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Paper Citation Record · LEDGER

Lorentzian angles and trigonometry including lightlike vectors

As of 18 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 2 inbound Pith citation observations for arXiv:1908.10022.

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

pith.paper-citation-record.v1
1908.10022 v2

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:04:25.593988Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T10:18:32.062602Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-12T22:02:14.887214Z

Reference resolution

17 of 17 outbound references displayed

  • verified exact2
  • verified fuzzy10
  • unresolved5
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7a84024a-9b9c-4d1b-8dcd-a8f952e83ab4 · outbound

This paper cites Complex actions in two-dimensional topology change.

Lorentzian angles and trigonometry including lightlike vectors Complex actions in two-dimensional topology change

Reference 1

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unresolved
no resolver link, observed 2026-08-14T11:04:25.520206Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation c7589092-2882-46dd-b79f-c1f0da482089 · outbound

This paper cites Sorkin, Development of Simplicial Methods for the Metrical and Electromag- netic Fields , Ph.D.

Lorentzian angles and trigonometry including lightlike vectors Sorkin, Development of Simplicial Methods for the Metrical and Electromag- netic Fields , Ph.D

Reference 2

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verified fuzzy
raw_fallback, observed 2026-08-14T11:04:25.890800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 3bd17cfc-c3ab-460f-831e-a215a0bd2f2a · outbound

This paper cites The Time-evolution Problem in Regge Calculus.

Lorentzian angles and trigonometry including lightlike vectors The Time-evolution Problem in Regge Calculus

Reference 3

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verified fuzzy
raw_fallback, observed 2026-08-14T11:04:25.873544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 7db83a8d-1bda-4fbd-81e3-10d18e13de60 · outbound

This paper cites The null-surface boundary term in the variation of the gravitational action-functional.

Lorentzian angles and trigonometry including lightlike vectors The null-surface boundary term in the variation of the gravitational action-functional

Reference 4

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verified fuzzy
raw_fallback, observed 2026-08-14T11:04:25.855231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 4ac06db8-0305-46b5-a2a6-c15912224628 · outbound

This paper cites an unresolved cited work.

Lorentzian angles and trigonometry including lightlike vectors Unresolved cited work

Reference 5

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unresolved
raw_fallback, observed 2026-08-14T11:04:25.840706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 21b879b5-ae25-4c62-aded-7210351f1917 · outbound

This paper cites Peyresq Physics 20: Micro and macro structure of spacetime.

Lorentzian angles and trigonometry including lightlike vectors Peyresq Physics 20: Micro and macro structure of spacetime

Reference 6

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verified fuzzy
raw_fallback, observed 2026-08-14T11:04:25.827968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 913f1491-fa89-4d2a-aee2-afcc87a0df6b · outbound

This paper cites Mann Fest.

Lorentzian angles and trigonometry including lightlike vectors Mann Fest

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:04:25.811876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 5f734394-a96a-459e-a43a-3537f2c3a1a9 · outbound

This paper cites Boundary and Corner Terms in the Action for General Relativity.

Lorentzian angles and trigonometry including lightlike vectors Boundary and Corner Terms in the Action for General Relativity

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-14T11:04:25.552845Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T11:04:25.552845Z digest=sha256:5b945e8326b6820429aa1a8056320ad2af7c0aa8017f046fcf8afc213aed34b7

Observation 6a3feceb-02eb-4f81-8bf2-bebf98b02661 · outbound

This paper cites General relativity without coordinates.

Lorentzian angles and trigonometry including lightlike vectors General relativity without coordinates

Reference 9

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verified fuzzy
raw_fallback, observed 2026-08-14T11:04:25.797747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation b1382792-ebad-4f51-88ae-644edd93c11b · outbound

This paper cites A Boundary Term for the Action in ‘Regge Calculus’.

