Pith. sign in

Paper Citation Record · LEDGER

A Lorentzian splitting theorem for continuously differentiable metrics and weights

As of 10 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 4 inbound Pith citation observations for arXiv:2507.06836.

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

pith.paper-citation-record.v1
2507.06836 v1

Coverage vector

measured 65 of 65 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:16:22.856051Z

measured 69 of 69 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-26T11:30:54.786651Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T08:29:42.396610Z

Reference resolution

65 of 65 outbound references displayed

  • verified exact2
  • verified fuzzy45
  • unresolved18
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2a930f60-283c-475b-adda-431b3e7fdfba · outbound

This paper cites Ambrosio.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Ambrosio

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.760276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:15.669269Z digest=sha256:e8297b99c32f27ec363f86d58970bdb0f3ab442fc1ede3d6c942738cdf3c2a39

Observation f2230192-4002-4cc5-84b8-d5993bd89010 · outbound

This paper cites Bakry and Michel ´Emery.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Bakry and Michel ´Emery

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.742606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:15.753502Z digest=sha256:5bc049647d482b9024d39cdc7301ae84f64b8633a34e8eb08c6b68ae42f20df4

Observation cbe4cca2-fd4e-470a-bac2-debcfd4a7d81 · outbound

This paper cites Beem, Paul E.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Beem, Paul E

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.727509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:15.882711Z digest=sha256:cbea487dd9906061844a2276d17c0518a0b5d2ea3c267348b56adb584c55b5ca

Observation 6fce1f4d-a810-429f-bbdb-53615dcdd824 · outbound

This paper cites an unresolved cited work.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:16:28.710041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:15.975665Z digest=sha256:ad6e3203fb956f87202ad4e38f5456207421f43142b1cc65251f951baa727f74

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

This paper cites A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes.

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.

source=pdf_text observed=2026-08-06T19:16:16.089753Z digest=sha256:cbded59bc5a8ad05046dfc746fc0e8b189e606b97ea4921cd0612a2aa66ee1c1

Observation 51d57707-445b-4c99-b47a-43d7b7071edf · outbound

This paper cites Ordinary differential equations.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Ordinary differential equations

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.693988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:16.206132Z digest=sha256:7b760eb19f13233f229aab079efffe3d0e9ccf1575010cfc2ec2fd7bd4d16cf9

Observation c0cbf69f-322a-4475-8c67-ae669a5f875b · outbound

This paper cites an unresolved cited work.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:16:28.674304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:16.331469Z digest=sha256:53ac7b6469a699bb1947a11ebf31a3b3a13a62b20cb6040a6b20238e74a92b5d

Observation 03599bad-2a28-4d03-b141-cc70e2bb74ae · outbound

This paper cites R´ enyi’s entropy on Lorentzian spaces.

A Lorentzian splitting theorem for continuously differentiable metrics and weights R´ enyi’s entropy on Lorentzian spaces

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.657374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:16.484726Z digest=sha256:616c2aa405b591586c79e6311bb7ed265f37cfcd8abb26c4ed710db652e3a0cc

Observation b3fbc1e4-5916-431a-8e04-ef93f8d4d46e · outbound

This paper cites Exact d'Alembertian for Lorentz distance functions.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Exact d'Alembertian for Lorentz distance functions

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-06T19:16:16.644569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T19:16:16.644569Z digest=sha256:6d01b9fa6acb0a564192db9ee29975424f227de50c1af15865a39bfaf09786f4

Observation bb0b733c-38c7-45d1-bd10-21fb86cb5f1b · outbound

This paper cites New perspectives on the d’Alembertian from general relativity.

A Lorentzian splitting theorem for continuously differentiable metrics and weights New perspectives on the d’Alembertian from general relativity

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.639868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:16.765583Z digest=sha256:03ce37fd9f2d3185c2d96ec9c4c411780d75d480b86df59028a0122becebff20

Observation 23ce7d29-66d4-4128-960e-fdfa9b1532a2 · outbound

This paper cites Timelike Ricci bounds for low regularity spacetimes by optimal transport.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Timelike Ricci bounds for low regularity spacetimes by optimal transport

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.622665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:16.899110Z digest=sha256:50ba26c7d8a53d0f58e1e8aba32c03e067b9d0d124126c299bc158e3a299862c

Observation 4189471b-c623-4eca-a183-45454848e80e · outbound

This paper cites An elliptic proof of the splitting theorems from Lorentzian geometry.

