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Paper Citation Record · LEDGER

On the domains of first order differential operators on the Sierpi\'{n}ski gasket

As of 8 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2506.08679.

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

pith.paper-citation-record.v1
2506.08679 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:22:26.631991Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

32 of 32 outbound references displayed

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  • verified fuzzy24
  • unresolved8
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4843a2b7-6462-4c39-ac18-5e217aff70d1 · outbound

This paper cites Strichartz, and Alexander Teplyaev.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Strichartz, and Alexander Teplyaev

Reference 1

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.262409Z digest=sha256:29a478897d8ae84b3d3f5a656e1f2898c0c53a6e56059ff8fe340c5085b8761e

Observation bf9f102b-12a5-4bb4-93cf-7ce1c42683e6 · outbound

This paper cites Strichartz.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Strichartz

Reference 2

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.310496Z digest=sha256:63c3971882e242da931dc0f8ce72e0b3e9f76a4ab49b4a82ab406f36b90ed1e3

Observation be231ffa-ffa9-45fd-81e6-e644f0302665 · outbound

This paper cites Kelleher.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Kelleher

Reference 3

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.362564Z digest=sha256:6924614021a7a7985b1b638ef6225a07d1f2bee8aa718cbf36bb6386248021bb

Observation 30e167e3-0aa1-4cd8-acf8-88c15b105263 · outbound

This paper cites Barlow and Edwin A.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Barlow and Edwin A

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.822598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.416817Z digest=sha256:6978fe65a458f82e13d31ce99170575bc905295137ebb40f2d3f64aca4de9fe6

Observation a857f4f7-c7a7-4aef-a1d9-c95983e2f931 · outbound

This paper cites Integrals and potentials of differential 1-forms on the S ierpinski gasket.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Integrals and potentials of differential 1-forms on the S ierpinski gasket

Reference 5

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.491408Z digest=sha256:dc3170abb09bdf4e43219e6eb7f799d826127f05162ce6375885599958ef30f6

Observation 2159b75e-3f93-4dc1-89fa-a2a58e4116c7 · outbound

This paper cites Derivations as square roots of D irichlet forms.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Derivations as square roots of D irichlet forms

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.805472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.559956Z digest=sha256:0a883fdeec7e2269b27f35a0471d903d9152881bed67ca7aeeb21c7785afa070

Observation c7c0d2fc-8335-4ab5-987f-b1032290e69d · outbound

This paper cites Fredholm modules on P.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Fredholm modules on P

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-07T05:22:24.608971Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T05:22:24.608971Z digest=sha256:54fd438d6a3c961dab30ea94d6c6285970d882f93180a7069c05b7a82d585421

Observation 789f2c8a-6ad9-4463-a396-7300d64908f3 · outbound

This paper cites Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators , volume 1718 of Lecture Notes in Mathematics.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators , volume 1718 of Lecture Notes in Mathematics

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.790900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.667979Z digest=sha256:c373996aea99f4e676ebf2002a3f6be17f242fd53a19ab4ebbf3789b8f346928

Observation 356556a6-19da-4917-9db5-9de2ab60e522 · outbound

This paper cites Random walks and diffusions on fractals.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Random walks and diffusions on fractals

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-07T05:22:24.747709Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T05:22:24.747709Z digest=sha256:e97a07b6c23437b09f465f6717b68845223656f1a8b0f12def9fa9ae899e2ab2

Observation abf208bc-23de-438f-b8ba-2be6ede3ba1c · outbound

This paper cites Energy measures and indices of D irichlet forms, with applications to derivatives on some fractals.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Energy measures and indices of D irichlet forms, with applications to derivatives on some fractals

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.776452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 807e1250-de7e-4caf-baaa-27bfeb2a4710 · outbound

This paper cites Upper estimate of martingale dimension for self-similar fractals.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Upper estimate of martingale dimension for self-similar fractals

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.768210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.867986Z digest=sha256:3eec36589910c6efe3125700a2e7069fa9e40ae4e8f5cd1ce95157e43562d940

Observation 4ea4728f-98ef-4e28-b18c-d378405f13d0 · outbound

This paper cites Kelleher, and Alexander Teplyaev.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Kelleher, and Alexander Teplyaev

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.759291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.940784Z digest=sha256:200acf2a2966e2613b889722f71555662fc20507b2eee27ff48a29097413fdf9

Observation bc393a9a-8084-4f07-b6a5-816fc2794fff · outbound

This paper cites On the viscous B urgers equation on metric graphs and fractals.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket On the viscous B urgers equation on metric graphs and fractals

Reference 13

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.087385Z digest=sha256:a64b26b9c380aa4c7676e523dd3566f205786676102b6a2fd171fce92a262f71

Observation 3dd4bb08-9fdf-44ce-9e3b-641c67b3f56c · outbound

This paper cites Approximation of partial differential equations on compact resistance spaces.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Approximation of partial differential equations on compact resistance spaces

Reference 14

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.187672Z digest=sha256:91c3b3f91e23e34c42044cada210d02a7d0a03c64e6e88eb9de21b6c17e6143d

Observation fdbc7e0b-1be5-40c2-b9aa-0883e9ca3b77 · outbound

This paper cites Vector analysis for D irichlet forms and quasilinear PDE and SPDE on metric measure spaces.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Vector analysis for D irichlet forms and quasilinear PDE and SPDE on metric measure spaces

Reference 15

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.299671Z digest=sha256:524fb4262f02c525ca5565ede4a5cc5a421e6520445cfbf1c9fb0528d0d3bcc9

Observation dca27edc-16a2-4c48-adc8-df45da6bb55f · outbound

This paper cites On equations of continuity and transport type on metric graphs and fractals.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket On equations of continuity and transport type on metric graphs and fractals

