Paper Citation Record · LEDGER

Rainbow percolation

As of 18 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2608.12954.

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

pith.paper-citation-record.v1
2608.12954 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:03:38.867497Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

27 of 27 outbound references displayed

verified exact8
verified fuzzy0
unresolved13
parse uncertain0
malformed identifier6
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e1644197-0ff3-4155-bb97-95b8b8cd79b1 · outbound

This paper cites Disconti- nuity of the magnetization in one-dimensional 1/|x−y| 2 Ising and Potts models.

Rainbow percolation Disconti- nuity of the magnetization in one-dimensional 1/|x−y| 2 Ising and Potts models

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.351405Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1984aad-6733-485f-8cb9-9ee792bdd281 · outbound

This paper cites Discontinuity of the percolation density in one dimensional 1/|x−y| 2 percolation models.

Rainbow percolation Discontinuity of the percolation density in one dimensional 1/|x−y| 2 percolation models

Reference 2

Resolution: verified exact; doi, observed 2026-08-15T20:03:39.419127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b30c5b4b-8fec-4519-a567-9c4733932af2 · outbound

This paper cites Distances in 1/|x−y| 2d percolation models for all dimensions.

Rainbow percolation Distances in 1/|x−y| 2d percolation models for all dimensions

Reference 3

Resolution: malformed identifier; no resolver link, observed 2026-08-15T20:03:38.463605Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 366129ca-9066-4f57-aa9e-56c93d5c947b · outbound

This paper cites Isoperimetric lower bounds for critical exponents for long-range percolation.

Rainbow percolation Isoperimetric lower bounds for critical exponents for long-range percolation

Reference 4

Resolution: verified exact; doi, observed 2026-08-15T20:03:39.406116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0bf616bb-5701-4498-b856-6af93583db56 · outbound

This paper cites Percolation in the hyperbolic plane.

Rainbow percolation Percolation in the hyperbolic plane

Reference 5

Resolution: malformed identifier; no resolver link, observed 2026-08-15T20:03:38.470199Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8622632-81dc-4210-b78f-c2b55f63d252 · outbound

This paper cites Transience, recurrence and critical behavior for long-range percolation.

Rainbow percolation Transience, recurrence and critical behavior for long-range percolation

Reference 6

Resolution: verified exact; doi, observed 2026-08-15T20:03:39.390458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4bd22f2e-8508-4cd5-9bde-f61dbeebe4d7 · outbound

This paper cites Graph diameter in long-range percolation.

Rainbow percolation Graph diameter in long-range percolation

Reference 7

Resolution: verified exact; doi, observed 2026-08-15T20:03:39.220543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation df4b2230-89f8-488c-bb61-1202ef31f549 · outbound

This paper cites On the scaling of the chemical distance in long-range percolation models.

Rainbow percolation On the scaling of the chemical distance in long-range percolation models

Reference 8

Resolution: verified exact; doi, observed 2026-08-15T20:03:39.211456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 86ab1712-7ca0-4e90-bdad-e1d7d8ea08b4 · outbound

This paper cites Sharp asymptotic for the chemical distance in long-range percolation.

Rainbow percolation Sharp asymptotic for the chemical distance in long-range percolation

Reference 9

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T20:03:39.788199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 64b4a807-e720-4e7d-9bb7-222c3b4467ad · outbound

This paper cites Geometric inhomogeneous random graphs.

Rainbow percolation Geometric inhomogeneous random graphs

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.508453Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eba48a51-715f-4804-9047-b0b7bce7a87e · outbound

This paper cites Scale-free percolation.

Rainbow percolation Scale-free percolation

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.581948Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4db21deb-0ce6-4836-a074-6f0196d86bd1 · outbound

This paper cites Distances in critical long range percolation.

Rainbow percolation Distances in critical long range percolation

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.634941Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7e9ac00-0816-4172-8a80-53e7de2e672e · outbound

This paper cites Long-range models in 1D revisited.