A Lorentzian splitting theorem for continuously differentiable metrics and weights An elliptic proof of the splitting theorems from Lorentzian geometry

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-06T19:16:17.000394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T19:16:17.000394Z digest=sha256:2ecbf4a7661401f3993e67c7319b6863e2f02618bffd310124266ab10bb51a40

Observation 2c7030d3-2bf5-465f-a348-fab6eeee6523 · outbound

This paper cites Caffarelli, M.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Caffarelli, M

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.605289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:17.115099Z digest=sha256:664a57bcdce750d8083056048c26ab48fae24f5f11794255700254c35e13a028

Observation 157faa7e-42f1-4cc1-8636-ed10fe521e75 · outbound

This paper cites On the smoothness of isometries.

A Lorentzian splitting theorem for continuously differentiable metrics and weights On the smoothness of isometries

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.588262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:17.204668Z digest=sha256:ffbb068d24d78dd21e0a4c13df5ed1655c1e0069efd273ce5be8bd9f1de18710

Observation bfa2bdc4-673c-4014-a466-983fe7209963 · outbound

This paper cites Hawking’s singularity theorem for Lipschitz Lorentzian metrics.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Hawking’s singularity theorem for Lipschitz Lorentzian metrics

Reference 15

Resolution
unresolved
no resolver link, observed 2026-08-06T19:16:17.293209Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T19:16:17.293209Z digest=sha256:b714ccac91d130aad6942fcd771e1fbf4616e070ac2d0e54f67bae493d3991e9

Observation 2867f513-4130-4bf6-bf88-00cbedebcfc2 · outbound

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

A Lorentzian splitting theorem for continuously differentiable metrics and weights Splitting theorems for weighted Finsler spacetimes via the $p$-d'Alembertian: beyond the Berwald case

Reference 16

Resolution
verified exact
local_arxiv, observed 2026-08-06T19:16:23.450558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:17.378938Z digest=sha256:83e43f0e102d5dc601a34bd33a410303c995ae3d82795d1519d16dd4852fe8be

Observation 4b300966-25b1-4612-8680-ba74d4c4b222 · outbound

This paper cites an unresolved cited work.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:16:28.571689Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:17.435587Z digest=sha256:11c0e5a75aac841f093eb10bb6f98eb7e2117a98f8ab45cc2a5d4702eff0ca86

Observation 8d90d85d-e157-4f55-a246-da01c89e8fcd · outbound

This paper cites On the geometry of synthetic null hypersurfaces.

A Lorentzian splitting theorem for continuously differentiable metrics and weights On the geometry of synthetic null hypersurfaces

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-06T19:16:17.525306Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T19:16:17.525306Z digest=sha256:173de551f6bbefec12415c21f6aac563a980b166a7afd93cc47d7bfed4b98822

Observation 2215153b-2d36-4ee0-8746-4d4bed10d823 · outbound

This paper cites Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.554837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:17.609552Z digest=sha256:fc45b9bbbb9afdb89cce1584f03bcfff94c3947c6c08c1a5bb39769fe7711637

Observation 4d4b5bca-cd52-44d6-a72f-ff5f32bb8a7e · outbound

This paper cites Optimal transport in Lorentzian syn- thetic spaces, synthetic timelike Ricci curvature lower bounds and applications.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Optimal transport in Lorentzian syn- thetic spaces, synthetic timelike Ricci curvature lower bounds and applications

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.537361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:17.698721Z digest=sha256:1cf06bc05cd181199336b44156cd113520ec8454aa039e204bb7ffec70d3f251

Observation f39d457f-7a96-481c-b9d8-a8ef5baa169e · outbound

This paper cites The splitting theorem for manifolds of non- negative Ricci curvature.

