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Paper Citation Record · LEDGER

Lower tails for triangles inside the critical window

As of 23 August 2026, this Paper Citation Record lists 69 of 69 outbound references and 1 inbound Pith citation observation for arXiv:2411.18563.

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

pith.paper-citation-record.v1
2411.18563 v1

Coverage vector

measured 69 of 69 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T11:24:50.546949Z

measured 70 of 70 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T19:47:31.283256Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-10T22:30:51.865922Z

Reference resolution

69 of 69 outbound references displayed

  • verified exact2
  • verified fuzzy43
  • unresolved24
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ad53a046-4541-4688-9827-c59a247bac68 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.928240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.196118Z digest=sha256:1556b5c91d073a7e688116714447dcf96a45702d16b206dfe47919531929f34c

Observation 393f5f54-8b8f-459d-a845-7d73f81d216a · outbound

This paper cites Balogh, R.

Lower tails for triangles inside the critical window Balogh, R

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.908251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.202299Z digest=sha256:22b409563e86511b2fd58b3d2de77dec174e4b3660ebfe459c9576a2998b547b

Observation 5cec8517-f50b-417a-b5f7-78d0cc9af738 · outbound

This paper cites Balogh, R.

Lower tails for triangles inside the critical window Balogh, R

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.888714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.207484Z digest=sha256:f50cac948bd695aa256aa9f98e0282ec3b148a17f5c726ba94de0b403dc8f74e

Observation 2e60524d-f71f-40ec-a160-22eca7e38b17 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.870845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.213317Z digest=sha256:9940bba9b70fd55be1c388d844bbbda5625bacbf10371e9d8071a05379327ef9

Observation 2782de1c-ff1c-40f7-a45e-690235fae596 · outbound

This paper cites Bayati, D.

Lower tails for triangles inside the critical window Bayati, D

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.849416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.218401Z digest=sha256:94fa15f4d7ba8ad88678b8bfc056bd1d70e9802ef894cfa2dd21ab59a0662f0c

Observation ac919e1f-6640-44e8-b1a8-c4e5270511de · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.830481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.223542Z digest=sha256:5fa7366a6ed76c7157195227e8dd1565774168ccf1cdfb568caee4c216d374f3

Observation 14eae68a-1147-4ee5-a178-c87905e454fb · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.807210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.229606Z digest=sha256:be6c9087268b4e56126d5a00bc0a3bdeb7c0478b3b0013fccaaaa9b4d5c83d95

Observation 5fe3de8f-b9db-4eab-84d6-fbb9a8a3be06 · outbound

This paper cites Biskup, L.

Lower tails for triangles inside the critical window Biskup, L

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.787207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.234306Z digest=sha256:fab5ea64168c2f4b87c65206f337766861e06e706f6fe7934ad6c6982382fbdd

Observation 857491b2-fa33-4aa5-ac1a-413f8d0603cf · outbound

This paper cites Bollob´ as.

Lower tails for triangles inside the critical window Bollob´ as

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.763312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.238911Z digest=sha256:32d630075aeb78795481789808c597e0327f25a54874e29d4d2edc9678758488

Observation b710bdd4-7822-400e-ae4e-1da1b2655c5a · outbound

This paper cites Bollob´ as, C.

Lower tails for triangles inside the critical window Bollob´ as, C

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.735107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.245000Z digest=sha256:1a1846111f5a7fbc2a6afdeacc2d2782b850b6d1b6f77bbf0dbd2cbe2cb364f6

Observation e3515934-fe72-40b6-9306-0ec65433d6b9 · outbound

This paper cites Borgs, J.

Lower tails for triangles inside the critical window Borgs, J

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.715332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.249883Z digest=sha256:aef56f787af05a1dd67a3fd9279f5f782d823d73041948b18cdfd62dc51d8322

Observation dde69bdb-1bc9-4665-bb27-2febf0b46edb · outbound

This paper cites Borgs and R.

Lower tails for triangles inside the critical window Borgs and R

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.692769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.254895Z digest=sha256:4a90d4f8b6658098372e628063571c3c6087cbd859a21b92d7c5ed17444f489f

Observation 57eefaec-03de-473f-a3d5-4d040750271b · outbound

This paper cites Bubley and M.

Lower tails for triangles inside the critical window Bubley and M

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.668756Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.260424Z digest=sha256:9945658a1a85a55f953261753cd5f2ffb40a3f537df50cdc4a5acab1d04f7ee4

Observation ef7e577f-bad1-4bca-8daa-a86710825282 · outbound

This paper cites Chatterjee.

