Paper Citation Record · LEDGER

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms

As of 10 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 1 inbound Pith citation observation for arXiv:2501.18391.

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

pith.paper-citation-record.v1
2501.18391 v2

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T23:50:42.818590Z

measured 41 of 41 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:22:12.821936Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T20:22:13.417389Z

Reference resolution

40 of 40 outbound references displayed

verified exact0
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External citation measurements

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Outbound references

Observation b19144a5-9070-4d1c-a063-791fe5bb2d4d · outbound

This paper cites Necessary and suﬃcient conditions for the exis- tence of m-perfect processes associated with Dirichlet forms.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Necessary and suﬃcient conditions for the exis- tence of m-perfect processes associated with Dirichlet forms

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.399953Z

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.

Observation 929970c3-3359-4a92-8eb7-28fdd291b379 · outbound

This paper cites A general corresponden ce between Dirichlet forms and right processes.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms A general corresponden ce between Dirichlet forms and right processes

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.385565Z

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.

Observation 43254e96-55ea-45d7-a5ce-7eee51b6b667 · outbound

This paper cites Cal culus and heat ﬂow in metric measure spaces and applications to spaces with Ricci bounds from below.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Cal culus and heat ﬂow in metric measure spaces and applications to spaces with Ricci bounds from below

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.371455Z

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.

Observation b7bc6059-9e31-4a79-95ee-6d2f6c27f153 · outbound

This paper cites $p$-Brownian motion and the $p$-Laplacian.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms $p$-Brownian motion and the $p$-Laplacian

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-09T23:50:42.652878Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e2e19ff7-59f5-4064-a1c8-bc043c98c688 · outbound

This paper cites Quelques aspects non lin´ eaires du principe du maximum.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Quelques aspects non lin´ eaires du principe du maximum

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.357004Z

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.

Observation 6fe9ff2f-a402-40da-9aa4-a394186d5757 · outbound

This paper cites Beurling and J.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Beurling and J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.343272Z

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.

Observation 23232e94-0ce4-4061-9ab6-455a5284a9af · outbound

This paper cites Beurling and J.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Beurling and J

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.329596Z

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.

Observation 20f3016b-56f7-4132-b32b-828f2557c89f · outbound

This paper cites No nlinear Dirichlet forms associated with quasiregular mappings.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms No nlinear Dirichlet forms associated with quasiregular mappings

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.315848Z

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.

Observation 308f362c-1f52-44d6-b14b-83c19a8dd3a8 · outbound

This paper cites The normal contr action property for non- bilinear Dirichlet forms.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms The normal contr action property for non- bilinear Dirichlet forms

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.301724Z

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.

Observation ab6c1b1c-43ae-4aca-b62a-90188738a75a · outbound

This paper cites Reﬂexive Orlicz spaces hav e uniformly normal structure.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Reﬂexive Orlicz spaces hav e uniformly normal structure

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.287826Z

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.

Observation 6e7ce402-3f3d-4a2c-9930-3068231d10fb · outbound

This paper cites Symmetric Markov processes, time change, and boundary theory , volume 35 of London Mathematical Society Monographs Series.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Symmetric Markov processes, time change, and boundary theory , volume 35 of London Mathematical Society Monographs Series

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.273815Z

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.

Observation e837d627-90f4-44e6-a647-75718c5d98a0 · outbound

This paper cites Geometry of Banach spaces, duality mappings and nonlinear p rob- lems, volume 62 of Mathematics and its Applications.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Geometry of Banach spaces, duality mappings and nonlinear p rob- lems, volume 62 of Mathematics and its Applications

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.260182Z

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.

Observation b79666ca-a0d7-4de9-9ffa-3b9274089866 · outbound

This paper cites Nonlinear Markov s emigroups, nonlinear Dirichlet forms and applications to minimal surfaces.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Nonlinear Markov s emigroups, nonlinear Dirichlet forms and applications to minimal surfaces

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.246358Z

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.

Observation 2088bcdf-15ca-4757-9c85-d94ba2409c54 · outbound

This paper cites Energy spaces, Dirichlet forms and cap acities in a nonlinear setting.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Energy spaces, Dirichlet forms and cap acities in a nonlinear setting

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.232854Z

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.

Observation d28e7d6d-1fb9-4e7e-a217-35cdcf2d7366 · outbound

This paper cites Nonlinear dirichlet forms.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Nonlinear dirichlet forms

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.219234Z

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.

Observation bf1a05cb-c614-4d18-b650-785da363a208 · outbound

This paper cites A semigrou p approach to nonlinear L´ evy processes.Stochastic Process.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms A semigrou p approach to nonlinear L´ evy processes.Stochastic Process

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.205826Z

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.

Observation af34b2c0-4362-4d6a-b6fb-e8f5c5e5922f · outbound

This paper cites Optimal Lp Hardy-type inequalities.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Optimal Lp Hardy-type inequalities

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.192564Z

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.

Observation 6f73157f-55a1-4db1-81f1-f0afb1084c3a · outbound

This paper cites Springer, Heidelberg, 2011.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Springer, Heidelberg, 2011

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.178862Z

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.

Observation 36d264b1-01d8-485d-b2dd-837e3fe29143 · outbound

This paper cites Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, english edition, 1999.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, english edition, 1999

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.165303Z

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.

Observation 3c43f742-714c-45a9-b50e-e752949022af · outbound

This paper cites A non-local quasi-linear ground stat e representation and criticality theory.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms A non-local quasi-linear ground stat e representation and criticality theory

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.151694Z

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.

