Paper Citation Record · LEDGER

The Generalized Skew Spectrum of Graphs

As of 8 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2505.23609.

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

pith.paper-citation-record.v1
2505.23609 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:50:03.631661Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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 fuzzy8
unresolved9
parse uncertain1
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 41d8d50f-b570-48f8-869e-9b11c962248c · outbound

This paper cites an unresolved cited work.

The Generalized Skew Spectrum of Graphs Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:07.074456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 56aa75b3-a23c-4249-a4df-5be25d861342 · outbound

This paper cites an unresolved cited work.

The Generalized Skew Spectrum of Graphs Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:06.936467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d41e83af-d861-42ec-98eb-bbbe95cbf535 · outbound

This paper cites an unresolved cited work.

The Generalized Skew Spectrum of Graphs Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:06.708151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5a287f03-2ce3-47c1-9681-912dadf5b6d6 · outbound

This paper cites an unresolved cited work.

The Generalized Skew Spectrum of Graphs Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:05.895349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3a4c04a6-7390-495d-9a74-205fa0f91148 · outbound

This paper cites an unresolved cited work.

The Generalized Skew Spectrum of Graphs Unresolved cited work

Reference 5

Resolution: parse uncertain; raw_fallback, observed 2026-08-07T12:50:06.454040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 47d0953a-951b-49d1-af28-c91a2d9416c5 · outbound

This paper cites an unresolved cited work.

The Generalized Skew Spectrum of Graphs Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:06.285283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 10a32caa-3765-4e70-b604-308c4bd05205 · outbound

This paper cites an unresolved cited work.

The Generalized Skew Spectrum of Graphs Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:06.094928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 85aa92ee-7b66-4b45-8791-1f72238d7746 · outbound

This paper cites an unresolved cited work.

The Generalized Skew Spectrum of Graphs Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:05.725468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 16ba2628-644a-4eb3-af12-0a825bc511ef · outbound

This paper cites an unresolved cited work.

The Generalized Skew Spectrum of Graphs Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:50:05.500732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1c473f9c-3632-4663-aad4-822e079535b3 · outbound

This paper cites Here, σ · g represents the group operation combining two elements, while σ(j) denotes the image of j under σ.

The Generalized Skew Spectrum of Graphs Here, σ · g represents the group operation combining two elements, while σ(j) denotes the image of j under σ

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:05.293105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7022bf40-d455-4ca9-9ab3-234fe638e8ba · outbound

This paper cites (33) Hence, 1 |Sn−2| X h∈Sn−2 f ′ i (σhg(n − 1), σhg(n)) = f ′ i (σ(n − 1), σ(n)) = fi(σ) (34) So the term breaks in 1 n−2 Pn−2 j=1 Pi(g1, σ, j).

The Generalized Skew Spectrum of Graphs (33) Hence, 1 |Sn−2| X h∈Sn−2 f ′ i (σhg(n − 1), σhg(n)) = f ′ i (σ(n − 1), σ(n)) = fi(σ) (34) So the term breaks in 1 n−2 Pn−2 j=1 Pi(g1, σ, j)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:05.147171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5d9ef090-f0ed-4a97-99f0-c0f5d2cb1bb5 · outbound

This paper cites (37) So the term breaks in 1 n−2 Pn−2 j=1 Pi(g2, σ, j).

The Generalized Skew Spectrum of Graphs (37) So the term breaks in 1 n−2 Pn−2 j=1 Pi(g2, σ, j)

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:04.873276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 12657c88-8ad2-4931-831c-71318e39fb2f · outbound

This paper cites Grouping these terms, we can write 1 |Sn−2| X h∈Sn−2 f ′ i (σhg(n − 1), σhg(n)) = 1 (n − 2)! n−2X j=1 (n − 3)!f ′(σ(j), σ(n)) = 1 n − 2 n−2X j=1 f (σ · (n − 1, j)).

The Generalized Skew Spectrum of Graphs Grouping these terms, we can write 1 |Sn−2| X h∈Sn−2 f ′ i (σhg(n − 1), σhg(n)) = 1 (n − 2)! n−2X j=1 (n − 3)!f ′(σ(j), σ(n)) = 1 n − 2 n−2X j=1 f (σ · (n − 1, j))

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:04.581618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 396a5615-d8a9-4d0a-9107-2a9d8f41ba00 · outbound

This paper cites (43) 17 So the term breaks in 1 n−2 Pn−2 j=1 Pi(g4, σ, j).

The Generalized Skew Spectrum of Graphs (43) 17 So the term breaks in 1 n−2 Pn−2 j=1 Pi(g4, σ, j)

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:04.343193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e5588696-500c-4231-8f0a-f472bfd33aa1 · outbound

This paper cites (46) So the term breaks in 1 n−2 Pn−2 j=1 Pi(g5, σ, j).

The Generalized Skew Spectrum of Graphs (46) So the term breaks in 1 n−2 Pn−2 j=1 Pi(g5, σ, j)

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:04.127350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 334db8c1-a5f2-492f-851a-69d344b505c0 · outbound

This paper cites (50) So the term breaks in 1 n−2 Pn−2 j=1 Pi(g6, σ, j).

The Generalized Skew Spectrum of Graphs (50) So the term breaks in 1 n−2 Pn−2 j=1 Pi(g6, σ, j)

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:03.989625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 966cc28c-d244-4b58-b38b-7d0f1236b95a · outbound

This paper cites post-concatenation.

The Generalized Skew Spectrum of Graphs post-concatenation

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:50:03.803620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2d5969b8-edba-4ada-b1af-517205c2759b · outbound

This paper cites Hierarchical Graph Pooling with Structure Learning.

The Generalized Skew Spectrum of Graphs Hierarchical Graph Pooling with Structure Learning

Reference 203

Resolution: unresolved; no resolver link, observed 2026-08-07T12:50:02.044686Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.