Paper Citation Record · LEDGER

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis

As of 19 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2507.21604.

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

pith.paper-citation-record.v1
2507.21604 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:46:08.208874Z

measured 22 of 22 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 2026-05-19T14:25:48.416301Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-19T14:27:24.154005Z

Reference resolution

21 of 21 outbound references displayed

verified exact2
verified fuzzy15
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7336d912-5deb-4eb9-8e0d-fabccdb5a599 · outbound

This paper cites Andres and M.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Andres and M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.433849Z

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 ce9ab93f-46da-4a97-8c6f-d0174b50b23a · outbound

This paper cites an unresolved cited work.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:46:08.425211Z

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 a0afd580-5b13-489f-8549-b91478b25dee · outbound

This paper cites an unresolved cited work.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:46:08.416512Z

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 e9a14eb7-e8f7-4920-99ee-c15227e07bd5 · outbound

This paper cites an unresolved cited work.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:46:08.407935Z

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 e3232cf2-0499-4acc-99d6-702ff70c63e9 · outbound

This paper cites an unresolved cited work.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:46:08.399296Z

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 a5e8101f-de04-42e6-967a-2177c89cbb8f · outbound

This paper cites Fabes and D.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Fabes and D

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.390651Z

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 dacb0682-fd0d-472c-a745-e8a49b4b9679 · outbound

This paper cites Fukushima, Y.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Fukushima, Y

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.381648Z

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 58017e90-8f02-4272-ace8-082940e40a26 · outbound

This paper cites Grigor’yan, E.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Grigor’yan, E

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.373405Z

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 4e9f82f4-7ded-4752-ac2a-d64969dd7b7d · outbound

This paper cites Grigor’yan, E.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Grigor’yan, E

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.365203Z

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 63280db4-e518-4e42-ac9d-15082ce437b9 · outbound

This paper cites Grigor’yan, E.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Grigor’yan, E

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.356421Z

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 e3db40f5-457b-4395-9b0a-7df59cec87cf · outbound

This paper cites Grigor’yan, E.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Grigor’yan, E

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.348080Z

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 3012744a-40c5-4803-b106-ed5fab5893a2 · outbound

This paper cites Grigor’yan, E.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Grigor’yan, E

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.339388Z

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 f61e12f5-2f2a-469f-a038-bba5a339568b · outbound

This paper cites Grigor’yan, E.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Grigor’yan, E

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.330606Z

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 d94b7206-6b29-4f66-9b18-55a7d27345b9 · outbound

This paper cites Grigor’yan, J.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Grigor’yan, J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.321981Z

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 f828386d-8c33-47e2-b18d-d343fe483a64 · outbound

This paper cites Hu and G.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Hu and G

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.312867Z

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 0b1568b9-cee3-43bf-ba82-8d1913aad3ad · outbound

This paper cites Hu and Z.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Hu and Z

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.302419Z

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 aa2233a6-e6ae-4fea-b757-28b622305b8c · outbound

This paper cites Kassmann, Harnack inequalities: An introduction, Bound.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Kassmann, Harnack inequalities: An introduction, Bound

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.291460Z

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 ec8c2a84-46a0-42b4-9d2b-962893cf8400 · outbound

This paper cites The parabolic Harnack inequality for nonlocal equations.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis The parabolic Harnack inequality for nonlocal equations

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-06T12:46:08.259833Z

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 d1c0735b-b04d-4b7c-8593-baeebc02113d · outbound

This paper cites Weak parabolic Harnack inequality and H\"older regularity for non-local Dirichlet forms.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Weak parabolic Harnack inequality and H\"older regularity for non-local Dirichlet forms

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-06T12:46:08.244798Z

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 b3151f89-d6f6-420a-a1b4-f8f7904667cc · outbound

This paper cites Moser, A Harnack inequality for parabolic di fferential equations, Comm.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Moser, A Harnack inequality for parabolic di fferential equations, Comm

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.280924Z

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 07d771d7-16ae-45c0-9421-39df057589f9 · outbound

This paper cites Nash, Continuity of solutions of parabolic and elliptic equations, Amer.

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Nash, Continuity of solutions of parabolic and elliptic equations, Amer

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:46:08.270075Z

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 03753309-807d-46a5-b935-bf036f23e059 · inbound

A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities cites this paper.

A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-19T14:27:24.155412Z

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.