Paper Citation Record · LEDGER

Walk dimension and vanishing curve modulus in metric measure spaces

As of 21 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2606.27869.

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

pith.paper-citation-record.v1
2606.27869 v2

Coverage vector

measured 25 of 25 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-02T10:07:08.010259Z

measured 25 of 25 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

25 of 25 outbound references displayed

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Outbound references

Observation f2a0d5f6-0ea7-44c1-bcca-347ce2160e5d · outbound

This paper cites Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope.

Walk dimension and vanishing curve modulus in metric measure spaces Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.310034Z

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Observation 714b5180-4813-4596-8cfc-89424514b13c · outbound

This paper cites an unresolved cited work.

Walk dimension and vanishing curve modulus in metric measure spaces Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.329444Z

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Observation daf24277-82eb-4881-81c8-93d82266cb55 · outbound

This paper cites A course in metric geometry , volume 33 of Graduate Studies in Mathematics.

Walk dimension and vanishing curve modulus in metric measure spaces A course in metric geometry , volume 33 of Graduate Studies in Mathematics

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.333183Z

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Observation 31d2a0f7-b594-4ad2-bfee-5215c06f8e97 · outbound

This paper cites Functional analysis, S obolev spaces and partial differential equations.

Walk dimension and vanishing curve modulus in metric measure spaces Functional analysis, S obolev spaces and partial differential equations

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.337147Z

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Observation 8da1b1af-fa92-42a1-8181-d84eca1ffdb0 · outbound

This paper cites Stability of heat kernel bounds under pointed G romov- H ausdorff convergence.

Walk dimension and vanishing curve modulus in metric measure spaces Stability of heat kernel bounds under pointed G romov- H ausdorff convergence

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.341145Z

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Observation 40a4977e-a10c-4c37-b295-858993f3ffbe · outbound

This paper cites Elliptic Harnack inequalities for mixed local and nonlocal p -energy form on metric measure spaces, 2026.

Walk dimension and vanishing curve modulus in metric measure spaces Elliptic Harnack inequalities for mixed local and nonlocal p -energy form on metric measure spaces, 2026

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.344773Z

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Observation 15db47a2-87ca-466a-b89c-fe019877fde0 · outbound

This paper cites On microsets, Assouad dimension and lower dimension of random fractals, and Furstenberg's homogeneity.

Walk dimension and vanishing curve modulus in metric measure spaces On microsets, Assouad dimension and lower dimension of random fractals, and Furstenberg's homogeneity

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.349068Z

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Observation ed4c657b-a394-458c-bdcf-81b6d1679abb · outbound

This paper cites On the Resistance Conjecture, 2026.

Walk dimension and vanishing curve modulus in metric measure spaces On the Resistance Conjecture, 2026

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.353227Z

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Observation f385876a-acc9-4788-9f87-1c0b0ad8704e · outbound

This paper cites On the energy image density conjecture of Bouleau and Hirsch, 2025.

Walk dimension and vanishing curve modulus in metric measure spaces On the energy image density conjecture of Bouleau and Hirsch, 2025

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.357026Z

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Observation d74ef6f8-1645-400b-9cb4-7f81b49a8e20 · outbound

This paper cites Density of continuous functions in S obolev spaces with applications to capacity.

Walk dimension and vanishing curve modulus in metric measure spaces Density of continuous functions in S obolev spaces with applications to capacity

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.362110Z

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Observation 87aae151-4892-4a4e-8029-27877e6f66e0 · outbound

This paper cites Dirichlet forms and symmetric M arkov processes , volume 19 of De Gruyter Studies in Mathematics.

Walk dimension and vanishing curve modulus in metric measure spaces Dirichlet forms and symmetric M arkov processes , volume 19 of De Gruyter Studies in Mathematics

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.388290Z

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Observation 6e31e0c5-172f-44b3-96a9-3750de2ef5f9 · outbound

This paper cites Generalized capacity, H arnack inequality and heat kernels of D irichlet forms on metric measure spaces.

