Paper Citation Record · LEDGER

Hypercubic structures behind $\hat{Z}$-invariants

As of 11 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 1 inbound Pith citation observation for arXiv:2501.12985.

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

pith.paper-citation-record.v1
2501.12985 v1

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T16:42:13.846910Z

measured 21 of 21 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:19:10.552595Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T16:19:10.915704Z

Reference resolution

20 of 20 outbound references displayed

verified exact6
verified fuzzy4
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 01e5374e-479a-4745-9ba7-5ba9e7b42b75 · outbound

This paper cites Quantum Langlands duality of representations of W-algebras.

Hypercubic structures behind $\hat{Z}$-invariants Quantum Langlands duality of representations of W-algebras

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T16:42:13.755678Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd03308c-8cdc-48c1-9b31-b7756d38a00f · outbound

This paper cites Creutzig, S.

Hypercubic structures behind $\hat{Z}$-invariants Creutzig, S

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:42:14.287248Z

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 e910139a-5f8c-4a34-a1a8-93b715588aca · outbound

This paper cites an unresolved cited work.

Hypercubic structures behind $\hat{Z}$-invariants Unresolved cited work

Reference 3

Resolution: verified exact; doi, observed 2026-08-10T16:42:13.948491Z

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 0d445e4c-f136-498e-930c-054270d5426d · outbound

This paper cites an unresolved cited work.

Hypercubic structures behind $\hat{Z}$-invariants Unresolved cited work

Reference 4

Resolution: verified exact; doi, observed 2026-08-10T16:42:13.934685Z

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 158db092-3312-4df6-b883-ba42433e0b3b · outbound

This paper cites an unresolved cited work.

Hypercubic structures behind $\hat{Z}$-invariants Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-10T16:42:13.775895Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17429e82-2584-49ad-9ecd-459dbb5b7d68 · outbound

This paper cites Feigin, A.M.

Hypercubic structures behind $\hat{Z}$-invariants Feigin, A.M

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:42:14.274990Z

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 d657f764-cf81-48fc-8e43-efbf6ace572c · outbound

This paper cites Logarithmic CFTs connected with simple Lie algebras.

Hypercubic structures behind $\hat{Z}$-invariants Logarithmic CFTs connected with simple Lie algebras

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T16:42:13.785099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72025ab9-5459-481b-bb2e-a48df437c61d · outbound

This paper cites Gukov, D.

Hypercubic structures behind $\hat{Z}$-invariants Gukov, D

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-10T16:42:13.790747Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9803c4b0-5615-4e4a-951b-a8266a2c60a1 · outbound

This paper cites an unresolved cited work.

Hypercubic structures behind $\hat{Z}$-invariants Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:42:14.262128Z

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 43342270-2a6d-4445-bcbd-63791fc5071b · outbound

This paper cites A Lie algebraic pattern behind logarithmic CFTs.

Hypercubic structures behind $\hat{Z}$-invariants A Lie algebraic pattern behind logarithmic CFTs

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T16:42:13.800858Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f458e257-6950-4294-8060-79e32828e1df · outbound

This paper cites Murakami.

Hypercubic structures behind $\hat{Z}$-invariants Murakami

Reference 11

Resolution: verified exact; raw_fallback, observed 2026-08-10T16:42:14.058636Z

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 00eb6ea6-b2e5-46cc-afb2-73b14a48cfe2 · outbound

This paper cites Murakami.

Hypercubic structures behind $\hat{Z}$-invariants Murakami

Reference 12

Resolution: verified exact; doi, observed 2026-08-10T16:42:13.909692Z

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 4c61dae0-3dc7-4869-86e8-3eda1194ee4a · outbound

This paper cites Matsusaka, Y.

Hypercubic structures behind $\hat{Z}$-invariants Matsusaka, Y

Reference 13

Resolution: verified exact; doi, observed 2026-08-10T16:42:13.896702Z

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 91e9a67b-db00-41f2-b69a-31e9e042e8d3 · outbound

This paper cites Projective covers of the simple modules for the triplet $W$-algebra $\mathcal{W}_{p_+,p_-}$.

Hypercubic structures behind $\hat{Z}$-invariants Projective covers of the simple modules for the triplet $W$-algebra $\mathcal{W}_{p_+,p_-}$

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T16:42:13.820122Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37d4ee3a-850d-461e-9840-8471f41caa99 · outbound

This paper cites an unresolved cited work.

Hypercubic structures behind $\hat{Z}$-invariants Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:42:14.250201Z

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 669423ef-ce2f-4e63-8d9b-323a57ce6c0f · outbound

This paper cites Sugimoto.

Hypercubic structures behind $\hat{Z}$-invariants Sugimoto

Reference 16

Resolution: verified exact; doi, observed 2026-08-10T16:42:13.882793Z

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 3be52619-13fa-450f-910c-1e5f682e0480 · outbound

This paper cites Sugimoto.

Hypercubic structures behind $\hat{Z}$-invariants Sugimoto

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:42:14.237647Z

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 3ed3b4c8-d59f-4518-a8d5-5fd3e7596a8c · outbound

This paper cites Atiyah-Bott formula and homological block of Seifert fibered homology $3$-spheres.

Hypercubic structures behind $\hat{Z}$-invariants Atiyah-Bott formula and homological block of Seifert fibered homology $3$-spheres

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-10T16:42:13.838319Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5050eac-f6c5-498e-80f6-595dc9bb3abc · outbound

This paper cites Tsuchiya, S.

Hypercubic structures behind $\hat{Z}$-invariants Tsuchiya, S

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:42:14.225246Z

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 9d5068a6-58af-4d53-bf2f-4caf6f8359e1 · outbound

This paper cites an unresolved cited work.

Hypercubic structures behind $\hat{Z}$-invariants Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:42:14.212363Z

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

Observation 6c9be093-d8c7-4696-9bd4-d65c62d6a673 · inbound

Nesting behind $\hat{Z}$-invariants cites this paper.

Nesting behind $\hat{Z}$-invariants Hypercubic structures behind $\hat{Z}$-invariants

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:19:11.041170Z

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.