Observation 84c693a8-f66a-49df-9432-0f2850b73c53 · outbound

This paper cites Dirichlet forms and symmetric Markov processes, volume 19 of de Gruyter Studies in Mathematics.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Dirichlet forms and symmetric Markov processes, volume 19 of de Gruyter Studies in Mathematics

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.137690Z

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.

Observation bb0af5ad-1c49-44f0-921a-e55330ba5f1e · outbound

This paper cites Analytic and geometric background of recurrence and no n- explosion of the Brownian motion on Riemannian manifolds.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Analytic and geometric background of recurrence and no n- explosion of the Brownian motion on Riemannian manifolds

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.123885Z

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.

Observation 7f4d82b4-b608-4a2e-83be-249c94230c1a · outbound

This paper cites Towards an Lp-potential theory for sub-Markovian semigroups: variational inequalities and balayage theory.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Towards an Lp-potential theory for sub-Markovian semigroups: variational inequalities and balayage theory

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.110354Z

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.

Observation b5584af4-6400-4e38-88a1-02287ff8b271 · outbound

This paper cites The open mapping and closed graph theorems in topological ve ctor spaces.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms The open mapping and closed graph theorems in topological ve ctor spaces

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.096302Z

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.

Observation b93ebd47-d4b2-40e7-9d5e-1cc315b6ccf1 · outbound

This paper cites Schilling.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Schilling

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.082453Z

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.

Observation 20289cc6-12a9-4b4d-b95a-c34ca7ac353c · outbound

This paper cites (1 , p)-Sobolev spaces based on strongly local Dirichlet forms.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms (1 , p)-Sobolev spaces based on strongly local Dirichlet forms

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.069123Z

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.

Observation 462cf765-13bb-465f-a4fd-dd52a7956ce0 · outbound

This paper cites Mar kov processes associated with semi-Dirichlet forms.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Mar kov processes associated with semi-Dirichlet forms

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.054681Z

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.

Observation ed1832cd-9123-4630-9a9b-29052c4b71df · outbound

This paper cites Introduction to the theory of (nonsymmetric) Dirichlet forms.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Introduction to the theory of (nonsymmetric) Dirichlet forms

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.040889Z

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.

Observation 69e1db4b-4f43-4d42-a376-1ef3a29e2014 · outbound

This paper cites Semi-Dirichlet forms and Markov processes , volume 48 of De Gruyter Studies in Mathematics.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Semi-Dirichlet forms and Markov processes , volume 48 of De Gruyter Studies in Mathematics

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.026477Z

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.

Observation 1a2f2f0f-4eb8-459c-b277-7a6385ce8b38 · outbound

This paper cites Topics in the theory of positive solu tions of second-order ellip- tic and parabolic partial diﬀerential equations.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Topics in the theory of positive solu tions of second-order ellip- tic and parabolic partial diﬀerential equations

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:43.012548Z

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.

Observation 90e88505-7c12-4fb4-8eff-7d27092bae6e · outbound

This paper cites Ground state alte rnative for p-Laplacian with potential term.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Ground state alte rnative for p-Laplacian with potential term

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:42.998579Z

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.

Observation 21ea8dd6-a929-4e60-8689-837f5e5a1dd3 · outbound

This paper cites Nonlinear Beurling-Deny criteria.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Nonlinear Beurling-Deny criteria

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-09T23:50:42.780988Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 982e4c92-b194-45c1-ae0b-c922b57ef3fa · outbound

This paper cites Weak Poincar´ e inequalities and L2-convergence rates of Markov semigroups.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Weak Poincar´ e inequalities and L2-convergence rates of Markov semigroups

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:42.984206Z

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.

Observation 7dccd0ff-4ce3-46aa-a348-0437b7031514 · outbound

This paper cites Energy forms.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Energy forms

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-09T23:50:42.790625Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 65dfcab7-d15f-4f48-9d9d-905ab9d60387 · outbound

This paper cites A note on reﬂected Dirichlet forms.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms A note on reﬂected Dirichlet forms

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:42.969251Z

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.

Observation bd9d6ebf-1427-4716-961b-b7912a4116a3 · outbound

This paper cites (Weak) Hardy and Poincar´ e inequaliti es and criticality theory.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms (Weak) Hardy and Poincar´ e inequaliti es and criticality theory

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:42.953885Z

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.

Observation 7edb838f-5069-467e-90f8-67bd4b3b766d · outbound

This paper cites Positivity preserving forms have the Fatou property.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Positivity preserving forms have the Fatou property

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:42.939192Z

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.

Observation f3e76aec-e13b-471a-b0d2-7d4e81087472 · outbound

This paper cites an unresolved cited work.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-09T23:50:42.924480Z

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.

Observation 1149f286-3e89-4981-9b30-bb945a5b86a5 · outbound

This paper cites Silverstein.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms Silverstein

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:42.910420Z

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.

Observation 3890f030-eecc-44dc-85ca-85b1b7a235dd · outbound

This paper cites On nonlinear Dirichlet forms.

The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms On nonlinear Dirichlet forms

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:50:42.896045Z

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.

Pith citing papers

Observation d2834501-f4ed-44ab-9bd4-58e70de4a851 · inbound

Nonlinear resistance forms cites this paper.

Nonlinear resistance forms The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:22:13.556620Z

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.