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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 2026-08-07T06:34:17.273281+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

  • verified exact0
  • 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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.262409Z digest=sha256:ae6e1db7fc6095466c61f45e7a61f9f2407c2614f96842ac454982f620d49704

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
raw_fallback, observed 2026-08-07T05:22:27.839947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.310496Z digest=sha256:1185a56ef15343408b3888b4e3fc0f8d862ea8c2fd18ee5c6cd01cfc70cb5896

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
raw_fallback, observed 2026-08-07T05:22:27.831601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.362564Z digest=sha256:ef6677a3f0094aa0a4416fbff8cb07cdace58ae48c07854359ca846d5dac6f01

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.416817Z digest=sha256:bd61c77a6f8e65104f89a1af4efbf016dc3ef706265836d4a6f435b10d660c0d

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.491408Z digest=sha256:f4630a3aaec7d896c277fb52c79f8431c9649993c10e7f9634124e8b8a081c39

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.559956Z digest=sha256:a2eb33b6f22adcfb77b80ae0ac5b996b3727caf696f03a88db8473c200a27556

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=sha256:0a156ab539fd2c23de7ac3324c75486515175b051e3a2321ec6a175361e0d74a

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.667979Z digest=sha256:b070b77574b6a2ece3d68e48d5c37f9973319a86bbae79a627d29c3bbba65d72

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=sha256:8b571ffe9de0304d0308f5cf1b564c4271f62bdfc607c6b773d6172ce8408acb

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.809463Z digest=sha256:37a1a41464d046783b7a3fb6ccbd17303916d4652f05e703cd37f29dee0b701d

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.867986Z digest=sha256:c2e267d1284a0e1029e855d84f4dc5a223cf600c7aba2a7f844d5cc6a7a3f336

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:24.940784Z digest=sha256:1a05ca22642beb9bd8d87f9bbdcc9f76e00fbf37f962acc116e8f799a7dca5db

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
raw_fallback, observed 2026-08-07T05:22:27.751118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.087385Z digest=sha256:d78697a4e4ddba6132d8452c09be7369b078cd8884e078b5b916eaa2917c0b90

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
raw_fallback, observed 2026-08-07T05:22:27.742484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.187672Z digest=sha256:91de75bbaf07e0f4280624cd3eb7dfa35662cd277fa418087de2aac7097e12f1

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
raw_fallback, observed 2026-08-07T05:22:27.732576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.299671Z digest=sha256:d29d6e5d603738144a5cddd53bb47690c6d14012110e72ecdbd3768894006a34

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:cac53667fd8569896f88ba39ef2d5c9698a033a0aa3d14d5b95faaf12fd5d917

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
raw_fallback, observed 2026-08-07T05:22:27.723986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.459263Z digest=sha256:9bb753a41bc66ac8c1ff995eb5f8c330eebdec5500c4334d027ea9c48c596276

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
raw_fallback, observed 2026-08-07T05:22:27.714104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.548585Z digest=sha256:3bef509e1a81d980fae31d52264684e07ad0cdc820898d938aab7f34588a6ab5

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.669013Z digest=sha256:c823c930bcb376ea16630189795a196e661ded53bb8ff227bfa740127b9a1d33

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
raw_fallback, observed 2026-08-07T05:22:27.694731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:25.763492Z digest=sha256:51ba496e790feb24307dd0b9b796eb93a6dc3473224ac0ece3ac0cb1b430bea6

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=sha256:8472920e420e90b69ff274b2e0006e54305b42b256525be8348f3bda1e48d739

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:db7a18ce280730dd2bec60a2bff764742f418f3662aab8dc5bcb9facb3cabc67

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:bf78a43294d84c258fc4fda977126af98711afd6d75da1a89c32a7d78d1af216

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.114190Z digest=sha256:9988898521a8efbee098e20c8274a77361e32df813bfa9ef38486a72badc4ba0

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.202463Z digest=sha256:be8b23591539c6a4d512cb2abe7819c83a5b61eaa6d6969d44d2ef6bdcb11eaf

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.273225Z digest=sha256:753c117c39db07a54c076e767e5b6a08183c0da70ce23ac46ac0715ab9a46ce1

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.319975Z digest=sha256:ab27402d0519630cb00d6a9e003e924fe202e7f3920dcee07303502707411271

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.392939Z digest=sha256:671cf0a66d582e5e71bb72cc90ace55377af2f35c69c5feca9bf599d5b4c24b0

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.476760Z digest=sha256:75de2159ee14e91c20064ed9afa04639ec7a89d45e1af6d4a93bbf5d28c60e2a

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.529582Z digest=sha256:70bd566c916c471ddcd877146729fd7be47f95644d2360e4a5589b89c3d0106c

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.572204Z digest=sha256:72ac4c75021333c17ef09e9369c48e66c17c2a25e2c51ea8219938b36c5608c1

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T05:22:26.631991Z digest=sha256:7392b2409d4de058c5a41d5cbd88b05b8267c981e09fd7986950a4d32bd23b78

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