Paper Citation Record · LEDGER

Characterization of the D'Alembertian by the Poincar\'e Invariance

As of 21 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2506.02513.

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

pith.paper-citation-record.v1
2506.02513 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:31:43.189039Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:31:41.365585Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T11:31:43.274925Z

Reference resolution

24 of 24 outbound references displayed

verified exact1
verified fuzzy18
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a546adcb-7535-4a0f-8d74-f44068257be7 · outbound

This paper cites Characterization of the D'Alembertian by the Poincar\'e Invariance.

Characterization of the D'Alembertian by the Poincar\'e Invariance Characterization of the D'Alembertian by the Poincar\'e Invariance

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:31:43.336680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4304280c-a036-42ab-b83d-3b7068a33153 · outbound

This paper cites To this end, we start introducing basic notation.

Characterization of the D'Alembertian by the Poincar\'e Invariance To this end, we start introducing basic notation

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:46.860968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ef4de4b8-6a0d-445c-9648-c789cda3835e · outbound

This paper cites Proof of Theorem 1 For ξ = (τ, ξ) ∈ R × Rn, we introduce eξ ∈ C∞(R × Rn; R) by eξ(x) = eξ(t, x) = exp(τ t+ ξ · x) for x = (t, x) ∈ R × Rn.

Characterization of the D'Alembertian by the Poincar\'e Invariance Proof of Theorem 1 For ξ = (τ, ξ) ∈ R × Rn, we introduce eξ ∈ C∞(R × Rn; R) by eξ(x) = eξ(t, x) = exp(τ t+ ξ · x) for x = (t, x) ∈ R × Rn

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:46.744228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6f424edc-c37e-4a04-b553-dd081d52859c · outbound

This paper cites We designate a point in the Euclid space Rn as x = (x1,.

Characterization of the D'Alembertian by the Poincar\'e Invariance We designate a point in the Euclid space Rn as x = (x1,

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:46.634521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 372afda2-ee46-4b7c-9206-fe3bfc4ee3f3 · outbound

This paper cites For related subjects, we refer the reader to the references [13–19].

Characterization of the D'Alembertian by the Poincar\'e Invariance For related subjects, we refer the reader to the references [13–19]

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:46.472120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d0f399b3-5188-4581-abe9-98d97895eced · outbound

This paper cites an unresolved cited work.

Characterization of the D'Alembertian by the Poincar\'e Invariance Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:31:46.317845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1608f7b3-cd0b-427f-9e23-e578c191e3ad · outbound

This paper cites De Faria, and W.

Characterization of the D'Alembertian by the Poincar\'e Invariance De Faria, and W

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:46.176017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e80c2b69-35f2-4cb8-97ef-2715812bff20 · outbound

This paper cites Scheck, Classical Field Theory, On Electrodynamics, Non-Abelian Gauge Theories and Gravitation , 2nd.

Characterization of the D'Alembertian by the Poincar\'e Invariance Scheck, Classical Field Theory, On Electrodynamics, Non-Abelian Gauge Theories and Gravitation , 2nd

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:46.045696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ca2d6baf-7075-4518-b076-f642b6bf2482 · outbound

This paper cites Zeidler, Quantum Field Theory I: Basics in Mathematics and Physics (Springer, Heidelberg, 2006).

Characterization of the D'Alembertian by the Poincar\'e Invariance Zeidler, Quantum Field Theory I: Basics in Mathematics and Physics (Springer, Heidelberg, 2006)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:45.947740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 802b722d-7aeb-47b3-bcd9-6dbc41dda9de · outbound

This paper cites Zeidler, Quantum Field Theory II: Quantum Electrodynamics (Springer, Heidelberg, 2009).

Characterization of the D'Alembertian by the Poincar\'e Invariance Zeidler, Quantum Field Theory II: Quantum Electrodynamics (Springer, Heidelberg, 2009)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:45.773366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3d7aebce-aec1-468e-854b-6de9e8ec75b9 · outbound

This paper cites Zeidler, Quantum Field Theory III: Gauge Theory (Springer, Heidelberg, 2011).

Characterization of the D'Alembertian by the Poincar\'e Invariance Zeidler, Quantum Field Theory III: Gauge Theory (Springer, Heidelberg, 2011)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:45.606669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5a67ac3b-ced0-4bdb-b871-a5deff32cf91 · outbound

This paper cites an unresolved cited work.