Walk dimension and vanishing curve modulus in metric measure spaces Generalized capacity, H arnack inequality and heat kernels of D irichlet forms on metric measure spaces

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.516738Z

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Observation ea32131b-f49d-451d-bf96-7d98bfb92bc8 · outbound

This paper cites Lectures on analysis on metric spaces.

Walk dimension and vanishing curve modulus in metric measure spaces Lectures on analysis on metric spaces

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.648909Z

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Observation c83fbf45-c0e3-486d-82cc-62474be9c9c3 · outbound

This paper cites Quasiconformal maps in metric spaces with controlled geometry.

Walk dimension and vanishing curve modulus in metric measure spaces Quasiconformal maps in metric spaces with controlled geometry

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.758485Z

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Observation cdbdbfc0-fe42-4dce-9441-56012fc468f8 · outbound

This paper cites an unresolved cited work.

Walk dimension and vanishing curve modulus in metric measure spaces Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:06.900132Z

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Observation ecf8e678-3294-4b00-a6e4-a2c06d0439a9 · outbound

This paper cites An elementary proof that walk dimension is greater than two for B rownian motion on S ierpi\'nski carpets.

Walk dimension and vanishing curve modulus in metric measure spaces An elementary proof that walk dimension is greater than two for B rownian motion on S ierpi\'nski carpets

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:07.016148Z

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Observation 1850b48e-f281-4dd2-9720-5939aaeacbf9 · outbound

This paper cites Conductive homogeneity of compact metric spaces and construction of p -energy , volume 5 of Memoirs of the European Mathematical Society.

Walk dimension and vanishing curve modulus in metric measure spaces Conductive homogeneity of compact metric spaces and construction of p -energy , volume 5 of Memoirs of the European Mathematical Society

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:07.220516Z

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Observation 5965aff0-8cb6-44a5-b341-1a547252f1dc · outbound

This paper cites Keith and T.

Walk dimension and vanishing curve modulus in metric measure spaces Keith and T

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:07.381917Z

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Observation b5a195ef-4a2d-4491-8fe5-d612f4e7d715 · outbound

This paper cites On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates.

Walk dimension and vanishing curve modulus in metric measure spaces On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:07.466840Z

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Observation 98159dd7-6d21-42b1-ad27-d4ab19964e15 · outbound

This paper cites On the conformal walk dimension: quasisymmetric uniformization for symmetric diffusions.

Walk dimension and vanishing curve modulus in metric measure spaces On the conformal walk dimension: quasisymmetric uniformization for symmetric diffusions

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:07.536793Z

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Observation 40425610-61a6-4f2a-8f6e-d083c557d87b · outbound

This paper cites Contraction properties and differentiability of $p$-energy forms with applications to nonlinear potential theory on self-similar sets.

Walk dimension and vanishing curve modulus in metric measure spaces Contraction properties and differentiability of $p$-energy forms with applications to nonlinear potential theory on self-similar sets

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:07.628190Z

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Observation fd9da3a9-dc87-49c9-9546-a4ed0d3de12b · outbound

This paper cites Scale-invariant boundary H arnack principle on inner uniform domains in fractal-type spaces.

Walk dimension and vanishing curve modulus in metric measure spaces Scale-invariant boundary H arnack principle on inner uniform domains in fractal-type spaces

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:07.728142Z

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Observation c3160a88-6c7a-4570-8274-b3cddaa46e29 · outbound

This paper cites Gromov-Hausdorff distances in Euclidean spaces.

Walk dimension and vanishing curve modulus in metric measure spaces Gromov-Hausdorff distances in Euclidean spaces

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:07.827196Z

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Observation 1759ceb2-b51b-40a3-b163-c8ee7b1c7392 · outbound

This paper cites On singularity of $p$-energy measures on metric measure spaces.

Walk dimension and vanishing curve modulus in metric measure spaces On singularity of $p$-energy measures on metric measure spaces

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:07.864478Z

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Observation daee4694-290c-45c5-b394-d95d096c18fd · outbound

This paper cites On the dichotomy of p -walk dimensions on metric measure spaces, 2025.

Walk dimension and vanishing curve modulus in metric measure spaces On the dichotomy of p -walk dimensions on metric measure spaces, 2025

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T10:07:08.010259Z

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Pith citing papers

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