Paper Citation Record · LEDGER

Critical threshold for regular graphs

As of 12 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2412.00635.

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

pith.paper-citation-record.v1
2412.00635 v2

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T05:20:59.002495Z

measured 10 of 10 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

10 of 10 outbound references displayed

verified exact0
verified fuzzy8
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b99bb8ea-1b96-44d2-ab41-b58aba997f1d · outbound

This paper cites Strict monotonicity for critical points in percolation and ferromagnetic models.

Critical threshold for regular graphs Strict monotonicity for critical points in percolation and ferromagnetic models

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:20:59.175338Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ec1f45b6-4d49-48b1-a4b1-3357bbe6db08 · outbound

This paper cites Essential enhancements revisited.

Critical threshold for regular graphs Essential enhancements revisited

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-12T05:20:58.962708Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c3dbfa6-694c-44d5-8e54-78b2784f71d5 · outbound

This paper cites Percolation beyond Z ^d , many questions and a few answers.

Critical threshold for regular graphs Percolation beyond Z ^d , many questions and a few answers

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:20:59.159879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a902479c-6d61-45c6-9cd4-b5a5bc2bb385 · outbound

This paper cites Bounds on connective constants of regular graphs.

Critical threshold for regular graphs Bounds on connective constants of regular graphs

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:20:59.143928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation eccc7e21-68df-4a20-a753-e5e3043f5928 · outbound

This paper cites Probability on trees and networks , volume 42.

Critical threshold for regular graphs Probability on trees and networks , volume 42

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-12T05:20:58.978420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e7f31251-de93-4e5e-b74b-d253066941ff · outbound

This paper cites Random walks and percolation on trees.

Critical threshold for regular graphs Random walks and percolation on trees

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:20:59.117303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f41b9a9a-4954-4db7-ad96-f34c4757ee99 · outbound

This paper cites Random walks, capacity and percolation on trees.

Critical threshold for regular graphs Random walks, capacity and percolation on trees

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:20:59.102467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d134e095-6c03-4295-b409-6356d3c9b7c9 · outbound

This paper cites Strict monotonicity of percolation thresholds under covering maps.

Critical threshold for regular graphs Strict monotonicity of percolation thresholds under covering maps

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:20:59.087412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation dddfec2e-c5f9-4f3e-ae4e-b5477aa6e207 · outbound

This paper cites Modern discrete probability: An essential toolkit.

Critical threshold for regular graphs Modern discrete probability: An essential toolkit

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:20:59.071797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8581d0e3-1626-4a5f-b233-0eeb9d5ca560 · outbound

This paper cites Interpolation schemes in percolation theory.

Critical threshold for regular graphs Interpolation schemes in percolation theory

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:20:59.056013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

No inbound Pith citation observations are available.