Paper Citation Record · LEDGER

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24

As of 5 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2604.10914.

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

pith.paper-citation-record.v1
2604.10914 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-10T16:11:05.165028Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T07:13:18.280356Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

28 of 28 outbound references displayed

verified exact3
verified fuzzy16
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ceba3124-c8db-448d-af53-86061872fefd · outbound

This paper cites Bellissard, Gap labelling theorems for Schrödinger operators, in:From Number Theory to Physics, Springer, 1992, pp.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Bellissard, Gap labelling theorems for Schrödinger operators, in:From Number Theory to Physics, Springer, 1992, pp

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.314010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a41c83ae-e9f4-442e-8b11-dbcdaf495e44 · outbound

This paper cites Bost and A.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Bost and A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.275221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 498bf339-bda0-4aca-805e-b0389ce7a863 · outbound

This paper cites an unresolved cited work.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-05-17T16:39:58.272306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 6216fd73-4d79-445c-aff3-2824de758ba0 · outbound

This paper cites an unresolved cited work.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-05-17T16:39:58.289672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a73d9422-e861-421d-b252-1b3faf99f36c · outbound

This paper cites Cohn and N.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Cohn and N

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.300570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 34d8405d-4cc8-4939-9093-cbb9c943c065 · outbound

This paper cites Dual linear programming bounds for sphere packing via modular forms.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Dual linear programming bounds for sphere packing via modular forms

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-11T09:11:04.915429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 3e10c67f-2759-442b-b56c-25830c7a9b6f · outbound

This paper cites Connes,Noncommutative Geometry, Academic Press.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Connes,Noncommutative Geometry, Academic Press

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.323502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 57bdc27a-38cc-48f5-b751-21da5e6d102b · outbound

This paper cites an unresolved cited work.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-05-17T16:39:58.310504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation d46f38c3-e683-4dd8-8385-7e5ef068dad0 · outbound

This paper cites an unresolved cited work.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-05-17T16:39:58.262329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation fea0e27a-3c22-43f3-8cf0-703f643ac507 · outbound

This paper cites Damanik and A.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Damanik and A

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.326530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 963dc700-91b0-44dc-99b7-53b5d5520320 · outbound

This paper cites A Breakthrough in Sphere Packing: The Search for Magic Functions.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 A Breakthrough in Sphere Packing: The Search for Magic Functions

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-07-04T21:25:30.922236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 885911d2-bb4a-4389-977f-f9575934dbca · outbound

This paper cites Ebeling,Lattices and Codes, 3rd ed., Springer Spektrum.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Ebeling,Lattices and Codes, 3rd ed., Springer Spektrum

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.335536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4affb0c6-539a-4947-86b7-70c4fb0fc6c4 · outbound

This paper cites Frenkel, J.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Frenkel, J

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.341471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation fd49625a-ef8d-49bc-b023-85ff8b349c2d · outbound

This paper cites Gleason, Weight polynomialsof self-dualcodesand theMacWilliams identities, Actes Congrès Int.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Gleason, Weight polynomialsof self-dualcodesand theMacWilliams identities, Actes Congrès Int

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.293129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a8002612-dc53-4ba3-93c5-82230cbb3b33 · outbound

This paper cites an unresolved cited work.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-05-17T16:39:58.296334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation db87727e-ae61-4de5-b852-2692a0458372 · outbound

This paper cites Sphere Packing and Quantum Gravity.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Sphere Packing and Quantum Gravity

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-11T09:11:05.006104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 31c08b5b-fcfc-445b-9d6c-4204da446d65 · outbound

This paper cites Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Pro- duktentwicklung.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Pro- duktentwicklung

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.332422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 765a2660-749e-4529-96ce-c29f03f67946 · outbound

This paper cites Hof, On diffraction by aperiodic structures,Comm.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Hof, On diffraction by aperiodic structures,Comm

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.303926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation c63be44c-ea27-4de9-a6b8-724fbfe61d46 · outbound

This paper cites an unresolved cited work.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-05-17T16:39:58.338805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation e2b5f749-32de-448c-8c48-66c1998d4320 · outbound

This paper cites Leech and N.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Leech and N

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.278286Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation d7c97bea-6996-45a5-b00e-8ee71ef684a4 · outbound

This paper cites an unresolved cited work.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-05-17T16:39:58.319584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4a3576ec-ae82-473c-89cc-03fe0654f147 · outbound

This paper cites Niemeier, Definite quadratische Formen der Dimension 24 und Diskriminante 1,J.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Niemeier, Definite quadratische Formen der Dimension 24 und Diskriminante 1,J

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.329477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation c480b4c0-24a7-4e64-b36e-c47d4c3e34b6 · outbound

This paper cites an unresolved cited work.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-05-17T16:39:58.265836Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 932e6974-adb1-4761-9a42-5240e6b34235 · outbound

This paper cites Pless and N.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Pless and N

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.316716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 268c96a7-188e-429f-a12e-f2b9f8a7f595 · outbound

This paper cites Radchenko and M.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Radchenko and M

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.269164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a33148bd-6ef6-45c6-bd65-4160f528cbe9 · outbound

This paper cites Serre,A Course in Arithmetic, Springer.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Serre,A Course in Arithmetic, Springer

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.307630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation bb5e6170-4f2f-43f5-8e10-4e6596db0db1 · outbound

This paper cites an unresolved cited work.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-05-17T16:39:58.281828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 83b3464f-4a69-47aa-b26d-2c638cfb5837 · outbound

This paper cites Zagier, Elliptic modular forms and their applications, in:The 1-2-3 of Modular Forms, Springer, 2008, pp.

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24 Zagier, Elliptic modular forms and their applications, in:The 1-2-3 of Modular Forms, Springer, 2008, pp

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T16:39:58.285514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Pith citing papers

Observation 566edd75-801c-48ac-9077-bf7ed87d28b1 · inbound

A dual linear programming bound for sphere packing in dimension 36 cites this paper.

A dual linear programming bound for sphere packing in dimension 36 Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T07:13:18.280356Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.