Lower tails for triangles inside the critical window Chatterjee

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.646344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.265006Z digest=sha256:771fb5be055138a7bfc1892adf40a69facf3920f47c8e72d7466bd659b8017d7

Observation d8b5c223-4962-47f9-b24c-43794ce7823e · outbound

This paper cites Chatterjee.

Lower tails for triangles inside the critical window Chatterjee

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.626036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.269447Z digest=sha256:ab19656903d530ee5c7b338b9f955cabd52a178f218745234407ac1b2f775341

Observation 173dc5a2-5440-44c7-9ea1-6115dbe6be50 · outbound

This paper cites Chatterjee and A.

Lower tails for triangles inside the critical window Chatterjee and A

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.606585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.274146Z digest=sha256:4b308906eab6312b531e3d0b368e14e11ebaa4a3a3f3ee8ae6c0743e2e04ea54

Observation 5293fcb9-0c6f-4f0a-9a8d-feb1bc729f13 · outbound

This paper cites Chatterjee and S.

Lower tails for triangles inside the critical window Chatterjee and S

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.590204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.279493Z digest=sha256:c6c5d28f783c2e2d08252d69bc50d3fed9a608e31a907a04f577eb04e63df4a2

Observation a4bc880e-b319-44f9-8c89-355957b4d3e6 · outbound

This paper cites Structure of lower tails in sparse random graphs.

Lower tails for triangles inside the critical window Structure of lower tails in sparse random graphs

Reference 18

Resolution
verified exact
local_arxiv, observed 2026-08-12T11:24:50.646885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.285009Z digest=sha256:ec873ae59ff50944f507513f2dc5babe829c3173aa61bce3139c970e142d3751

Observation 4b772d91-33c2-49c2-b9b5-01da2333b956 · outbound

This paper cites Cook and A.

Lower tails for triangles inside the critical window Cook and A

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.570816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.290125Z digest=sha256:c850f1ed674f9512292daaa196a5bd4cc95cede21498011326d409587bba2713

Observation 9de064d5-592a-4e2d-b169-2e9b240cfa54 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.552976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.295539Z digest=sha256:d5d7db158d57275609ee35d1783f12ba4ad2eaec4d381cd2a53e608349c0e691

Observation 018a8c85-9ca6-4abe-9e74-b4584953a081 · outbound

This paper cites Davies, M.

Lower tails for triangles inside the critical window Davies, M

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.532336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.300303Z digest=sha256:c675f7bca0f23fe051320b6566d1bc227c3b98728ee6a062ce44ece40e681dbd

Observation 0c5eb5ad-b37c-411e-947e-ae43462c4656 · outbound

This paper cites Davies, M.

Lower tails for triangles inside the critical window Davies, M

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.511336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.305238Z digest=sha256:5c6ef8ee24fb90ef609850eb086fbfdfef803009131fb5d80978b2b82db7bca2

Observation 5e2626d7-8456-4f1c-8b7a-cbbf0c5dca96 · outbound

This paper cites DeMarco and J.

Lower tails for triangles inside the critical window DeMarco and J

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.492508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.310601Z digest=sha256:db59d23ffe0000725e67552f2e702372c0b478c8d49ca8f0596b24025591d61e

Observation 2241b520-9f69-4b7b-a6ec-dc29cbba1d16 · outbound

This paper cites Dembo, A.

Lower tails for triangles inside the critical window Dembo, A

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.472903Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.315462Z digest=sha256:32d5cd339ab6655606bd9e4897c5b94556e81e7f11153f26d83256b71645fa7b

Observation f13a32cc-e85b-4d92-ba04-7bc7f2137579 · outbound

This paper cites Duminil-Copin.

Lower tails for triangles inside the critical window Duminil-Copin

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.450413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.320085Z digest=sha256:5992d535610858ef89de129e66dfab20d3cb7fc897521fbfd01fb22566eb75be

Observation 714d1bbc-cb72-4394-bfed-18f8bdc09e55 · outbound

This paper cites Dyer and A.

Lower tails for triangles inside the critical window Dyer and A

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.426359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.324761Z digest=sha256:d4814af5a53c6e4a1fef95ce57c197da1e24c29df9f552243ff6baf2595f74cb

Observation 22154bc5-3842-4247-a7da-cd66a64ba4cc · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.406647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.329216Z digest=sha256:68237ff116eda65e2bc7bc6683a0431f9df3a3a082b3fbfa25af1ef1797ac186

Observation 1f706429-9419-4eb9-ab8d-e239e4fafb2e · outbound

This paper cites Erd˝ os, D.

