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Paper Citation Record · LEDGER

The Planar Lattice Two-Neighbor Graph Percolates

As of 12 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 1 inbound Pith citation observation for arXiv:2412.20781.

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

pith.paper-citation-record.v1
2412.20781 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:21:24.410031Z

measured 36 of 36 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-31T04:33:20.248950Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

35 of 35 outbound references displayed

  • verified exact3
  • verified fuzzy29
  • unresolved3
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 91818181-74e0-4835-86c6-d3b2f92ac0db · outbound

This paper cites Aizenman and G.

The Planar Lattice Two-Neighbor Graph Percolates Aizenman and G

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.963268Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.233577Z digest=sha256:eeffe678bea1dff705a21e5dfa97dba3b7424b56f3b3ef34c462a6fed5ef8fbe

Observation 6b5ad699-14ab-4854-b96b-5e77cd7104d5 · outbound

This paper cites Balister and B.

The Planar Lattice Two-Neighbor Graph Percolates Balister and B

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.949456Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.239672Z digest=sha256:cd9ba8026c8f0d4c93f1081b40ac1b38f8a7adddcc9c19ddb1f184ec117bba28

Observation 6ba70dd5-1ede-4ffa-be12-8c90d6feeaec · outbound

This paper cites Essential enhancements revisited.

The Planar Lattice Two-Neighbor Graph Percolates Essential enhancements revisited

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-10T23:21:24.244829Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-10T23:21:24.244829Z digest=sha256:396c4c66f40b21a8ac794aead31e393da0b38f2c6ef0557bfd9ef0b622fc8f68

Observation fc0e434b-9488-418e-9d3e-e804f6dfbc6f · outbound

This paper cites Beekenkamp, Sharpness of the phase transition for the orthant model, Math.

The Planar Lattice Two-Neighbor Graph Percolates Beekenkamp, Sharpness of the phase transition for the orthant model, Math

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.935663Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.250800Z digest=sha256:db728f845a8c737123e38a4f7d06445ce51e96bde5ccb4fc9abfac201e9e6fe3

Observation 091b9265-c0da-48b4-80a4-569b839e939c · outbound

This paper cites Chemical distance for the half-orthant model.

The Planar Lattice Two-Neighbor Graph Percolates Chemical distance for the half-orthant model

Reference 5

Resolution
verified exact
local_arxiv, observed 2026-08-10T23:21:24.497019Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.256174Z digest=sha256:66c6c165d26192d82f19ba2c6fba7223b00ec9e2677975a8f29a9466b52a90f4

Observation b63104c3-c541-4711-b833-2c97588cea99 · outbound

This paper cites Bollob \'a s and O.

The Planar Lattice Two-Neighbor Graph Percolates Bollob \'a s and O

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.920420Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.262441Z digest=sha256:a8484f567b9d703c187a72034ed2cff4b0f32413632b1154252b33d24947047d

Observation 7e6e7d4f-ac7c-4d95-9e45-1193cd6688a2 · outbound

This paper cites de Lima, S.

The Planar Lattice Two-Neighbor Graph Percolates de Lima, S

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.906382Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.267928Z digest=sha256:f42b63b84c6dc2d577ded5e337f612511eb91001427bc824f219fe56bd8a4086

Observation 79821088-308d-4582-b72d-8560849bec56 · outbound

This paper cites de Lima, R.

The Planar Lattice Two-Neighbor Graph Percolates de Lima, R

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.891916Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.272908Z digest=sha256:57710f554d4fc357f48b7e8b280da4a57d6573d4f28eeda823ceaee32e93f38a

Observation d6aafc7a-7b48-4296-93b7-8af747a2c694 · outbound

This paper cites Friedli, D.

The Planar Lattice Two-Neighbor Graph Percolates Friedli, D

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.878018Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.278844Z digest=sha256:6aa333dc7fdeb8854991df1c99650090f6170bc1cf347532305c5f118628093e

Observation 50a97da3-9fd4-4170-b967-84b425aecfff · outbound

This paper cites Grimmett and S.

The Planar Lattice Two-Neighbor Graph Percolates Grimmett and S

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.864414Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.283643Z digest=sha256:ce464b473c8ff927cc2f1fbc0aee48faf68341d0649706e13890291532d1496c

Observation 7999546c-1b05-4bd4-8372-71851274eeba · outbound

This paper cites Grimmett and Z.

The Planar Lattice Two-Neighbor Graph Percolates Grimmett and Z

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.850803Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.289724Z digest=sha256:de901fa9d6b5cc5ad04a4bb21b50c7d5915f0e55d5a9a4e336498d188a775fb1

Observation 91d261d2-536c-4b52-95f0-cfb5109baffe · outbound

This paper cites Gou \'e r \'e and R.