Rainbow percolation Long-range models in 1D revisited

Reference 13

Resolution: verified exact; doi, observed 2026-08-15T20:03:39.140041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0c6cbb7b-4f16-4119-8e84-a73d25735df6 · outbound

This paper cites The age-dependent random connection model.

Rainbow percolation The age-dependent random connection model

Reference 14

Resolution: malformed identifier; doi_truncated, observed 2026-08-15T20:03:38.986670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 83c6e175-ed10-437b-9411-bf4ba5cf5016 · outbound

This paper cites Recurrence ver- sus transience for weight-dependent random connection models.

Rainbow percolation Recurrence ver- sus transience for weight-dependent random connection models

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.646066Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b49617d4-6499-40c3-ba7a-c76e32f2c322 · outbound

This paper cites Finiteness of the percolation threshold for inhomogeneous long-range models in one dimension.

Rainbow percolation Finiteness of the percolation threshold for inhomogeneous long-range models in one dimension

Reference 16

Resolution: verified exact; doi, observed 2026-08-15T20:03:38.967371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 062f4c20-b1f7-4bd1-a7c8-8d9fb7926033 · outbound

This paper cites Percolation phase transition in weight- dependent random connection models.

Rainbow percolation Percolation phase transition in weight- dependent random connection models

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.652743Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0e8d089-abbf-486e-b24d-68bdfa23de40 · outbound

This paper cites A lower bound for the critical probability in a certain percolation pro- cess.

Rainbow percolation A lower bound for the critical probability in a certain percolation pro- cess

Reference 18

Resolution: verified exact; doi, observed 2026-08-15T20:03:38.952299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 92ffa2b0-c3ac-4963-a4f1-6a32e3ebfdfe · outbound

This paper cites An intermediate phase with slow decay of correla- tions in one dimensional 1/|x−y| 2 percolation, Ising and Potts models.

Rainbow percolation An intermediate phase with slow decay of correla- tions in one dimensional 1/|x−y| 2 percolation, Ising and Potts models

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.731132Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 81914b1e-244c-4dff-a59e-bd8a5fbf89a0 · outbound

This paper cites Cluster-size decay in supercritical kernel-based spatial random graphs.

Rainbow percolation Cluster-size decay in supercritical kernel-based spatial random graphs

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.803593Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cba3169c-cd0e-43b3-a3ca-81d9a4f8f020 · outbound

This paper cites A note on the Borel–Cantelli lemma.

Rainbow percolation A note on the Borel–Cantelli lemma

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.850053Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce009fc5-48f2-4e40-ac8c-0b4156aa163e · outbound

This paper cites an unresolved cited work.

Rainbow percolation Unresolved cited work

Reference 22

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T20:03:39.677521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2063e891-4a65-479c-9205-94e8c181fc5e · outbound

This paper cites One dimensional 1/|j−i| s percolation models: The existence of a transition fors≤2.

Rainbow percolation One dimensional 1/|j−i| s percolation models: The existence of a transition fors≤2

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.856766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1721cd75-0d53-4002-8114-2cbc4bd408ca · outbound

This paper cites Fast Monte Carlo algorithm for site or bond perco- lation.

Rainbow percolation Fast Monte Carlo algorithm for site or bond perco- lation

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.859483Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f4aefe0a-b60c-43ff-8c32-2fd2e6205766 · outbound

This paper cites Long range percolation in one dimension.

Rainbow percolation Long range percolation in one dimension

Reference 25

Resolution: malformed identifier; no resolver link, observed 2026-08-15T20:03:38.862434Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6477cdef-f0be-4a13-8608-191e9b216bce · outbound

This paper cites Boundary-connectivity via graph theory.

Rainbow percolation Boundary-connectivity via graph theory

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.865029Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8341bca6-bfcd-4e91-8ccc-f582fbaaa215 · outbound

This paper cites Ultra-small scale-free geometric networks.

Rainbow percolation Ultra-small scale-free geometric networks

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T20:03:38.867497Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.