Paper Citation Record · LEDGER

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory

As of 12 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2604.14596.

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

pith.paper-citation-record.v1
2604.14596 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-10T10:15:35.157086Z

measured 27 of 27 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 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

27 of 27 outbound references displayed

verified exact3
verified fuzzy9
unresolved15
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3f31b3a5-5c42-4d85-8aaf-893b6fcf3f2a · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.208338Z

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 bfbc8a03-e74d-44f7-b20e-283aebdc0cbc · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.242153Z

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 f549b80d-3fbf-4963-a755-f4e691486359 · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.234183Z

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 371184fb-f85e-4c49-a1ab-f1dd4de25fa3 · outbound

This paper cites Falconer,Fractal Geometry: Mathematical Foundations and Applications, 3rd ed.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Falconer,Fractal Geometry: Mathematical Foundations and Applications, 3rd ed

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T00:53:19.238294Z

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 85553df8-032b-42a7-9bf7-0c39d1eefd4f · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.231148Z

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 16eac09d-b57d-4912-b485-574807adb6cc · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.204861Z

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 9c29a944-5dd9-4cd0-ba33-3e5980172d33 · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.219190Z

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 55d3d066-04d8-4c85-bb5b-44f83c9bbf17 · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.212513Z

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 82b3cf43-cb36-4396-9bef-2ed2e354f514 · outbound

This paper cites Hurwitz, Über die Composition der quadratischen Formen von beliebig vielen Variablen,Nachr.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Hurwitz, Über die Composition der quadratischen Formen von beliebig vielen Variablen,Nachr

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T00:53:19.223221Z

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 9d87625e-e849-42ac-aaea-d9269673860e · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.227216Z

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 27855596-f6e4-4fae-baef-6ba261ca7b28 · outbound

This paper cites Polchinski, Renormalization and effective Lagrangians,Nucl.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Polchinski, Renormalization and effective Lagrangians,Nucl

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T00:53:19.253905Z

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 b86e2c81-b349-4b8d-8a45-dfd66dd6501f · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.215969Z

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 7ac5f7e3-7895-4cb8-8449-57ce8f7bcb30 · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.245576Z

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 688f23b6-710d-485f-9c60-4098548dafa5 · outbound

This paper cites Immirzi, Real and complex connections for canonical gravity,Class.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Immirzi, Real and complex connections for canonical gravity,Class

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T00:53:19.249768Z

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 92e924e9-cc57-46e1-8d8a-277a1446717b · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.194204Z

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 b2052559-4387-4a38-a08c-a67e286f06e0 · outbound

This paper cites A Deterministic Fractal Set Derived from the Sequence of Prime Numbers.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory A Deterministic Fractal Set Derived from the Sequence of Prime Numbers

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-27T00:04:12.385307Z

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 6555a8dc-d5c1-4d80-8a31-6545d7c1d718 · outbound

This paper cites Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-27T00:04:12.542062Z

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 2d851f26-8220-42f3-b7fa-d66b39212109 · outbound

This paper cites Rudnick and P.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Rudnick and P

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T00:53:19.201191Z

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 cd17ca6e-57bd-4b0a-bc79-ef051f7a6b49 · outbound

This paper cites Bogomolny and J.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Bogomolny and J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T00:53:19.177854Z

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 99a15e14-5065-4e20-8df3-931e6458e999 · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.180964Z

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 46ed8127-efcd-4edf-8a5c-ee0e4b1ae829 · outbound

This paper cites Conrey, The Riemann hypothesis,Notices Amer.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Conrey, The Riemann hypothesis,Notices Amer

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T00:53:19.184384Z

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 099e6b7d-afb2-4335-ad1a-f3cc4d6a6c73 · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.187507Z

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 94f4508d-0c98-4958-9b01-10326562101f · outbound

This paper cites Witten, String theory dynamics in various dimensions,Nucl.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Witten, String theory dynamics in various dimensions,Nucl

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T00:53:19.190870Z

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 9714a273-7221-4201-a58e-457667d7ed6f · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.174307Z

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 4a64469f-25ae-4a66-a4fb-c64626f8b9fa · outbound

This paper cites an unresolved cited work.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-05-20T00:53:19.197526Z

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 7f4c6abb-f41f-49d9-9d04-152e6e4a883d · outbound

This paper cites Wolf, 1/f noise in the distribution of prime numbers,Physica A241(3–4), 493–499.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Wolf, 1/f noise in the distribution of prime numbers,Physica A241(3–4), 493–499

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T00:53:19.178432Z

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 1eef538f-ab59-41f2-a946-e90f870e82bb · outbound

This paper cites Planck 2018 results. VI. Cosmological parameters.

Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory Planck 2018 results. VI. Cosmological parameters

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-10T10:24:22.158288Z

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

No inbound Pith citation observations are available.