Lower tails for triangles inside the critical window Erd˝ os, D

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.388690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.334187Z digest=sha256:e6505235823d274f3a69b65a25972a14caae29d1ae64db5833023b762680c1b1

Observation 478b6a62-d92f-4531-80c3-75b255cc6e42 · outbound

This paper cites Erd˝ os and A.

Lower tails for triangles inside the critical window Erd˝ os and A

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.369839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.338929Z digest=sha256:e3e677959535f3173c175c4bf39cc14c69088102f3870e05ab376e65bf7b06de

Observation f859c4ba-9594-41e3-9ae3-4740524a7cb6 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.351073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.343846Z digest=sha256:323be8e9a564b6e88fe4d76bee46711dffac43ab10c08bc16277bfcde99d2b2e

Observation 5f647d36-24c5-4be9-ba68-edbcffea8b8a · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.333760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.348612Z digest=sha256:6bbf6f1a28f6db5ff9ecd497838ebaea48c88cadd8e855b692b312d1dba27662

Observation e594bd33-7288-420c-9b20-a629a52f93db · outbound

This paper cites Friedli and Y.

Lower tails for triangles inside the critical window Friedli and Y

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.316141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.353735Z digest=sha256:954b5dcc75d4a1e10e3b422944f642be1feb69f805cd258f5ae47aebba36d17a

Observation 57cbe780-df73-4492-94ec-8099e4cb62c3 · outbound

This paper cites Galvin and J.

Lower tails for triangles inside the critical window Galvin and J

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.296605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.358662Z digest=sha256:9d58c50ff5464b366a7e99e644efd462758d986c7f6d6a931abba1edbf30d6d7

Observation 3000eaa1-ee99-4a60-b1ea-84bd58c54555 · outbound

This paper cites Galvin, G.

Lower tails for triangles inside the critical window Galvin, G

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.279918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.363693Z digest=sha256:bd9d4276052483409b6b0c270a21bc9ef9854e920a336b83e85651590aedbdfc

Observation 732570d6-05ed-4cf2-be06-8548dfaa1dab · outbound

This paper cites Guerra and F.

Lower tails for triangles inside the critical window Guerra and F

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.263970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.368975Z digest=sha256:e2db0f48c8a16de3c835ce16639729fee00f63687ef140e29211e1e325438f8a

Observation 61c2ec79-6c72-4063-845d-52bafb5a8477 · outbound

This paper cites Harel, F.

Lower tails for triangles inside the critical window Harel, F

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.245556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.374176Z digest=sha256:45c7f9113154ec5a41de63530be544abde6ffe401f209f968b3cfcab02cc9fce

Observation d4ffbd46-647d-4ddc-9395-594141cb3a8e · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 37

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.228502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.379335Z digest=sha256:00fa3b32b9250dc71601b1fbaaf16e6cb9afc2a63eeed2a57328fe860961dae9

Observation 2b92ffc1-2594-4d1f-9bfc-6762d22d80a0 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.211830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.384533Z digest=sha256:e1ee3064e5b34484a7ff23159c73ac88b7b1824952b9292bf4d52de7d24ee341

Observation b94d8822-6b42-40b4-b72b-f6e2d8045ad7 · outbound

This paper cites Janson, T.

Lower tails for triangles inside the critical window Janson, T

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.193872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.390084Z digest=sha256:7d5109ed657532d0219dae35683f4a8966a873f216de3998eeeb269dec27b8e4

Observation 7b7db2d0-1ceb-4271-8289-71cceadd10fc · outbound

This paper cites Janson, K.

Lower tails for triangles inside the critical window Janson, K

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.177296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.395287Z digest=sha256:647300a0a03a48421ee8761d1c09413965ca629e06256c68e824d322badb61c3

Observation 3b0343a7-6f0e-487e-ada6-aaa0c4ff31c0 · outbound

This paper cites Janson and A.

Lower tails for triangles inside the critical window Janson and A

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.160221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.400284Z digest=sha256:4edd449fe517a99b1e12866b75d00e47fa9c879a1c405db7eb56d1329dc89e7c

Observation 91d783c2-4915-4de3-976c-3e6dd169e9f8 · outbound

This paper cites Janson and L.