A Lorentzian splitting theorem for continuously differentiable metrics and weights The splitting theorem for manifolds of non- negative Ricci curvature

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.520240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:17.812617Z digest=sha256:7ca9913de45e06571d4e9090f268ced8e0cd3a62b28b9d07c7faa52bfbb7545e

Observation 6521d099-ff23-4ca2-8d39-1078cc260788 · outbound

This paper cites Chru´ sciel and James D.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Chru´ sciel and James D

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.505297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:17.902443Z digest=sha256:51f2a01f383615624cd5910b9c3651595ab2adb865f3df463780b221d5b44bf5

Observation 96ceb83b-f55e-4449-8271-d986c8973801 · outbound

This paper cites Eschenburg.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Eschenburg

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.489471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:17.953683Z digest=sha256:0558daa92b8f4a5d453c826ee7bd96e71c9f1da67388870b71e1341e0ed9855e

Observation d112e8e4-3bdc-475c-b147-7a83a3ab592d · outbound

This paper cites an unresolved cited work.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:16:28.473620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.046976Z digest=sha256:b2517eb232e9cda15c040435fbe0f886a688e7f20236a05e62c1d904a76dab40

Observation 54cd3645-7f02-4d4f-8205-8018e9780fdf · outbound

This paper cites Evans and W.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Evans and W

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.456809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.129243Z digest=sha256:1091db4a9ef60942138a87c1bcb18a6d966f22071d928957be9f63369cc586be

Observation 9e12acd3-cabb-49c2-a939-674cbf32037a · outbound

This paper cites Feldman and R.J.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Feldman and R.J

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.439730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.218463Z digest=sha256:992d37e7de7b6c704410818f73ddf49fe8625a069b04e6c315a868561accc9cf

Observation b8e32f2c-5fae-497a-9d89-d2782dfa9787 · outbound

This paper cites Galloway.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Galloway

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.424344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.303770Z digest=sha256:ca4263c4282a3ee26f38c5dfab59dc611bc995b7682cdad7011eb2bf4af0bdac

Observation 5bfe3460-9c88-4a87-aa93-633eb3e0ba1d · outbound

This paper cites A note on the Lorentzian splitting theorem.

A Lorentzian splitting theorem for continuously differentiable metrics and weights A note on the Lorentzian splitting theorem

Reference 28

Resolution
verified exact
local_arxiv, observed 2026-08-06T19:16:23.142116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.390416Z digest=sha256:1a818649f89e631d0272d1aaa1662a72bd77bb5f3b0bb6d4b4f37ba6cd837027

Observation 2651bda8-e1f1-4390-ae97-8d431e987d34 · outbound

This paper cites Strings and other distributional sources in general relativity.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Strings and other distributional sources in general relativity

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.407371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.485512Z digest=sha256:fb6d2ffb73792dfb7c3647daaff448dbcf3a95749ba1737ca7a41b8f1099ddab

Observation bcb61d69-7258-4ec4-9575-67a94a45d529 · outbound

This paper cites An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature.

A Lorentzian splitting theorem for continuously differentiable metrics and weights An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.389168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.549993Z digest=sha256:ddc0e3d69f96b05d84bcfc09deb17581c0ec79f51262dad248d4bf16452c7d28

Observation 4aa78ed5-4252-45f5-9e55-16f87aec736e · outbound

This paper cites The splitting theorem in nonsmooth context.

A Lorentzian splitting theorem for continuously differentiable metrics and weights The splitting theorem in nonsmooth context

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.368963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.611628Z digest=sha256:ac89e098b2d1451852c65711e335e03f383862d26472c6150463a5f60d23e106

Observation cede061b-1cf6-44a1-9ec3-ff343cf6f347 · outbound

This paper cites Trudinger.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Trudinger

Reference 32

Resolution
unresolved
no resolver link, observed 2026-08-06T19:16:18.678800Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T19:16:18.678800Z digest=sha256:b8c43d4c33c1a2a3de75a98a839c93216a0d2bb6da640639b5de81eb775d2b4d

Observation e0a8a064-a275-4687-a3c2-7a7f622dc60b · outbound

This paper cites Singularity theorems for C 1-Lorentzian metrics.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Singularity theorems for C 1-Lorentzian metrics

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.335787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.745166Z digest=sha256:81bec49018c3a359ef3612e16839a55097d838cbddd234045880a9d92e77b050

Observation df16ad6c-aea2-4234-a7d6-08fae63f078b · outbound

This paper cites On isometries and on a theorem of Liouville.

