Paper Citation Record · LEDGER

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis

As of 19 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 1 inbound Pith citation observation for arXiv:2507.19235.

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

pith.paper-citation-record.v1
2507.19235 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:04:37.647671Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T23:18:32.868280Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

36 of 36 outbound references displayed

verified exact1
verified fuzzy21
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c3102762-748a-419a-8b32-08b871ef19be · outbound

This paper cites Amour and M.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Amour and M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.312722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e002cb66-cccc-4ea5-9e45-d1e4343d79c1 · outbound

This paper cites An´ e, S.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis An´ e, S

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.296499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 84081c84-c2e1-4f18-857b-c9aad80f158d · outbound

This paper cites Bakry and M.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Bakry and M

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.279384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a695acbf-148a-45b2-b8fa-17999ac1d94b · outbound

This paper cites Bakry and M Ledoux.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Bakry and M Ledoux

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.263565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 14e6723a-8063-444e-be8e-c8d4d8b9836e · outbound

This paper cites Bauer, P.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Bauer, P

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.248584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5905f196-fe3e-472f-b3b7-c316bee44d0b · outbound

This paper cites Recent progress on the random conductance mode l.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Recent progress on the random conductance mode l

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.232169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 88cca271-6060-43d9-a9b8-4db9840d0dc3 · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:38.216123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8779bcd9-497d-460e-910f-331db0384012 · outbound

This paper cites Chung, Y.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Chung, Y

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.196631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 568f8012-6913-406a-abca-4c03829628f5 · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:38.180633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 90e91828-1ccf-43ca-8179-474a04effdaa · outbound

This paper cites Noyau de la chaleur et discr´ etisation d’une vari´ et´ e riemannienne.Israel J.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Noyau de la chaleur et discr´ etisation d’une vari´ et´ e riemannienne.Israel J

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.163692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 322cd1be-5d35-4f0c-bebe-c246407fa73e · outbound

This paper cites Coulhon and L.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Coulhon and L

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.145815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ce90a821-0001-4553-b304-d52c05e211a8 · outbound

This paper cites Some isoperimetric inequalities and eigenval ues estimates.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Some isoperimetric inequalities and eigenval ues estimates

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.128155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 76c3daf8-1079-428f-a271-f29c54ee0f10 · outbound

This paper cites Delmotte.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Delmotte

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.112477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation eaa7831c-5b0a-44ce-8234-4a67e5018d50 · outbound

This paper cites Gallot, D.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Gallot, D

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.096517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 152188f0-98cb-4cd1-a5db-7be944664770 · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:38.080452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cef6d3ed-95cd-4b0e-b309-86ba85d6baae · outbound

This paper cites Haeseler, M.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Haeseler, M

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.063710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3fc4cefe-2266-4c36-a3dc-2c77ce000494 · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:38.046670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e22db3de-fa16-4a40-8036-b6e21e693349 · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:38.030471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b9891eb8-b98a-46b3-8963-71f2397de2ff · outbound

This paper cites Klartag, G.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Klartag, G

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:38.011470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 42ee547b-e108-4b55-bc6f-492d616d7a32 · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:37.992193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4ce0bb64-27f8-446a-b103-720ea0d68318 · outbound

This paper cites Li and S.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Li and S

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:37.973294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1117c45f-a223-4f36-8f0c-7da2db666c55 · outbound

This paper cites Lin and S-T.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Lin and S-T

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:37.957336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 99b3b143-35c3-400c-a150-669eb9d1bb21 · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:37.941758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cfbf0b28-c63b-4eaa-b974-a8bd2f48a9fd · outbound

This paper cites Lott and C.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Lott and C

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:37.926535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 41f58b98-8a35-433d-976b-3488c8fc2e35 · outbound

This paper cites Lyons and Y.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Lyons and Y

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:37.906329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 30e84938-15b9-494a-9755-d4cc0e8fad8e · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:37.888614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 690b010f-8612-413d-ba37-2a4381c3c03a · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:37.870404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c7159e0a-d248-476f-8593-617a272b61df · outbound

This paper cites Li-Yau inequality under $CD(0,n)$ on graphs.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Li-Yau inequality under $CD(0,n)$ on graphs

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:04:37.702562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e4fba3a5-8f5d-4aed-8069-dca8c5c7e510 · outbound

This paper cites Ricci curvature of Markov chains on metric s paces.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Ricci curvature of Markov chains on metric s paces

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:37.853340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 30775cba-073b-4ed3-97e3-3a2256e7e618 · outbound

This paper cites Pajot and E.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Pajot and E

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:37.834702Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0c31fa45-f8fe-405d-bf75-46a6ca9780ec · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:37.816361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 61e2485c-5c8d-4dc7-8fc5-1d9f6c145a52 · outbound

This paper cites Saloﬀ-Coste.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Saloﬀ-Coste

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:04:37.797305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9a582863-6cc8-473c-8dbe-4a68f2c36b33 · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:37.779030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a1b685fd-9b63-4b42-be3a-580572a58eb0 · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:37.761817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6963ddcb-eaf0-4e81-8f56-57a6a5cc51e9 · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:37.743896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9e45298e-eb3f-4f00-9d90-6773d7effe41 · outbound

This paper cites an unresolved cited work.

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:04:37.724997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation 92dd76a8-c131-4e10-92bb-4e3c4a394d1e · inbound

Nonnegative Bakry--\'Emery Curvature on Bounded-Degree Graphs Implies Volume Doubling and Poincar\'e Inequalities cites this paper.

Nonnegative Bakry--\'Emery Curvature on Bounded-Degree Graphs Implies Volume Doubling and Poincar\'e Inequalities Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:32.868280Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.