Characterization of the D'Alembertian by the Poincar\'e Invariance Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:31:45.455217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b1c45bc0-dda9-43c1-8094-ae76e0c3075e · outbound

This paper cites H¨ ormander,Linear Partial Differential Operators , Die Grundlehren der Mathematischen Wissenschaften 116, Springer 1963.

Characterization of the D'Alembertian by the Poincar\'e Invariance H¨ ormander,Linear Partial Differential Operators , Die Grundlehren der Mathematischen Wissenschaften 116, Springer 1963

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:45.303573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fbcae2b5-6a56-4df3-915a-067239f0bd9b · outbound

This paper cites Peetre, R´ ectification ` a l’article≪Une caract´ erisation abstraite des op´ rateurs diff´ erentiels≫, Math.

Characterization of the D'Alembertian by the Poincar\'e Invariance Peetre, R´ ectification ` a l’article≪Une caract´ erisation abstraite des op´ rateurs diff´ erentiels≫, Math

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:45.181780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2ff4ed6f-b52f-424b-8a5f-cc5ba84fdd77 · outbound

This paper cites Nomura, Spherical Harmonics and Group Representations , Nippon Hyoron Publ., 2018 (in Japanese).

Characterization of the D'Alembertian by the Poincar\'e Invariance Nomura, Spherical Harmonics and Group Representations , Nippon Hyoron Publ., 2018 (in Japanese)

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:45.019422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 163d1b1a-108e-4b6a-b673-44b3d7b59891 · outbound

This paper cites Shimakura, Elliptic Partial Differential Operators , Kinokuniya Publ., 1978 (in Japanese).

Characterization of the D'Alembertian by the Poincar\'e Invariance Shimakura, Elliptic Partial Differential Operators , Kinokuniya Publ., 1978 (in Japanese)

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:44.872815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 84ebc455-3a0a-4e47-9ec1-94eabf9fa979 · outbound

This paper cites Nakazato, T.

Characterization of the D'Alembertian by the Poincar\'e Invariance Nakazato, T

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:44.695804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e67cc109-7334-4df2-8c22-69b7481efd72 · outbound

This paper cites Bargmann, On Unitary Ray Representations of Continuous Groups, Ann.

Characterization of the D'Alembertian by the Poincar\'e Invariance Bargmann, On Unitary Ray Representations of Continuous Groups, Ann

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:44.518901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 245c95b4-06c5-4d30-b398-84bb28e8a7fd · outbound

This paper cites an unresolved cited work.

Characterization of the D'Alembertian by the Poincar\'e Invariance Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:31:44.355726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 14eb5856-bf15-42af-af60-c8c371c951ee · outbound

This paper cites Hamermesh, Galilei Invariance and the Schr¨ odinger Equation, Ann.

Characterization of the D'Alembertian by the Poincar\'e Invariance Hamermesh, Galilei Invariance and the Schr¨ odinger Equation, Ann

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:44.112686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation dceb6178-9d02-4719-94a4-20858c93e847 · outbound

This paper cites Levy-Leblond, Galilei Group and Nonrelativistic Quantum Mechanics, J.

Characterization of the D'Alembertian by the Poincar\'e Invariance Levy-Leblond, Galilei Group and Nonrelativistic Quantum Mechanics, J

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:43.888462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4fdfec4c-849a-4921-8267-f59a197da9a0 · outbound

This paper cites Roncadelli, A Simplified Approach to the Schr¨ odinger Equation, Nuovo Cimento 50A (1979), 509–514.

Characterization of the D'Alembertian by the Poincar\'e Invariance Roncadelli, A Simplified Approach to the Schr¨ odinger Equation, Nuovo Cimento 50A (1979), 509–514

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:31:43.777102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 159e9617-7b5b-484e-9a49-63626156979a · outbound

This paper cites an unresolved cited work.

Characterization of the D'Alembertian by the Poincar\'e Invariance Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:31:43.605289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 813007e8-395d-46f6-a190-8cfb3802fa59 · outbound

This paper cites an unresolved cited work.

Characterization of the D'Alembertian by the Poincar\'e Invariance Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:31:43.490331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation a546adcb-7535-4a0f-8d74-f44068257be7 · inbound