The Planar Lattice Two-Neighbor Graph Percolates Gou \'e r \'e and R

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.836258Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.295148Z digest=sha256:94da552241e2066392544d860180f2e393a202a4fc6d02decdc3b5b0258eaa65

Observation 5c677f38-42ee-46f2-ab8a-3dcc23d70d78 · outbound

This paper cites Gou \'e r \'e , Percolation in a multiscale B oolean model , ALEA Lat.

The Planar Lattice Two-Neighbor Graph Percolates Gou \'e r \'e , Percolation in a multiscale B oolean model , ALEA Lat

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.822042Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.300433Z digest=sha256:6d67c7322fcd30f8024bdab5f716f641a96f17784a283baf330b6127b4fa8155

Observation 47109d11-8ef2-4678-a562-e25c051eb5b3 · outbound

This paper cites Ghosh and Y.

The Planar Lattice Two-Neighbor Graph Percolates Ghosh and Y

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.807467Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.305830Z digest=sha256:89dd2ce7ca01e99ab2ae8d50431a2127abb721a7a5853bcbf94f9d0aebcf12a1

Observation bf9d6608-28e3-4c9f-9f45-1263d2d7af67 · outbound

This paper cites Grimmett, Percolation, Springer, 1999.

The Planar Lattice Two-Neighbor Graph Percolates Grimmett, Percolation, Springer, 1999

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.793266Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.310627Z digest=sha256:42e9db19f1265db7a994d32a00d370ba6ae8341da9c8c306c52228a3c9c7e527

Observation 63f5ca9b-cc38-48ea-87ba-82239d3ece8c · outbound

This paper cites Algorithms.

The Planar Lattice Two-Neighbor Graph Percolates Algorithms

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.778758Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.315606Z digest=sha256:9854288924e90cb42447da7cf588d440ada1495905bee673267702d64b36b0d4

Observation cd6f6ae5-f000-4ce5-95f4-9fdcff242477 · outbound

This paper cites 333, Springer, 2006.

The Planar Lattice Two-Neighbor Graph Percolates 333, Springer, 2006

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.764189Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.320319Z digest=sha256:83264c5264dcfd3b2213ba05c027a57de036966fdfa3edc070a2d478d01c8c47

Observation d07c8a50-025e-4ef8-8198-0e5dda775d6b · outbound

This paper cites Holroyd and Z.

The Planar Lattice Two-Neighbor Graph Percolates Holroyd and Z

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.750791Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.324871Z digest=sha256:b1818a92adabf799bb494e22b394ad11c5f6a6feb7ed5b51c3710184bebab251

Observation d31808f1-feac-404c-8e29-bbc00bed2d1c · outbound

This paper cites a ggstr \.

The Planar Lattice Two-Neighbor Graph Percolates a ggstr \

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.737064Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.330077Z digest=sha256:92ac52e7d3e6e36bae185f2b3c0f619087272f144742651f2d554db44993d539

Observation 5e1b40ad-e8b2-40b5-8014-bc7ab3b1517c · outbound

This paper cites Holroyd and T.

The Planar Lattice Two-Neighbor Graph Percolates Holroyd and T

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.722715Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.335291Z digest=sha256:a3c062fd42cbb1502d480f6f933f8352a31f98b57d96aff96337c2daec296ed0

Observation b69de13c-c5d7-4e68-8d92-07aa02fe8581 · outbound

This paper cites Holmes and Th.

The Planar Lattice Two-Neighbor Graph Percolates Holmes and Th

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.709207Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.340279Z digest=sha256:74f00642057a8e9951b65f03e61e65ecb30cd79f4502a03c14677ce9bc8658cf

Observation e130d92b-3820-463a-b757-a52333e4bc76 · outbound

This paper cites an unresolved cited work.

The Planar Lattice Two-Neighbor Graph Percolates Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:21:24.695368Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.345554Z digest=sha256:41f173ae80a9755d48859c95b59fcdcde9a35e6884d3e6239aacf0d447f6db1e

Observation 45cf08a8-a545-49ff-a6b7-f58230edea67 · outbound

This paper cites an unresolved cited work.

The Planar Lattice Two-Neighbor Graph Percolates Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:21:24.681281Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.350341Z digest=sha256:05cf9c1f10913b768fb88ae32f7600b0a920b6acf87e96a9efa2cf7d8d403bb2

Observation 338b589e-54e5-4ba0-b2f4-25e07ff01b79 · outbound

This paper cites Iliev, E.

The Planar Lattice Two-Neighbor Graph Percolates Iliev, E

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.667176Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.355687Z digest=sha256:82cd63ebfec5796ecddd0e7a33c37965bdc5885886dabcef141b5c884293256e

Observation 0c04987f-07dc-4004-833b-5c7513e0e147 · outbound

This paper cites Jacobsen, Critical points of P otts and O(N) models from eigenvalue identities in periodic temperley--lieb algebras , J.

