Paper Citation Record · LEDGER

Algebraic Aspects of Periodic Graph Operators

As of 15 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 1 inbound Pith citation observation for arXiv:2502.03659.

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

pith.paper-citation-record.v1
2502.03659 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T04:21:16.255659Z

measured 42 of 42 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T12:17:29.865965Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T12:17:29.930842Z

Reference resolution

41 of 41 outbound references displayed

verified exact2
verified fuzzy23
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5bb56830-2a86-40af-93ab-66edccfbc75d · outbound

This paper cites B¨ attig.A toroidal compactification of the two-dimensional Bloch-manifold.

Algebraic Aspects of Periodic Graph Operators B¨ attig.A toroidal compactification of the two-dimensional Bloch-manifold

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.844425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2eb2e93d-0381-4b97-b70c-409466b3671d · outbound

This paper cites B¨ attig.

Algebraic Aspects of Periodic Graph Operators B¨ attig

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.830048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d1430cc8-85ed-4a2c-99b5-c4e4d94d9808 · outbound

This paper cites B¨ attig, H.

Algebraic Aspects of Periodic Graph Operators B¨ attig, H

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.815903Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f4715e77-3bc8-4e37-993a-57e03360608d · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.802100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d8d4c1c6-a79e-4b61-b9e6-a4ec03e7a1ec · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.788159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3aa9e9d0-846c-4d4e-9d82-8960df1518ee · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-09T04:21:16.100282Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5c1f33ec-f3b2-4bcf-bdbb-3590b5c029fd · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.764532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation eb38f1dd-9ecf-467a-bb32-b6ae0f8aa97c · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.750941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c7a20990-c52b-4194-8df6-efc2ce77cb53 · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.738226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation eaeec5ee-7359-4b89-bccb-20323bdd497a · outbound

This paper cites Faust, W.

Algebraic Aspects of Periodic Graph Operators Faust, W

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.724353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0819b6ff-2ed0-43d3-80e1-bb9609d89b5b · outbound

This paper cites Faust, J.

Algebraic Aspects of Periodic Graph Operators Faust, J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.710895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 825f72b7-487f-40e3-b3d1-1c52ed44fb61 · outbound

This paper cites Faust, J.

Algebraic Aspects of Periodic Graph Operators Faust, J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.697774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9055cb35-b47d-4c79-b5f6-90169bf0e299 · outbound

This paper cites Faust and F.

Algebraic Aspects of Periodic Graph Operators Faust and F

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.684128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f7c18a7c-abca-46d4-a73f-6d838aa44048 · outbound

This paper cites Fillman, W.

Algebraic Aspects of Periodic Graph Operators Fillman, W

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.670127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation fb0b5930-15af-45ea-9835-cee35481fc4a · outbound

This paper cites Fillman, W.

Algebraic Aspects of Periodic Graph Operators Fillman, W

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.656339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2f7a3b57-7a0a-4773-b911-28552d017985 · outbound

This paper cites Filonov and I.

Algebraic Aspects of Periodic Graph Operators Filonov and I

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.642706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 38d8d8e2-b9cd-4678-aaac-ec193d50c9dc · outbound

This paper cites Filonov and I.

Algebraic Aspects of Periodic Graph Operators Filonov and I

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.628925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5c0c1b2c-636f-492a-9f3e-94623011371b · outbound

This paper cites Fisher, W.

Algebraic Aspects of Periodic Graph Operators Fisher, W

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.615234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 70efeb4c-628a-47c4-9071-962b9d4d7959 · outbound

This paper cites Gieseker, H.

Algebraic Aspects of Periodic Graph Operators Gieseker, H

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.601030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 97c691fb-a985-45fb-af3d-98bf4a28c920 · outbound

This paper cites Higuchi and Y.

Algebraic Aspects of Periodic Graph Operators Higuchi and Y

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.587565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 04a9bab6-a99a-4cb2-b96e-d495880eb18d · outbound

This paper cites Judge, S.

Algebraic Aspects of Periodic Graph Operators Judge, S

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.574640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 30658bc3-8440-4448-9aa1-190aa78ea0b3 · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.562404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 524906a7-fbe8-46e2-bc4a-ded9410e1d43 · outbound

This paper cites Kravaris.

Algebraic Aspects of Periodic Graph Operators Kravaris

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.549797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 51b46f5e-8dfa-463b-b3ea-1d3c0cd89a62 · outbound

This paper cites Kuchment.

Algebraic Aspects of Periodic Graph Operators Kuchment

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.537189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation df547ba4-fe2c-46e8-b25d-e86f79798c2e · outbound

This paper cites Kuchment and B.

Algebraic Aspects of Periodic Graph Operators Kuchment and B

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.523723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f06dd424-5c2a-4dea-9891-5b1c0fec987a · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.509924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ff2d9141-d837-40d2-a3d3-9592a9a3831a · outbound

This paper cites Li and S.

Algebraic Aspects of Periodic Graph Operators Li and S

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.495386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation eaa822e7-0ebf-4abc-84df-9ab9a3a55091 · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.481164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation af2fc3ad-de40-427f-a061-4575fb5f9e4e · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.467103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 724db371-b2c5-47c4-b2a7-b4b0da3b65d8 · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.453335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e108e503-180a-4cdc-8285-6f7da126b99e · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.439608Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 96e7c5c9-9c5d-4782-9455-b3b9ebbf60d7 · outbound

This paper cites Defect bound states in the continuum of bilayer electronic materials without symmetry protection.

Algebraic Aspects of Periodic Graph Operators Defect bound states in the continuum of bilayer electronic materials without symmetry protection

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-09T04:21:16.314241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8d48d91f-0698-43cf-b798-5b6accb73cca · outbound

This paper cites Parnovski and R.

Algebraic Aspects of Periodic Graph Operators Parnovski and R

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.425684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8735b8a4-a16d-4dcb-af35-2a3f6754fa0b · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.412033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 804e403e-3ff6-4443-bee1-9f3f76848404 · outbound

This paper cites Reed and B.

Algebraic Aspects of Periodic Graph Operators Reed and B

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.398220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1c68162b-c76d-4509-9b04-4198d8a69d79 · outbound

This paper cites Regan, F.

Algebraic Aspects of Periodic Graph Operators Regan, F

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.383474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ee72fed7-7ace-440f-952f-424108ae36eb · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.368965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 05d6c3c2-8f7f-473f-8c7b-99ba11666712 · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.354219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 828b9f19-a4e1-4f10-908b-994394cb1758 · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-09T04:21:16.341402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e31fb8a6-1231-4645-b7f3-be54e246fa49 · outbound

This paper cites an unresolved cited work.

Algebraic Aspects of Periodic Graph Operators Unresolved cited work

Reference 41

Resolution: verified exact; doi, observed 2026-08-09T04:21:16.292609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 19a01b11-5214-421e-bd8f-9c0f716d1946 · outbound

This paper cites Villalobos.

Algebraic Aspects of Periodic Graph Operators Villalobos

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T04:21:16.327771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

Observation 0388d72c-0066-42a2-932d-d3a76038dc16 · inbound

Absence of flat bands for discrete periodic graph operators with generic potentials cites this paper.

Absence of flat bands for discrete periodic graph operators with generic potentials Algebraic Aspects of Periodic Graph Operators

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:17:30.009293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.