A Lorentzian splitting theorem for continuously differentiable metrics and weights On isometries and on a theorem of Liouville

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.319320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.813036Z digest=sha256:fe405990b6c41849e721a3fe576d077374386de48be17d0cd55285611bf3c87b

Observation bb6a6bd4-74ae-47a3-bc3f-132c744ed079 · outbound

This paper cites an unresolved cited work.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:16:28.303139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.901897Z digest=sha256:2ef68b3e6b9ab6ff1d7c510df42703003d98c156a5c75d4419c66c8770646e3f

Observation 6fe0adc0-ec0e-4a83-9553-b978cb646aee · outbound

This paper cites Needle decompositions in Riemannian geometry.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Needle decompositions in Riemannian geometry

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.287301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:18.981873Z digest=sha256:48e74e637c57d7c0912234922a89c7269a4cd3850a9da872f9bdce2ae77fa64f

Observation 5bb98a04-03b0-4f6f-815c-bf4974e001ea · outbound

This paper cites The Hawking-Penrose singularity theorem for C 1-Lorentzian metrics.

A Lorentzian splitting theorem for continuously differentiable metrics and weights The Hawking-Penrose singularity theorem for C 1-Lorentzian metrics

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.271731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:19.063709Z digest=sha256:f35fac683e88d5b92acd4a5ed11b06afa5f01c89066531c278001842934b6205

Observation 3233025d-0bde-4713-b450-27629b7859e6 · outbound

This paper cites Lorentzian length spaces.Ann.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Lorentzian length spaces.Ann

Reference 38

Resolution
unresolved
no resolver link, observed 2026-08-06T19:16:19.157095Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T19:16:19.157095Z digest=sha256:332d7055a1195b72d9365c4e1d65e96257bbe90f42a0ba9f7b7bd1abd40d58de

Observation 2f566f3e-23c2-4657-b63f-93856ad07be1 · outbound

This paper cites an unresolved cited work.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:16:28.239330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:19.230159Z digest=sha256:90d4eb89f7fd2d7eed8ba4b067d2662357fdbe6fa6a619c99f5acabd3dd558e3

Observation 2070b612-5b15-4e2d-bb81-553852caf0b1 · outbound

This paper cites Lorentz meets Lipschitz.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Lorentz meets Lipschitz

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.220463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:19.339000Z digest=sha256:634f3fadf1ce6066bb7e4c768e10af3186cee9e71fe8307f1da31ae9f68c9c4f

Observation f61afeb9-67df-4d3d-a033-b880c41b93df · outbound

This paper cites LeFloch and Cristinel Mardare.

A Lorentzian splitting theorem for continuously differentiable metrics and weights LeFloch and Cristinel Mardare

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.203874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:19.439790Z digest=sha256:589fa13175adcabd5e85299d500f2878aa0ae679bf742c2d9374c393ec1ba456

Observation 296c23f9-769e-4f16-9108-bbc7cb766d1f · outbound

This paper cites Geometry of weighted Lorentz- Finsler manifolds II: A splitting theorem.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Geometry of weighted Lorentz- Finsler manifolds II: A splitting theorem

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:28.183052Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:19.543807Z digest=sha256:ae766204bc57d76c24c093f863ecdc1b473a99fe39338692ea1ebe4154c4ec79

Observation f6b5f082-759d-492f-bdd6-f8ab7f9b5b69 · outbound

This paper cites an unresolved cited work.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:16:28.058168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:19.620553Z digest=sha256:dbbd35453a4b9480e4492851763f1b3e85fdcf0134fa8d6e5f7483b0edfcd0fa

Observation dd9df1f7-543c-4334-a19d-59d2c47be09e · outbound

This paper cites an unresolved cited work.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:16:27.832043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:19.694964Z digest=sha256:f7a993a14519e67ce3e52f4933544ef67332e39891d322eef306f1d21c7d197e

Observation f301d709-5e0d-4475-816d-d1f5b71f57ff · outbound

This paper cites Structure theory of metric measure spaces with lower Ricci curvature bounds.J.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Structure theory of metric measure spaces with lower Ricci curvature bounds.J

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:27.621379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:19.813190Z digest=sha256:5c9ee9bc0a0456ffb78ab4245c8f642e99a993ea6af7e74ee9a6dd3a0de0dd9e

Observation 0beec40d-9e41-4e24-9136-96c8125b2923 · outbound

This paper cites An optimal transport formulation of the Einstein equations of general relativity.

A Lorentzian splitting theorem for continuously differentiable metrics and weights An optimal transport formulation of the Einstein equations of general relativity

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:27.415759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:19.914403Z digest=sha256:0e23dc99d64290e133b41c76aad1256deb258e9175c4951c6c3d53978df342b7

Observation 6164fafb-7342-4da6-b005-b2aea933192a · outbound

This paper cites an unresolved cited work.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work

Reference 47

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:16:27.265949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:20.016444Z digest=sha256:4ed0f98825890c40226d26e9de23a8405b2d52b0dc0664577a48d538e1d618fa

Observation 3b6f0ca5-7ce9-4d94-a72c-8725d03746f2 · outbound

This paper cites The existence of complete Riemannian metrics.

