Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T22:26:53.249140Z
Paper Citation Record · LEDGER
As of 16 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 1 inbound Pith citation observation for arXiv:2506.22057.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T22:26:53.249140Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-06T18:44:34.040568Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-06T18:44:35.644443Z
67 of 67 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 7d21ed2b-cbe2-4c97-aec5-d05bcab28b0e · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Resolv- ing the gravitational redshift across a millimetre-scale atomic sample,
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4373b512-5085-4151-b120-6e6609fa768d · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Gravitational redshift in quantum-clock in- terferometry,
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e6f8e081-9ae6-4dfd-957a-b3cf078cf61d · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Unresolved cited work
Reference 3
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 285d59d2-d751-436c-a09c-4f9bd4400382 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Unresolved cited work
Reference 4
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation db385597-b757-4740-9079-e819c02a4897 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Die Grundlage der allgemeinen Rela- tivit¨ atstheorie,
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d21386e0-aa65-4804-8296-54790d60ced7 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field ¨Uber das Relativit¨ atsprinzip und die aus demselben gezogenen Folgerungen,
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b2691d7c-371b-4bae-9d8b-a5f0b5802a82 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field ¨Uber den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes,
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0548b067-74ed-47d8-abc2-d1801334a909 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Gravitational red-shift in nuclear resonance,
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 621aae3a-f08d-480d-a903-ef390a0eab34 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field A gravitational redshift measurement of the white dwarf mass–radius relation,
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a761dc39-0a9c-4d12-81f4-db5865e46613 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field The gravita- tional redshift of Sirius B,
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4a578698-8f82-4e85-8097-f0d38ff0d882 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field General relativistic effects on the orbit of the S2 star with GRA VITY,
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8d72a7bb-3820-4e38-9897-0e7d90fa2d3b · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field The masses of isolated neutron stars inferred from the gravitational redshift measurements,
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e449d378-eb21-4a1a-a6c3-58c9ffaa5a71 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Detection of the gravitational redshift in the orbit of the star S2 near the galactic centre massive black hole,
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 84205186-38ff-42a9-a739-30df936bf28d · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Probing Post-Newtonian physics near the galactic black hole with stellar redshift measurements,
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d5f3042e-929a-4265-b72e-f3302ff4711f · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field The confrontation between general relativ- ity and experiment,
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d7c7a26c-83af-4a6b-b0fa-c0d922c85e24 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field A lab-based test of the gravitational red- shift with a miniature clock network,
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3c9c4ba7-f676-40c4-bff8-c6193345dfdc · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Gravitational redshift tests with atomic clocks and atom interferometers,
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c9ee93da-493d-4222-a82e-e7cf0da2b423 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Atom-interferometric test of the univer- sality of gravitational redshift and free fall,
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9122c584-12ec-40de-8499-aaeaf66506f1 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field The solar gravitational redshift from HARPS-LFC Moon spectra - A test of the general the- ory of relativity,
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8cedc6e8-6615-47f8-b227-5326c6a56e0f · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Test of the gravitational redshift with galileo satellites in an eccentric orbit,
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 41ab6e95-96ed-4acf-ba1f-bdc7d2e320ba · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Gravita- tional redshift test using eccentric Galileo satellites,
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 07a6f11a-f925-4400-9c5b-390264e76bfa · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Analysis of Sun/Moon gravi- tational redshift tests with the STE-QUEST space mis- sion,
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6bf123f6-e9ea-4d74-b306-bd006b0b6597 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Unresolved cited work
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a10b8dc4-4662-4687-8952-58db4ea4db39 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field One-electron atom in curved space-time,
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8196d1fa-4437-401b-bfd7-81b7c5954445 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Gravitational perturba- tion of the hydrogen spectrum,
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d2cae5ab-509e-4b9e-8047-a9c9d6863a64 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field High-frequency gravitational wave detection via opti- cal frequency modulation,
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e0c84f5e-6624-4265-b6cf-1a01e159a19b · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field The effects of gravitational waves on a hydrogen atom,
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9193f73e-a9f9-43d9-860f-bf84d48a56d8 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Search for high- frequency gravitational waves with Rydberg atoms,
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation aa41da71-6597-4193-ab39-c249f8414aae · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Mission design for the laser astrometric test of relativity,
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a292bcce-1a01-4e0f-aada-f4802aabeae8 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Advancing fundamental physics with the laser astrometric test of relativity,
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a71ed5e0-78cd-4e37-8fb9-ebdb9b507ba7 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Unresolved cited work
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9dbcba82-1482-4c2d-b078-e2727d7a9f7f · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cf3467f3-c512-435e-b9b8-725ac09e8792 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Mach’s principle and a rel- 8 ativistic theory of gravitation,