Lower tails for triangles inside the critical window Janson and L

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.142376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.405159Z digest=sha256:0289eca9e54105f01b3223dad0ebcceb1be577fad27ce22842a4b5f0b667d10c

Observation dcb008cc-4281-4f25-b1d3-d8e90f8aaa58 · outbound

This paper cites On the evolution of structure in triangle-free graphs.

Lower tails for triangles inside the critical window On the evolution of structure in triangle-free graphs

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-12T11:24:50.409996Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T11:24:50.409996Z digest=sha256:42f25d7ef9550d14005d833073e613b8c73aa44822e7ff60046b2edf7a1d9baf

Observation 2c3e4083-69a4-40b4-bd87-b528e3655ffc · outbound

This paper cites Jenssen, W.

Lower tails for triangles inside the critical window Jenssen, W

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.125098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.415324Z digest=sha256:8a364b50d50f278ae3987c665361d3c4ed796c088635c7e47671eb43c3379e9a

Observation 805fd801-8b7a-47b0-9385-3716ad621cfc · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.104350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.420192Z digest=sha256:b005fcde15dbc5d232baf5c7bf3036c84be9bbe8f5174caf34c9083d39a8ee2d

Observation 675eb094-16de-4088-82d8-e6a75e6cac4b · outbound

This paper cites Kozma and W.

Lower tails for triangles inside the critical window Kozma and W

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.084171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.424902Z digest=sha256:fc0cd3b12e554fa8612fd86c1a620f2e3f137cd47dac70ac5499cacfb541c5a3

Observation 37f416fc-be61-4d89-819b-34adb4a2c2c3 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 47

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:51.058072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.430180Z digest=sha256:746fd9ea7fd25e88e4d7db0c617e5af501ee7c43dfe2f1e5e2d55fe68484a1aa

Observation f48f692e-efa1-4f26-98f1-35008ecfbe59 · outbound

This paper cites Lov´ asz.Large Networks and Graph Limits , volume 60.

Lower tails for triangles inside the critical window Lov´ asz.Large Networks and Graph Limits , volume 60

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.036528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.435230Z digest=sha256:f6cda9c1711de09421852e8351409e3034273fa17efefe34ec7610aa4760ee20

Observation afa6cf1b-3d47-4818-932d-d7d0191cc817 · outbound

This paper cites Lubetzky and Y.

Lower tails for triangles inside the critical window Lubetzky and Y

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:51.014923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.439935Z digest=sha256:2bec36d04669548103cd96b2f6f49fc20edaf0555fee6ccbae40408457c2a4de

Observation 6217fce2-dca4-44cd-bb5d-b5d664d732e5 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:50.995701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.445022Z digest=sha256:57bab3b8d77179d67f9d56d16220d253b11e7c420115f4d594576d4ea6d03e2a

Observation 106dcbce-5123-4db5-9d0c-65ab72de4554 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:50.976745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.449816Z digest=sha256:d1cbd251c323469e30ec56251f1da0625f0336968d12dbfc414538bdeae02bc9

Observation 0f4dac09-11ec-4a94-b8bd-1480af6babf7 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:50.958675Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.455170Z digest=sha256:cba585a599aa53276252281c82c4f9f7dc1fb187007fa2aea0b9efbe4b3fc537

Observation 558035fd-034f-4d41-a516-4a1051edb92f · outbound

This paper cites Mousset, A.

Lower tails for triangles inside the critical window Mousset, A

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:50.942351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.460070Z digest=sha256:abfdb2c7e8de7f39342712802bfe1b9303b5f034185fed8306254019eb955b72

Observation e86c77a2-7da5-4dec-b7a1-95b7046ab5f2 · outbound

This paper cites Ollivier.

Lower tails for triangles inside the critical window Ollivier

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:50.924286Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.464769Z digest=sha256:46ae4c2ec121e0d38c1fbe515757a2a1e1b28e5dc7fb1e6ce28f0e2340bdf596

Observation d6db7145-fbae-4493-9486-998ea2dca736 · outbound

This paper cites Osthus, H.