A Lorentzian splitting theorem for continuously differentiable metrics and weights The existence of complete Riemannian metrics

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:27.039280Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:20.151439Z digest=sha256:760597664c371994f385805b8381de32983e8c44ea47da6bdfacf4789c0ca2b1

Observation 0a726505-74c2-4f92-8988-df407fefc515 · outbound

This paper cites On the curvature and heat flow on Hamiltonian systems.

A Lorentzian splitting theorem for continuously differentiable metrics and weights On the curvature and heat flow on Hamiltonian systems

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:26.799148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:20.318800Z digest=sha256:dfec5f664b8c3b40512da6cd270e55ea9d5fd85375123105a5f65a5c1195905b

Observation 4ad79790-c1a0-42a5-ad95-47a65cd0e1b0 · outbound

This paper cites Semi-Riemannian geometry, volume 103 of Pure and Applied Mathematics.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Semi-Riemannian geometry, volume 103 of Pure and Applied Mathematics

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:26.504790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:20.510436Z digest=sha256:541da9b1ec768b955a8cf505c99ca9a72de77d5543ec6734942ee46f56607392

Observation 89a40518-6b5e-46f9-bc9e-0a0af5b3666d · outbound

This paper cites Gravitational collapse and space-time singularities.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Gravitational collapse and space-time singularities

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:26.320958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:20.654724Z digest=sha256:4d56ce0aebde477575e054d914246d821dd896ea9a0a536a9b2612bf1ebc1355

Observation b97692f0-c72d-4771-a9b3-7b4a30c9e9f1 · outbound

This paper cites Global hyperbolicity for spacetimes with continuous metrics.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Global hyperbolicity for spacetimes with continuous metrics

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:26.139445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:20.813668Z digest=sha256:c72351d83e56d369eb2898f3164d63e30fa3f1f95e1d55259b369872ef738a79

Observation 8fe59411-3527-4f2e-a791-476ce5e42264 · outbound

This paper cites A note on the Gannon-Lee theorem.

A Lorentzian splitting theorem for continuously differentiable metrics and weights A note on the Gannon-Lee theorem

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:25.938455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:20.949369Z digest=sha256:296c85c7118ddfd2ab9acbc469e0470b2de8813bb45a7f5eb985ffdcab19edd1

Observation 2206d06e-7e3f-4bfc-8587-6e2c2311681e · outbound

This paper cites On the Geroch–Traschen class of metrics.

A Lorentzian splitting theorem for continuously differentiable metrics and weights On the Geroch–Traschen class of metrics

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:25.784326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:21.145618Z digest=sha256:bb5b488f999d865802351eb1afe8bfd9148550f2f4c8103f4d2914b36ad73e8d

Observation c57bacd8-ad5e-4220-8670-1a265c3a4b29 · outbound

This paper cites an unresolved cited work.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work

Reference 55

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:16:25.631688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:21.347441Z digest=sha256:aac69e87c495a35c996a7143b3f1bc556f8f7f1a87ca396a16a5f944c26009a1

Observation e0fb9537-b8d4-4f55-bb50-d7c232ca5242 · outbound

This paper cites Existence and regularity of isometries.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Existence and regularity of isometries

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:25.473528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:21.543465Z digest=sha256:45c807912f71155cc01b5982a3d191ce6faf8ec55760fb06243ef706aff9550b

Observation 5e9746be-c36a-4cbc-9a08-42ae48b92c7d · outbound

This paper cites Ricci curvature comparison in Riemannian and Lorentzian geometry.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Ricci curvature comparison in Riemannian and Lorentzian geometry

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:25.302454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:21.687875Z digest=sha256:92e7264d0a7dd58d15622898a6b6f630717e7b40913caf1aaa3ecce133e38cce

Observation fed9ce18-3005-4352-abed-546c139be0e7 · outbound

This paper cites an unresolved cited work.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:16:25.153339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:21.828730Z digest=sha256:5e9f507d9966abefcf0577bbc3cdeee78c1baa256c027be10c6fc1ffac195d2c

Observation d0f307c6-fc87-498f-b416-4b276a5c211d · outbound

This paper cites Trudinger and X.-J.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Trudinger and X.-J

