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Paper Citation Record · LEDGER

$p$-Modulus on radially symmetric trees

As of 9 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 0 inbound Pith citation observations for arXiv:2506.07377.

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

pith.paper-citation-record.v1
2506.07377 v1

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T06:01:40.604929Z

measured 16 of 16 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

16 of 16 outbound references displayed

  • verified exact2
  • verified fuzzy14
  • unresolved0
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 01cb36b3-c76d-492d-b5e7-a966a56031a2 · outbound

This paper cites Conformal Invarients: Topics in Geometric Function Theory.

$p$-Modulus on radially symmetric trees Conformal Invarients: Topics in Geometric Function Theory

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.993307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.493631Z digest=sha256:baad6f899203263c49e1d77cda79fedd58a25cb0dab9716367876abfd44c8b76

Observation c5b2cd3b-1b72-4357-8fa4-49a76ebb971c · outbound

This paper cites Modulus on graphs as a generalization of standard graph theoretic quantities.

$p$-Modulus on radially symmetric trees Modulus on graphs as a generalization of standard graph theoretic quantities

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.976752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.501451Z digest=sha256:14514b357ce5fa551b0f0df148246b3d05da5c0ae284562628335369f249dcca

Observation b3923591-dfbe-45b3-a72f-7a634fa1b90f · outbound

This paper cites Block- ing duality for p-modulus on networks and applications.

$p$-Modulus on radially symmetric trees Block- ing duality for p-modulus on networks and applications

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.956338Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.517882Z digest=sha256:a174d8814cbe2058d9b405b83e5022c7ca6be7bf5e689d8b2d077dd7b44a8e19

Observation 33a10fb0-b3e9-4813-99df-d0f25fa67e5d · outbound

This paper cites Fairest edge usage and minimum expected overlap for random spanning trees.

$p$-Modulus on radially symmetric trees Fairest edge usage and minimum expected overlap for random spanning trees

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.938102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.524421Z digest=sha256:fa82c79f4553327adae3aa067167d6cdede1979f234c32fbd6b1adac8e7ce7d0

Observation f82030b3-6aa7-479f-bb9b-e4ff43021e98 · outbound

This paper cites Modulus of families of walks on graphs.

$p$-Modulus on radially symmetric trees Modulus of families of walks on graphs

Reference 5

Resolution
verified exact
local_arxiv, observed 2026-08-07T06:01:40.707510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.531146Z digest=sha256:62caf41c276778ef264bea17d75a1a73630b84c9dd1b007f0b0045c4e935680c

Observation e45aacd9-93d1-4f8f-84af-eba921b4065f · outbound

This paper cites Modulus metrics on net- works.

$p$-Modulus on radially symmetric trees Modulus metrics on net- works

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.920275Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.543040Z digest=sha256:93a1a164455ac068533c834cf7f91676c091c05d77b070b008e7dadd8d2646eb

Observation 44d159cf-1d06-4a0f-8d06-c6eca265f198 · outbound

This paper cites Spanning tree modulus for secure broadcast games.

$p$-Modulus on radially symmetric trees Spanning tree modulus for secure broadcast games

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.903047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.551417Z digest=sha256:702925f99236493c8817552052dd5130a360d044580e3986b09696854e9da4ba

Observation c460e6e9-b786-47f8-a000-c7353c04d425 · outbound

This paper cites Doyle and J.

$p$-Modulus on radially symmetric trees Doyle and J

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.885732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.558305Z digest=sha256:2ae065552b448b58d7aec9beba693c3ade98215ba4bdf8c5d63f8fcab962bb9c

Observation 461ef62e-8953-4816-8105-b57130c26774 · outbound

This paper cites The Extremal Length of a Network.

$p$-Modulus on radially symmetric trees The Extremal Length of a Network

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.866772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.564291Z digest=sha256:aefc3a0e4453e68a23a1ab38aece8b3ce23b74ceecf2babdab942eef45dfda92

Observation a5dfe770-f9fb-4f5f-8a75-1f42892ccf67 · outbound

This paper cites Empilements de cercles et modules combinatoires.

$p$-Modulus on radially symmetric trees Empilements de cercles et modules combinatoires

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.844592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.569734Z digest=sha256:eed38cd5fb69c2a18ce637580340072b38f6af67ae57d4fcefb50a0e38a6bc8a

Observation 27c716f3-5071-45ae-bfc8-da3362a08162 · outbound

This paper cites Amazing and aesthetic aspects of Analysis.

$p$-Modulus on radially symmetric trees Amazing and aesthetic aspects of Analysis

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.821991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.574903Z digest=sha256:8511194bbf26d9180b247d4f518e775b5b80ea460cf03c76c4d3804064f0eaed

Observation 74866a1a-1472-4e18-9b67-bb0034a758b7 · outbound

This paper cites Probability on Trees and Networks.

$p$-Modulus on radially symmetric trees Probability on Trees and Networks

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.797999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.579980Z digest=sha256:17d56aa0dbebe3ca8ecd22523acbe1e4e3a73ff401d237d91581fe574e0de292

Observation 5b2889c4-2043-4c3a-ae1d-d931b25d0f4d · outbound

This paper cites Square tilings with prescribed combinatorics.

$p$-Modulus on radially symmetric trees Square tilings with prescribed combinatorics

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.775569Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.585937Z digest=sha256:839c02515efea231e266602aed1d43750c8518d76794aa6ade315b5d65ab54ce

Observation ce91625e-72ef-4a20-8af7-c63f001576cc · outbound

This paper cites Generalization of effective conductance centrality for egonetworks.

$p$-Modulus on radially symmetric trees Generalization of effective conductance centrality for egonetworks

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.752722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.592683Z digest=sha256:4d6a0eb069a807a9c9a424ef6318b4c3419f1579b1328157086098e0c8cc5c5b

Observation 3a9b2f2c-2152-481f-ae30-a605c85d95f7 · outbound

This paper cites Network clustering and community detection using modulus of families of loops.

$p$-Modulus on radially symmetric trees Network clustering and community detection using modulus of families of loops

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T06:01:40.731044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.599146Z digest=sha256:3fbdc513e3bce47d63827f5521b0800df377eb756cdc6c525c26f57e9dbf1ade

Observation 0c7e1cd2-fd0b-474e-ab5d-d2e3691df33d · outbound

This paper cites The homogenous tree as an electric network.

$p$-Modulus on radially symmetric trees The homogenous tree as an electric network

Reference 16

Resolution
verified exact
local_arxiv, observed 2026-08-07T06:01:40.672748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T06:01:40.604929Z digest=sha256:a57ddddc1825ed277021f8419cf78958e421711d01f75d12a9f5a93c52273b08

Pith citing papers

No inbound Pith citation observations are available.