The Planar Lattice Two-Neighbor Graph Percolates Jacobsen, Critical points of P otts and O(N) models from eigenvalue identities in periodic temperley--lieb algebras , J

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.652755Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.360577Z digest=sha256:591559955908301f35a4044389650fe990866c615f87a62fc8adb56310be171d

Observation 31aed12c-7a85-4b06-bee8-29a7a2747313 · outbound

This paper cites Percolation in lattice $k$-neighbor graphs.

The Planar Lattice Two-Neighbor Graph Percolates Percolation in lattice $k$-neighbor graphs

Reference 26

Resolution
verified exact
local_arxiv, observed 2026-08-10T23:21:24.474945Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.365383Z digest=sha256:994cc53f2e051f45abd0f75839f2c0ebe0056b2b37e5f17d3b5744299431101f

Observation f6db3711-4fe0-48a6-ab82-144a4e999db8 · outbound

This paper cites Kenyon, A.

The Planar Lattice Two-Neighbor Graph Percolates Kenyon, A

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.638084Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.370195Z digest=sha256:c4cb5e3c50c1b5a1b04792c7900f8d3e7879e7eb77ba6485dc19bcb9e620c13c

Observation 5d134cf5-ba30-45ac-920b-b0c7ffbd0673 · outbound

This paper cites 1, 71--95.

The Planar Lattice Two-Neighbor Graph Percolates 1, 71--95

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.623065Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.374803Z digest=sha256:331f148ec63c0a8db01f4be2e97273a89d20913fb3515113927a593551d66015

Observation 2dd80885-3f5b-4c00-a741-08cf2045ce62 · outbound

This paper cites Newman and C.

The Planar Lattice Two-Neighbor Graph Percolates Newman and C

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.607286Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.381911Z digest=sha256:dda42487817b41276c7a752a22a212637a9759e8156e9649d105444d4663c6c2

Observation c8a7e202-6980-4e44-9c82-5a89e8a61fee · outbound

This paper cites Rigidity and tolerance for perturbed lattices.

The Planar Lattice Two-Neighbor Graph Percolates Rigidity and tolerance for perturbed lattices

Reference 30

Resolution
verified exact
local_arxiv, observed 2026-08-10T23:21:24.453162Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.387026Z digest=sha256:61dc5c504e3fbc05cf0ddf81fa851a8e7cea1e327848a569b26aeacc546975e6

Observation 16429b1e-21bb-4131-b8df-0169bc77d9d4 · outbound

This paper cites P \"o nitz and P.

The Planar Lattice Two-Neighbor Graph Percolates P \"o nitz and P

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.591185Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.392018Z digest=sha256:a95b8ff027042ef668a43346ea5d005eb284eb29d30e708140e0488f18af709a

Observation 618b4cbc-59ca-4e41-b0c1-1ea1ae8ebdcf · outbound

This paper cites Quintanilla and R.

The Planar Lattice Two-Neighbor Graph Percolates Quintanilla and R

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.576555Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.396564Z digest=sha256:a2853e504df05a4343be88fb5a78f700e846f9631313417c3619d735e2bab03c

Observation 5f7bd02b-a96c-48aa-ada9-424e6d6ce418 · outbound

This paper cites van den Berg and A.

The Planar Lattice Two-Neighbor Graph Percolates van den Berg and A

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.561289Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.401272Z digest=sha256:7bddb808245db0f2557fd4c9350ad07dc329128b520e36a0854fb6b91cfd4496

Observation 3577f91d-1515-4b5b-a015-a5ea8bb6fa81 · outbound

This paper cites Wierman, AB percolation: a brief survey , Banach Cent.

The Planar Lattice Two-Neighbor Graph Percolates Wierman, AB percolation: a brief survey , Banach Cent

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.544958Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.405463Z digest=sha256:d1e1b496f203e19c520dac96bfc251c13bde0b69e8c880f426d28f02fea13917

Observation ffa9a270-96f0-4caf-9b50-8afe6046ba3c · outbound

This paper cites Zhang, A note on inhomogeneous percolation, Ann.

The Planar Lattice Two-Neighbor Graph Percolates Zhang, A note on inhomogeneous percolation, Ann

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:21:24.529518Z

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.

source=arxiv_source observed=2026-08-10T23:21:24.410031Z digest=sha256:8c90f3b7a89a500db77ac6c8b3f0fea9c1125bc367c5e5be833f79a0b5601c36

Pith citing papers

Observation 428cdba4-7476-4e49-b5d8-8da7b149c2e0 · inbound

Strongly-connected percolation on directed lattices cites this paper.

Strongly-connected percolation on directed lattices The Planar Lattice Two-Neighbor Graph Percolates

Reference 38

Resolution
unresolved
no resolver link, observed 2026-07-31T04:33:20.248950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-31T04:33:20.248950Z digest=sha256:ab94f07577d9b07897c8d2128e5223ceaa8e844ac0326b366f96f462f1cd827d