Pith. sign in

Paper Citation Record · LEDGER

The maximum length of $K_r$-Bootstrap Percolation

As of 4 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 2 inbound Pith citation observations for arXiv:1907.04559.

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

pith.paper-citation-record.v1
1907.04559 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-24T23:58:54.340345Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T19:33:37.147779Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T19:41:10.704951Z

Reference resolution

22 of 22 outbound references displayed

  • verified exact3
  • verified fuzzy19
  • unresolved0
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 63e448e2-c62d-4f35-9b4c-1192bef1d093 · outbound

This paper cites Metastability effects in bootstrap percolation.

The maximum length of $K_r$-Bootstrap Percolation Metastability effects in bootstrap percolation

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.573257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:a218e86f7a105f254851bff296df8f17c05ed47cc02f6562f9ec66d576f8d953

Observation f995396a-e12c-4f08-bcb9-481187d94249 · outbound

This paper cites An extremal problem for sets with applications to graph theory.

The maximum length of $K_r$-Bootstrap Percolation An extremal problem for sets with applications to graph theory

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.581694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:a9994adeae06607f7daa2b57162047bb7927672a068d9b4d4ed7aaf48c28f009

Observation 40c2bde7-6598-4579-8c8c-438f947cb940 · outbound

This paper cites Sharp thresholds for contagi ous sets in random graphs.

The maximum length of $K_r$-Bootstrap Percolation Sharp thresholds for contagi ous sets in random graphs

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.577550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:e464f27be0f5930099540b3267982bb0edd7305c6fc335b4cc01300f7be2c138

Observation bcccc14a-c5f1-4009-b665-b49e5014d69a · outbound

This paper cites The sharp threshold for bootstrap percolation in all dimensions.

The maximum length of $K_r$-Bootstrap Percolation The sharp threshold for bootstrap percolation in all dimensions

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.608570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:39ad28933dfb66f37f21f13aa4de3cb5a47d59a973273cad2c644c6af6333b33

Observation b7f58f59-a91a-47af-a6af-9680ff2035a2 · outbound

This paper cites Graph bootstrap percolation.

The maximum length of $K_r$-Bootstrap Percolation Graph bootstrap percolation

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.612670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:42066b7a6d998bf306b2edde3ebbfa34b722ecb3ea4bcfde380d1c01b0905345

Observation 76afb575-51e5-47e8-88e7-e6375e49dc92 · outbound

This paper cites Line ar algebra and bootstrap percolation.

The maximum length of $K_r$-Bootstrap Percolation Line ar algebra and bootstrap percolation

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.651933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:83159a2f7b13278bc56e1bfb1315f275ceb78e10090b4190fc672b0adcc197b1

Observation 8991a187-1c14-4264-b2d3-06340371da5f · outbound

This paper cites Random disease on the square grid.

The maximum length of $K_r$-Bootstrap Percolation Random disease on the square grid

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.616731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:b0756e74c4cd57c513c880ecc51878541fd93e5717a652b14406f53a0813f702

Observation bea7db4b-bacf-4110-88d4-f52fedc2c6f5 · outbound

This paper cites On sets of integers which contain no three terms in arithmetical progression.

The maximum length of $K_r$-Bootstrap Percolation On sets of integers which contain no three terms in arithmetical progression

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.603909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:d2ef86d5e579ba577546a503e832ae12cd6acccecf7c551a61e4074b7e0b1070

Observation 2eac8988-0f95-40ac-a491-ddcb7a308a5c · outbound

This paper cites On slowly percolating s ets of minimal size in bootstrap percolation.

The maximum length of $K_r$-Bootstrap Percolation On slowly percolating s ets of minimal size in bootstrap percolation

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.620976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:6a6b5726865e97508c853cb7057f71c7d05294e1251f9b8f9a75a845db996757

Observation cb56eaf6-5f8c-4f24-a59d-6119bacc9956 · outbound

This paper cites Maximum percolation t ime in two-dimensional bootstrap percolation.

The maximum length of $K_r$-Bootstrap Percolation Maximum percolation t ime in two-dimensional bootstrap percolation

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.625161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:159edf151b00fcee15e89291f272c766b592ee1f2bf1330c36b23b6fdad9a2cc

Observation 76369529-5c90-4153-953e-085922325c89 · outbound

This paper cites Weakly k-saturated graphs.

The maximum length of $K_r$-Bootstrap Percolation Weakly k-saturated graphs

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.647374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:cc0121d82e6fa40c32fa30b50556da5d4f120362c5efe90a0ffe6a8457d481a0

Observation 318c9c28-fd82-4739-962c-33f78b9be52e · outbound

This paper cites On the maximum running time in graph bootstrap percolation.

The maximum length of $K_r$-Bootstrap Percolation On the maximum running time in graph bootstrap percolation

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.599779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:7acc993abd415466ea04f5897cf6afac4b97f3891b2a6340c230e4b0161db8b6

Observation 6e0093a6-d5b7-41bd-bd20-bb054d750afe · outbound

This paper cites Bootstrap perc olation on a Bethe lattice.

