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Paper Citation Record · LEDGER

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

As of 17 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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:1ffcaf5a68dfa657dbd1b58ea3414429dcbf7edeed517277926461cf5e7ccc08

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:66e8ef56eb1c38c85c727b4c61306b4e722658c592b1a57da657212d25d082e8

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=sha256:4636a47994a4fec5c0084265924f7d15907f8bad8a16ff71dcc80cd7e82a6ede

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=sha256:07c5469d718ce4e7c82bd47e8e24bd620a6bfa0f38d938c09e25b53006bf99c7

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-06-27T10:46:11.287420Z digest=sha256:06ceeb539621914312f8f4e3e596f8ed6f1b081ff8583aecf5574a6a3324f517

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=sha256:9775a757ae06793c54fae9975892bae5da89c90952eb341caa0b8d6b34a84f71

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:f43a0cfb0e2b65211ae8ec4b205d88dbe36a7a5b82a1409165a793c03ecf4aa8

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=sha256:942922ed77010ffe760f23fbc746369e6ae223127dfde38a710e645bfd6357fc

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=sha256:8a34b9aea0fc561f5945ccd0352b72e8fbe7e79a87c275c807c765b80aea3500

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=sha256:9053109b953956ed3fcd9959519ab5c4d0ac988d63012d2f096ec5deb5e46a1b

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=sha256:82026f7e03926025d1318c060d5ee9e05cd847945ffe84088e21cfc8f27a705a

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:e0931a1525a8607332d8f9fff2fbac917ec62712d3d9af53d093cc97783d9770

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=sha256:544a0829df257bc13819ac564ad82e5491a30190669c5632c5f1c05feaf4586f

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=sha256:3a8e881f1aa0a58693bcddb2ca8bda4093ad61fde79d3b7f3ecbf07272277729

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=sha256:65f54636a1f176c0964992fdf22d81eadcabb4cc67126ad4024a1a563215e24a