:d4973d04d95a662df2529fafb375c211fefaa67ed5ad2b558d37c3bde13e4526

Pith citing papers

Observation 3b04a61c-a94b-45ff-b742-ea1e8f01e471 · inbound

Fox's Trapezoidal Conjecture for Four-Strand Turk's Head Knots and Links cites this paper.

Fox's Trapezoidal Conjecture for Four-Strand Turk's Head Knots and Links Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$

Reference 6

Resolution
unresolved
no resolver link, observed 2026-07-12T14:00:26.551941Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-12T14:00:26.551941Z digest=sha256:98511503899b7ea1fbeb997051e54cb35b372df80cb31580075444d4bb46d6db