Reference 16

Resolution
unresolved
no resolver link, observed 2026-08-07T05:22:25.360518Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T05:22:25.360518Z digest=sha256:f09191f064996100da639c9226b3f186e6fc5bf171d1bc8cb8edb93fe4e87800

Observation 7e189575-3d24-49de-8e86-f188a7b574e4 · outbound

This paper cites Rogers, and Alexander Teplyaev.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Rogers, and Alexander Teplyaev

Reference 17

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.459263Z digest=sha256:5b8634ac329ade9ecf17a0693a7e158891f2b7045b90d1403f5f68b41bb02227

Observation 396e9551-de34-442b-9208-72ad548cfd68 · outbound

This paper cites A harmonic calculus on the S ierpi\' n ski spaces.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket A harmonic calculus on the S ierpi\' n ski spaces

Reference 18

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.548585Z digest=sha256:36ba4e68b9b758cc160e384a9bf8e21964c552da27184b61d953728be01d15dd

Observation 18b600c1-99c4-4fe7-a230-20cac4624dd4 · outbound

This paper cites an unresolved cited work.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:27.704376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation ffe711bd-1615-42e3-8543-102287f8eb22 · outbound

This paper cites Harmonic calculus on p.c.f.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Harmonic calculus on p.c.f

Reference 20

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.763492Z digest=sha256:a8aa6582d8580907e2f281ac88b142085d709f05db8b4f7081eee6bdba3ecf0e

Observation 82c684ff-d667-45e9-9c5f-2410becd8ea4 · outbound

This paper cites Analysis on fractals , volume 143 of Cambridge Tracts in Mathematics.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Analysis on fractals , volume 143 of Cambridge Tracts in Mathematics

Reference 21

Resolution
unresolved
no resolver link, observed 2026-08-07T05:22:25.843594Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T05:22:25.843594Z digest=sha256:6ea4497017c0a9789c6e91be3b5de26989cca590dd87dc923161a4e5e5b4cdf0

Observation 76661994-5e3d-432f-8aba-f11d9fa83e80 · outbound

This paper cites Resistance forms, quasisymmetric maps and heat kernel estimates.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Resistance forms, quasisymmetric maps and heat kernel estimates

Reference 22

Resolution
unresolved
no resolver link, observed 2026-08-07T05:22:25.915329Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T05:22:25.915329Z digest=sha256:5e876e2edceedc7a66a0b785e7a5dcb5fa77dcc1de76c132ae3d422744522296

Observation 1c440772-2314-4b9a-bdf7-0af413c8f106 · outbound

This paper cites A diffusion process on a fractal.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket A diffusion process on a fractal

Reference 23

Resolution
unresolved
no resolver link, observed 2026-08-07T05:22:26.045263Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T05:22:26.045263Z digest=sha256:af14cc7bbd001a70a5bced338b17d6d468962d24a420ed73cf131a0178bcd97a

Observation eb9e68f3-eda6-4fe7-912a-f60c67dfbadf · outbound

This paper cites Dirichlet forms on fractals and products of random matrices.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Dirichlet forms on fractals and products of random matrices

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.665440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.114190Z digest=sha256:10cc99d9acec17205efc5984b101435d1601d09f490317fdb895ed3e32fdf96d

Observation a298bc99-35cf-4619-a0e4-ee5ccc5ae1c1 · outbound

This paper cites an unresolved cited work.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:22:27.656722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation fabdb0f1-e5fa-4892-86e0-52c182f81834 · outbound

This paper cites Strichartz.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Strichartz

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.646753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.273225Z digest=sha256:60cdfa72915f6d28ba7a03a1570c166745a9993b871699fdec6d468e3b257ad1

Observation ff2dbd18-7516-479c-8fdb-f14612503efb · outbound

This paper cites Stochastic calculus for continuous additive functionals of zero energy.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Stochastic calculus for continuous additive functionals of zero energy

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.489838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.319975Z digest=sha256:50a3ac5422a984d28dc01060f88763e9ee05599cbaab0341d4a77628e91dcf4a

Observation 157235ac-1cb5-4792-b2e6-79b52a52e30f · outbound

This paper cites The M alliavin calculus and related topics.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket The M alliavin calculus and related topics

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.373964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.392939Z digest=sha256:e5fe6e1e06b312d493b0eda350dce9c921c1941ccaeecddb0034c8352686f372

Observation 04ab982f-d948-491f-af9c-135e114d0fba · outbound

This paper cites First O rder D ifferential O perators and E quations of C ontinuity and T ransport- T ype on metric G raphs and F ractals.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket First O rder D ifferential O perators and E quations of C ontinuity and T ransport- T ype on metric G raphs and F ractals

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.185629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.476760Z digest=sha256:8007eadee6d678cbf29c1946f88c227a50ab067fb58b81c3a4eb02c39f74295a

Observation 0bb37db8-f2b7-4fd5-985a-3ce5413ad565 · outbound

This paper cites Strichartz.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Strichartz

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:27.054986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.529582Z digest=sha256:d50bbd73806b43d0ba0c50e04285f55843267a27b20343dd831f26c2d4d1e929

Observation d6e9f8c6-f6d6-4c05-bfd3-acc289c446f8 · outbound

This paper cites Strichartz.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Strichartz

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:26.948869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.572204Z digest=sha256:cb3865304867b105b6f061b96b4a67a583bc5e8acb8c210bbc0ac50216506667

Observation a408ec01-e37a-4e7c-8e66-7b26bf53ed2e · outbound

This paper cites Gradients on fractals.

On the domains of first order differential operators on the Sierpi\'{n}ski gasket Gradients on fractals

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:22:26.793563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.631991Z digest=sha256:1636e32b6f0c3dc714166bd55605622ce5a975976943af0d544b83617c41b740

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