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c93a908a-cefd-4840-8368-ffebc7799892 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field f(R) gravity with torsion: the metric-affine approach,
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a357aa83-e645-48a9-a9df-5111549bdeea · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field A bird’s eye view of f(R)-gravity,
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f65a4514-7bb4-45cd-993d-8389c5702204 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Resum- mation of massive gravity,
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f0bd8afd-0afb-43dc-b1b2-b7ed1e82067f · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Born–Infeld inspired modifications of gravity,
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 98f9edbb-ca70-4ea4-b643-c32b003a4775 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Light deflection and gravitational lensing effects inspired by loop quantum gravity
Reference 38
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c78a8a01-5db4-4e05-8b2b-8d14bd322190 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Unresolved cited work
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e88e4156-89b6-44ef-a6aa-3de886b066b2 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Quantum fields in teleparallel gravity: renormalization at one-loop,
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a558cded-da36-4b44-9dae-117f6019e69e · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field General relativity as an effective field theory: The leading quantum corrections,
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 69e63feb-c9fb-458a-a3f7-5eae4014f99a · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Infrared behavior of graviton-graviton scattering,
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c3373859-afff-4f66-8567-7e4e6218e1e0 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Quantum corrections to the Reiss- ner–Nordstr¨ om and Kerr–Newman metrics,
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7c3b454e-5209-4455-a683-a658a78cec1d · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Renormalization of higher-derivative quan- tum gravity,
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 896e2f60-508a-4611-ad73-c7f97ac0aa25 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field The quantum theory of gravi- tation, effective field theories, and strings: yesterday and today,
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation de49b9df-2874-4636-a7be-3a3ac7d8b06e · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Becker, M
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a0f1c2ef-7733-47e5-8ee1-2491a57bd4fa · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Dine, Supersymmetry and String Theory, Cambridge University Press, Cambridge (2007)
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 611768f3-8e63-43ce-ae7b-c8fa0b9601c8 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Unresolved cited work
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 224512e6-b97b-43c4-80b8-78b7a5bed129 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field New variables for classical and quantum gravity,
Reference 49
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d5b98313-44e9-4942-b376-a8b8723ee999 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Nonperturbative quantum geometries,
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 84d13712-f7cb-4e5b-9031-dadc721ab9f4 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Loop space representation of quantum general relativity,
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 63220ca0-62f4-4d13-adcd-38f502e73d84 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Loop quantum gravity,
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9f377f9e-0f95-4577-8211-b84cd00878dc · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Gravity generated by four one-dimensional unitary gauge symmetries and the Stan- dard Model,
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 69b2f4e9-06e9-4024-b32f-403c2acc6c1e · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Teleparal- lel gravity: from theory to cosmology,
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 64f4615c-a7c5-4617-b0ba-8822d9051b33 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Aldrovandi and J
Reference 55
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 304b8b1d-1fb6-48de-aec0-8cce621e6ba3 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field The teleparallel equivalent of general rel- ativity,
Reference 56
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f482b77c-1d62-404f-86dd-3ed1a04404e2 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Light deflection in unified gravity and measurable deviation from general relativ- ity,
Reference 57
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 74ccf3b9-da33-47e0-ae0d-ca0d374ccb7e · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Perihelion precession of planetary orbits solved from quantum field theory
Reference 58
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 914791a2-1fc1-4043-9976-54ee56d3cbc5 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Unresolved cited work
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a73d5e78-350b-4ca7-a7b9-5e3c5b715d2b · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Corrigendum: Gravity gen- erated by four one-dimensional unitary gauge symme- tries and the Standard Model (2025 Rep. Prog. Phys. 88 057802),
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4b893edc-a2e9-49a8-b927-7724b787015b · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Unresolved cited work
Reference 61
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 30997364-d1f7-4ee4-833c-2aa821009670 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Unresolved cited work
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a1d9a666-4b2f-4c07-8ebb-a9dd82c5804a · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Unresolved cited work
Reference 63
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7353fd8a-e079-4e27-9d25-d5e58c278cc9 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Gravitational light deflection in Earth- based laser cavity experiments,
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 551bbb10-e8ce-4001-be75-bd2afb80d6c8 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Observation of gravitational waves from a binary black hole merger,
Reference 65
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b1156296-5294-4d77-8649-355e3d7bf625 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Tests of general relativity with GW150914,
Reference 66
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6fcc68ce-1ddd-499e-a3ad-5db7c1140110 · outbound
Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field Multi-messenger observations of a binary neutron star merger,
Reference 67
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3153decf-99fe-42c1-89e6-033c2c66815e · inbound
Extending unified gravity to account for graviton-graviton interaction Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.