Lorentzian angles and trigonometry including lightlike vectors A Boundary Term for the Action in ‘Regge Calculus’

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:04:25.782892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation b83aa48e-05d0-40cf-bc55-5b159dd153f8 · outbound

This paper cites Is the gravitational action additive?.

Lorentzian angles and trigonometry including lightlike vectors Is the gravitational action additive?

Reference 11

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verified exact
local_arxiv, observed 2026-08-14T11:04:25.680648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T11:04:25.566388Z digest=sha256:b8af4893628db2c15a6eb020728ef01c99a12899e4a084fba9d6bafdc8791e00

Observation 8d87dca0-2b24-47de-9f30-03b3990a11df · outbound

This paper cites Gravitational action with null boundaries.

Lorentzian angles and trigonometry including lightlike vectors Gravitational action with null boundaries

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-14T11:04:25.571237Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T11:04:25.571237Z digest=sha256:152ca8de51e22ddd4db007362991052070347d193293f6fa5eb51c2087e8eafd

Observation c6a8ccab-2142-44ea-9721-ca9be2430ac9 · outbound

This paper cites Semi-classical Limits of Simplicial Quantum Gravity.

Lorentzian angles and trigonometry including lightlike vectors Semi-classical Limits of Simplicial Quantum Gravity

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:04:25.765125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T11:04:25.575534Z digest=sha256:255e9443631f01482e2361724ff690027c14b866201bc5a366b700ca2982fabf

Observation ad91d2e4-811a-4627-b2ae-4b8f4bc51de7 · outbound

This paper cites Trigonometry in Lorentzian Geometry.

Lorentzian angles and trigonometry including lightlike vectors Trigonometry in Lorentzian Geometry

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:04:25.752399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T11:04:25.579969Z digest=sha256:4c8e6eb23b665e5876957bbee9515f23da26760e91c3a2a30701f785aa5e66a7

Observation cf63d727-5357-4461-bb9a-2e77c94855e2 · outbound

This paper cites The Sorkin-Johnston State in a Patch of the Trousers Spacetime.

Lorentzian angles and trigonometry including lightlike vectors The Sorkin-Johnston State in a Patch of the Trousers Spacetime

Reference 15

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:04:25.644298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 2203ba26-d8c9-4f77-9fdf-e6143236b2a2 · outbound

This paper cites an unresolved cited work.

Lorentzian angles and trigonometry including lightlike vectors Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:04:25.737847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-14T11:04:25.588608Z digest=sha256:e2db891924009b87352c79c323a12f109043260f322f75c7d8778b6e327b0c55

Observation cb5d16c7-0baa-442c-a29c-4bb806b0210d · outbound

This paper cites closely” as desired 35 Figure 9. The opening angle of a wedge with two lightlike edges: three sub-cases 36 Figure 10. Two ways to glue an “infinitesimal wedge.

Lorentzian angles and trigonometry including lightlike vectors closely” as desired 35 Figure 9. The opening angle of a wedge with two lightlike edges: three sub-cases 36 Figure 10. Two ways to glue an “infinitesimal wedge

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:04:25.724271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Pith citing papers

Observation 8000a4b6-4cc3-40f2-b2dd-15e0e8678312 · inbound

(2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality cites this paper.

(2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality Lorentzian angles and trigonometry including lightlike vectors

Reference 109

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verified exact
local_arxiv, observed 2026-08-12T22:02:14.895445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-12T22:02:14.438360Z digest=sha256:e39c0455e06c3fcaaf43dc30bbe86b71b11f4f67891675116a718cb7856ba2e5

Observation b6e797be-b81a-49cd-b7ee-8cbf94167a5c · inbound

Studying replica wormholes and the Page curve with simplicial quantum gravity cites this paper.

Studying replica wormholes and the Page curve with simplicial quantum gravity Lorentzian angles and trigonometry including lightlike vectors

Reference 30

Resolution
unresolved
no resolver link, observed 2026-08-16T10:18:32.062602Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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