Lower tails for triangles inside the critical window Osthus, H

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:50.900395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.469583Z digest=sha256:f89c6db98084a417687301fa94d073119c943acf6e73a82ea1e4f08c99114ba1

Observation e29083c2-49d3-4c4b-b0b4-53b89f560310 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 56

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:50.879371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.475417Z digest=sha256:5872e4579daf0de1341b15473047e8e7cec72525f2f9147a0fc38de94df095cc

Observation 9ee339d3-ed1c-4249-94b1-aa9f753bf03d · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 57

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:50.858809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.480705Z digest=sha256:928af864fd8b5be53241cd80577a1cbef65843f56d13d580f0ddc87c570a3c0f

Observation 6f8ab4dc-1877-4c29-a53b-fb65f9ed18cc · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:50.842355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.485792Z digest=sha256:de70df99324e5be4f25104c8774c225edad4c5ec9e57894d85bb4f56ed3c43c4

Observation 777c4855-17f7-4d53-a72a-ea820733acd2 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 59

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:50.825223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.492015Z digest=sha256:25472a7ffcafa511ea23cf3709e25200864cb0b29be10af43eedfa4e5c7ef499

Observation 61e1ff83-12b5-4d2d-b4ad-174e539a4ceb · outbound

This paper cites Saxton and A.

Lower tails for triangles inside the critical window Saxton and A

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:50.808996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.497523Z digest=sha256:350c66a36e728448b76f1013417dbe6a1f4cd1c4906f31a1bf8b5889d0030319

Observation 3037f240-4103-470e-a23f-3eda759a238e · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 61

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:50.791142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.503825Z digest=sha256:46413d30fedfd19b13412ad5548e86526af172038df0099dc1782b96eeafd543

Observation c7e02a9f-4b1a-4249-b48a-ddb38859a65e · outbound

This paper cites Sly and N.

Lower tails for triangles inside the critical window Sly and N

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:50.774188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.508791Z digest=sha256:ed7720eef821397388c88a83f71379302c2bfab65af2424e667eaa4579f4618b

Observation c8205f5b-c6bd-4b93-a89c-d31a567e0127 · outbound

This paper cites Srinivasan.

Lower tails for triangles inside the critical window Srinivasan

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:50.755624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.513921Z digest=sha256:012ddc1e2f5e785cd44759c5d22437978d7908462d2496268032f0896acf4114

Observation dc94690c-f03e-4f49-945b-b46bd616aeed · outbound

This paper cites Stark and N.

Lower tails for triangles inside the critical window Stark and N

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:50.735964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.519493Z digest=sha256:041c1a1442b51288de62d0895df6426138b41869e1e30cd9a659dc216064180c

Observation cfc94ec6-fb42-48db-8320-d3799109de04 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 65

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:50.719162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.524641Z digest=sha256:158820a415f0fa9993c1ba35ebdffd7067dc2b36dcc554ba2fcec58d00f31149

Observation 76cf2d45-f235-419b-b50a-f87c01bf13d5 · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 66

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:50.702395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.530253Z digest=sha256:dcaef0b239d8fc889587b1caf538c67dd6c3203f72ef767e8cc8fc610b9eacb6

Observation 6c32bf22-e9a0-4d81-a4f9-eb3d15688711 · outbound

This paper cites Yang and T.-D.

Lower tails for triangles inside the critical window Yang and T.-D

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:24:50.684635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.535718Z digest=sha256:efd7452d35019d291937c1c7b26101cfb9cdd20c846aaa11457f7632fe3d1f67

Observation 5df831ef-0b54-4295-9e93-89aff5f0619b · outbound

This paper cites Hypergraph independence polynomials with a zero close to the origin.

Lower tails for triangles inside the critical window Hypergraph independence polynomials with a zero close to the origin

Reference 68

Resolution
verified exact
local_arxiv, observed 2026-08-12T11:24:50.603992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.541428Z digest=sha256:06eac9f4a2909a8df735481d73f520991727d65544118d0c4e03f639a12f68a4

Observation 1de75309-8b48-4be4-86bc-1405a0c271eb · outbound

This paper cites an unresolved cited work.

Lower tails for triangles inside the critical window Unresolved cited work

Reference 69

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:24:50.667566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-12T11:24:50.546949Z digest=sha256:78d26713c449aed8c0081e7c850e76f98f5f6a8d26fd4cda655faccc9a3b2d68

Pith citing papers

Observation 263da7db-7c9e-4132-80f5-fc7851ac7f4b · inbound

Non-existence probabilities and lower tails in the critical regime via Belief Propagation cites this paper.

Non-existence probabilities and lower tails in the critical regime via Belief Propagation Lower tails for triangles inside the critical window

Reference 30

Resolution
verified exact
arxiv_id, observed 2026-05-10T22:30:51.869047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-05-10T19:47:31.283256Z digest=sha256:97737b4eaaf36f11450ac1618b8fd14871ed466cb2ad54656ee4a8715e67e34b