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:24.948130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:22.007949Z digest=sha256:6fb9c4a5d6160e1b499783ab41e91ae1b4e883bab3bfdfc4d148b605f6a4c5d5

Observation 6bd47d34-5d2d-4eff-b59f-00e2b6ab472c · outbound

This paper cites Springer-Verlag, Berlin, 2009.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Springer-Verlag, Berlin, 2009

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:24.774825Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:22.186892Z digest=sha256:59ef0a0438a70185ce736ba9be1d81c0d09cda9ba595a8801722a9af18f31e73

Observation df2f2ed9-f824-4611-9cb9-92ea57ef9ded · outbound

This paper cites Light rays, singularities, and all that.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Light rays, singularities, and all that

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:24.627787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:22.310230Z digest=sha256:5ab02911a86faa1179ed287425c59202bc28bd23fe281889b29edff44ff56f85

Observation 2af0a67d-d1c2-4695-a768-10907e96ac0c · outbound

This paper cites Scalar-tensor gravitation and the Bakry- ´Emery-Ricci tensor.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Scalar-tensor gravitation and the Bakry- ´Emery-Ricci tensor

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:24.449182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:22.468388Z digest=sha256:503bb9a8561899790631edd28a6f2f26567eed882d1cfa6050ccc8023131e54e

Observation 12b4d137-2999-41ae-b7ef-895818080ff6 · outbound

This paper cites Cosmological singularity theorems and split- ting theorems for N -Bakry-´ emery spacetimes.J.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Cosmological singularity theorems and split- ting theorems for N -Bakry-´ emery spacetimes.J

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:24.272809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:22.643847Z digest=sha256:1adef45a4f9bd8978bfa8a952af8d7d0cf135e536e764300f50927b9db45170d

Observation b00657f8-4e57-4e0e-b0e8-3fa103c98517 · outbound

This paper cites Curvature-dimension bounds for Lorentzian splitting theorems.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Curvature-dimension bounds for Lorentzian splitting theorems

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:24.102703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:22.758979Z digest=sha256:5f446fa58836c85c2225fc9e452af6abb908ab66bf260afebefab02cff6da723

Observation 51428bc6-8a11-44bd-a64f-81905e53522e · outbound

This paper cites Problem section.

A Lorentzian splitting theorem for continuously differentiable metrics and weights Problem section

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:16:23.898043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T19:16:22.856051Z digest=sha256:28df5a452c78935d8ad18c0ecb9c0ceaa79828fdc8e678e15c0ca35861fc5632

Pith citing papers

Observation 09f32baa-73c4-4c60-b5e9-9093680bd544 · 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 Lorentzian splitting theorem for continuously differentiable metrics and weights

Reference 6

Resolution
metadata mismatch
arxiv_id, observed 2026-05-12T10:51:30.582562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-05-08T17:26:24.568586Z digest=sha256:059986e5beb88a4253999ef1e100bd1bdf3d2b7998196ed79f073504c0c3a8d7

Observation f552f0cf-4e4b-43f6-87d2-ecf441483300 · inbound

Lorentzian coarea inequality cites this paper.

Lorentzian coarea inequality A Lorentzian splitting theorem for continuously differentiable metrics and weights

Reference 9

Resolution
verified exact
arxiv_id, observed 2026-05-12T03:11:18.639669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-05-12T03:11:09.902750Z digest=sha256:c7faf65016060abd0e7446e9572da9a47bd2fa1540917ba365cb1097fd563681

Observation e767dbb9-7e65-4151-83f3-beb0169299d3 · inbound

Lorentzian coarea inequality cites this paper.

Lorentzian coarea inequality A Lorentzian splitting theorem for continuously differentiable metrics and weights

Reference 9

Resolution
verified exact
arxiv_id, observed 2026-05-20T23:13:50.615867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-05-20T23:10:33.474875Z digest=sha256:026b5609999f93a7ad89d9a3bde6033c3138b897e4e836390141a58485180610

Observation 56b2441c-7ffc-4add-8463-f94e1e970bc3 · 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 Lorentzian splitting theorem for continuously differentiable metrics and weights

Reference 5

Resolution
verified exact
arxiv_id, observed 2026-07-04T08:29:42.398074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-26T11:30:54.786651Z digest=sha256:92951adda4c27598a9c598e4d64eb9e7fa0729e591cea1b81c100a24b010aa75