The maximum length of $K_r$-Bootstrap Percolation Bootstrap perc olation on a Bethe lattice

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.634109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:f487b2fffb9cb3d5227d96406609d09590b944cb6fd72727d5fd44b1960d8893

Observation 2a22325f-5c33-40de-bb99-088a4a8fe775 · outbound

This paper cites On random graphs I.

The maximum length of $K_r$-Bootstrap Percolation On random graphs I

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.638999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:e6c3f08ed182dbd0d3ed2527ae20c0aa256393e7795f9b181d51180fec1d03c6

Observation 335b0622-7903-41d7-a819-43673c1f4c38 · outbound

This paper cites An extremal problem for two families of sets.

The maximum length of $K_r$-Bootstrap Percolation An extremal problem for two families of sets

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.643116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:15e224cde359357bf9a83d39af688090577635fcf74554f6ce3e9db6bf30514c

Observation 3bbd7e82-02e0-45b9-b4c1-2519dacf64c1 · outbound

This paper cites The time of gra ph bootstrap percolation.

The maximum length of $K_r$-Bootstrap Percolation The time of gra ph bootstrap percolation

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.595352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:11540be1da3608f4550fee0df1062782e94b6ad97a0f8f8f8304aeaacaf4d518

Observation e3357ae7-f558-4f4d-93f4-a002f544bee2 · outbound

This paper cites Weakly saturated graphs are rigid.

The maximum length of $K_r$-Bootstrap Percolation Weakly saturated graphs are rigid

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.629749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:731d0d2b71188704f99ca602d9d26b765b7f18fac056865d9c7d8463ac28b378

Observation be575831-a6ff-41cf-8d22-81db70843c61 · outbound

This paper cites Sharp threshold for K4-percolation.

The maximum length of $K_r$-Bootstrap Percolation Sharp threshold for K4-percolation

Reference 18

Resolution
verified exact
arxiv_id, observed 2026-05-25T00:00:08.132592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:d2d3b9d6a4e723be0097ab65afb38d51413518a0f1d2745be1efe65271c977e1

Observation 1edf27ea-13f0-4e61-9707-b4058e760d32 · outbound

This paper cites The Saturation Time of Graph Bootstrap Percolation.

The maximum length of $K_r$-Bootstrap Percolation The Saturation Time of Graph Bootstrap Percolation

Reference 19

Resolution
verified exact
local_arxiv, observed 2026-05-25T00:00:08.119376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:a8e3818bc1f7de7a39edb8a05bd5621117163c56dc0aa9252298e133ad89ea81

Observation 1ada0af3-8a03-434c-adc9-9652cd3aaa5c · outbound

This paper cites Extremal bounds for bootst rap percolation in the hypercube.

The maximum length of $K_r$-Bootstrap Percolation Extremal bounds for bootst rap percolation in the hypercube

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.591007Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:5c75dcabd12ba97afb7abe7c16022690186b63ee6871c92a06f79bd10f89d3f4

Observation 3b1dd2b9-3c17-4b78-92d4-1e21b780f939 · outbound

This paper cites A Sharp Threshold for Bootstrap Percolation in a Random Hypergraph.

The maximum length of $K_r$-Bootstrap Percolation A Sharp Threshold for Bootstrap Percolation in a Random Hypergraph

Reference 21

Resolution
verified exact
arxiv_id, observed 2026-05-25T00:00:08.126194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:f7da5dcb53196768f0a0f7d21d62f12b53b55d371bc07647f67e7e0f68fb4af1

Observation 5e053555-c380-429a-a6c1-64061e8bc6a8 · outbound

This paper cites Maximal Percolation Time in Hypercubes Under 2-Bootstrap Percolation.

The maximum length of $K_r$-Bootstrap Percolation Maximal Percolation Time in Hypercubes Under 2-Bootstrap Percolation

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T00:00:08.586461Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T23:58:54.340345Z digest=sha256:96f913001a1b55fa6070ebb5a4338f2b355815c37a4384161b01f9f98a056afc

Pith citing papers

Observation 9a0f615c-055f-4725-8734-6f1917133a07 · inbound

Bootstrap percolation of extension hypergraphs cites this paper.

Bootstrap percolation of extension hypergraphs The maximum length of $K_r$-Bootstrap Percolation

Reference 2

Resolution
verified exact
arxiv_id, observed 2026-07-04T23:46:53.602680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-10T19:33:37.147779Z digest=sha256:1a358ccfcc68b13d15982289e9e9949dea6cd42c8bffbc2bfbecf10bf759574a

Observation 7c2af944-8e65-4298-b532-97bbda0523ef · inbound

Upper bounds on the running time of bootstrap percolation cites this paper.

Upper bounds on the running time of bootstrap percolation The maximum length of $K_r$-Bootstrap Percolation

Reference 2

Resolution
verified exact
arxiv_id, observed 2026-07-04T23:46:53.602680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-08T11:09:40.735819Z digest=sha256:f6a5ef9077c916a08f3d1c919aa457de4d91cb3f29c021a48a1773b1271edd98