Paper Citation Record · LEDGER

A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 21 inbound Pith citation observations for arXiv:2408.15968.

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pith.paper-citation-record.v1
2408.15968 v2

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measured 0 of 0 reference resolution

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measured 21 of 21 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 21 of 21 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T22:51:45.468025Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T08:29:42.399431Z

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Outbound references

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Pith citing papers

Observation 97744cf9-6f6a-48f7-95ca-6794745b3ff0 · inbound

Splitting theorems for weighted Finsler spacetimes via the $p$-d'Alembertian: beyond the Berwald case cites this paper.

Splitting theorems for weighted Finsler spacetimes via the $p$-d'Alembertian: beyond the Berwald case A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-23T07:05:30.666412Z

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 4f223aa3-f8a1-446f-b39d-c408ea5e220f · inbound

Trading linearity for ellipticity: a nonsmooth approach to Einstein's theory of gravity and the Lorentzian splitting theorems cites this paper.

Trading linearity for ellipticity: a nonsmooth approach to Einstein's theory of gravity and the Lorentzian splitting theorems A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-10T22:51:45.468025Z

Source-reported events for the cited work

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Observation c41993f9-bbb3-457c-be4b-a76aea8873b2 · inbound

New perspectives on the d'Alembertian from general relativity. An invitation cites this paper.

New perspectives on the d'Alembertian from general relativity. An invitation A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-09T21:36:02.884734Z

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Observation 3cd56330-219f-4c50-b075-c4da26eef989 · inbound

On the geometry of synthetic null hypersurfaces cites this paper.

On the geometry of synthetic null hypersurfaces A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-19T11:27:15.851020Z

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 e65f8108-244d-48fb-abd0-f0b183edd45c · inbound

Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry cites this paper.

Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T04:33:06.774240Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 736c85ac-6d50-4d04-8f69-f336ea07177b · inbound

Spacetime reconstruction by order and number cites this paper.

Spacetime reconstruction by order and number A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T21:02:32.406345Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bfeca220-f6e2-4f28-b1c4-268b8a2c5d9b · inbound

A Lorentzian splitting theorem for continuously differentiable metrics and weights cites this paper.

A Lorentzian splitting theorem for continuously differentiable metrics and weights A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:16.089753Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ebfd3bba-b2cf-42d6-b130-ffb6b84a8ac9 · inbound

Reshetnyak Majorisation and discrete upper curvature bounds for Lorentzian length spaces cites this paper.

Reshetnyak Majorisation and discrete upper curvature bounds for Lorentzian length spaces A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-18T18:26:43.617959Z

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 9ca68e0b-f4b9-4163-83af-5e9c1602ca0e · inbound

The equivalence between timelike Ricci curvature and the timelike Brunn Minkowski inequality on synthetic Lorentzian spaces cites this paper.

The equivalence between timelike Ricci curvature and the timelike Brunn Minkowski inequality on synthetic Lorentzian spaces A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 5

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T09:36:02.063089Z

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 0cb15b78-b6f8-418a-8485-126056fd570a · inbound

Infinitesimal Minkowskianity for manifolds with continuous Lorentzian metrics cites this paper.

Infinitesimal Minkowskianity for manifolds with continuous Lorentzian metrics A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-11T20:11:12.474470Z

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 5a5c6dea-dc3c-4e3a-8165-5893885a2aae · inbound

Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs cites this paper.

Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-11T20:16:10.931097Z

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 91b3d938-93e4-4670-8f0f-ea78039fdf8c · inbound

Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs cites this paper.

Timelike Ricci curvature lower bounds via optimal transport for Orlicz-type Lorentzian costs A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-14T21:38:01.041797Z

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 a8c32a8f-14ea-47cc-bcc2-7db5323a17d8 · inbound

Stability of Synthetic Timelike Ricci Bounds under $C^0$-Limits and Applications to Impulsive Gravitational Waves cites this paper.

Stability of Synthetic Timelike Ricci Bounds under $C^0$-Limits and Applications to Impulsive Gravitational Waves A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-12T10:51:30.607381Z

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 5cdfc284-7861-4d8d-b49c-62ef6d9c1b2a · inbound

Lorentzian coarea inequality cites this paper.

Lorentzian coarea inequality A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:11:18.636573Z

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 50919b42-0305-478f-8c0c-2320953df9c4 · inbound

Lorentzian coarea inequality cites this paper.

Lorentzian coarea inequality A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-20T23:13:50.591947Z

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 2bde941e-4179-4967-8841-cf1b6e2d5fc7 · inbound

A singularity theorem in terms of asymptotic expansion cites this paper.

A singularity theorem in terms of asymptotic expansion A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-07-03T13:08:08.111216Z

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 1fa4b757-07a5-4486-b189-28429992e6c9 · inbound

The alignment time function cites this paper.

The alignment time function A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-07-04T05:39:40.045113Z

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 57964ad1-80b9-483f-8cd6-218643618659 · inbound

Failure of local equi-Lipschitzness for families of Lorentz distances to Cauchy surface foliations cites this paper.

Failure of local equi-Lipschitzness for families of Lorentz distances to Cauchy surface foliations A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-07-04T08:29:42.400747Z

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 c9c5cd31-692b-45de-8405-b019584ebbdf · inbound

On one relaxation of the bounded-length-distortion condition in the context of metric measure spaces cites this paper.

On one relaxation of the bounded-length-distortion condition in the context of metric measure spaces A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 6

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T16:37:09.129931Z

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 a1143e4b-e75d-4f5f-bd87-9926ed83401f · inbound

Doubling for chronological diamonds in Lorentzian geometry cites this paper.

Doubling for chronological diamonds in Lorentzian geometry A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 2005

Resolution: unresolved; no resolver link, observed 2026-08-01T07:41:24.112348Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d0cb665-766e-49b2-a151-7e449eed8db6 · inbound

Ideal points, directed completion and the case of the maximally extended Schwarzschild spacetime cites this paper.

Ideal points, directed completion and the case of the maximally extended Schwarzschild spacetime A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T18:46:44.979435Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.