Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:41:01.539676Z
Paper Citation Record · LEDGER
As of 7 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 1 inbound Pith citation observation for arXiv:2507.05697.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:41:01.539676Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-05T16:02:29.579908Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-05T16:02:29.669103Z
67 of 67 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 21279f3a-5e0e-479d-8644-5964bfe6b54d · outbound
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 82d87b89-0622-4fca-876b-0d95d87cd954 · outbound
When does a tree activate the random graph? Aizenman, J.L
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 9da0a727-0a7d-460b-9ba8-a130faf295d1 · outbound
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 63120782-63e1-4431-8801-bc82dad8f4d6 · outbound
When does a tree activate the random graph? Alon, An extremal problem for sets with applications to graph theory , Journal of Combina- torial Theory, Series A, 40 (1985) 82–89
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 026d7923-9de5-497f-ae1d-b264a1e85442 · outbound
Reference 5
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b8f9a28c-14de-49df-af2f-de1aa5f6dffc · outbound
When does a tree activate the random graph? Fundamental Groups of Random Clique Complexes
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation a90d1fc3-e8c8-4e58-9545-90d9a1f698e2 · outbound
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0bd75418-eecc-4fb1-9944-94beef60f5e7 · outbound
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation c3ac6f7f-704c-4703-a6a8-e9074a7b2dc0 · outbound
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 51d0acde-349d-42a8-812f-b3c565cd87ff · outbound
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 98265ba1-5521-4e0c-9ee4-521a31bed6f9 · outbound
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e5f50236-7644-4044-b9b1-7982e6f50fa4 · outbound
When does a tree activate the random graph? Bernardi, ´E
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 77d70494-a588-4a76-b6b1-ebb32316feda · outbound
When does a tree activate the random graph? Bidgoli, A
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7b709cc1-aae0-469b-929a-a0aee900dc1a · outbound
When does a tree activate the random graph? Bollob´ as,Random graphs, second edition, Cambridge University Press, 2001
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 6bf01154-8400-4304-9938-39fde5fe6954 · outbound
When does a tree activate the random graph? Bollob´ as, The evolution of sparse graphs , Graph theory and combinatorics (Cambridge, 1983), Academic Press, London, (1984) 35–57
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 56308bf7-c0e9-4f52-a40a-4920d0b67171 · outbound
When does a tree activate the random graph? Bollob´ as,Weakly k-saturated graphs, Beitr¨ age zur Graphentheorie (Kolloquium, Manebach, 1967), Teubner, Leipzig (1968) 25–31
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 33e778dc-a3d3-42af-b2f1-77f92fb0c5f9 · outbound
When does a tree activate the random graph? Brightwell, K
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 483fda9a-6cec-4e15-9b79-b3f75282beb8 · outbound
When does a tree activate the random graph? Bulavka, M
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation c803c86e-3fde-48ea-a79b-0f6dd435fc34 · outbound
When does a tree activate the random graph? Unresolved cited work
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 69a51417-0c0b-4dbc-b0cb-eb842377be5d · outbound
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation aec5f165-ed07-487a-9ff4-e36607f63183 · outbound
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 3c039409-181f-4299-aa94-e82e4af46c17 · outbound
When does a tree activate the random graph? Unresolved cited work
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 91030598-4baf-4ee9-a520-3c1b94a737ed · outbound
When does a tree activate the random graph? On the triangle space of a random graph
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation be09fe7f-0a0a-4a7c-8f2c-54c299ae281c · outbound
When does a tree activate the random graph? DeMarco, J
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 656d535a-b670-4f06-be30-526b82b560bb · outbound
When does a tree activate the random graph? On the $H$-space of a random graph
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 5ea4ab46-1728-451a-a7b2-80d14bbb2d90 · outbound
When does a tree activate the random graph? Erd˝ os, Z
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0d130292-377a-4990-a00e-4765f4f7b78d · outbound
When does a tree activate the random graph? Faudree, R.J
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 535a7d2b-0884-4337-af75-537dfba101a9 · outbound
When does a tree activate the random graph? Fontes, R.H
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 542d4d21-7ccd-46d9-be44-86d066b97ed1 · outbound
When does a tree activate the random graph? Frankl, An extremal problem for two families of sets, European J
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b7ad477c-7153-471c-bc72-4e9b897af29d · outbound
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 52ff7ce6-b945-469d-bbcb-db5808e22b6b · outbound
When does a tree activate the random graph? Gravner, A.E
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 973638aa-fb42-47d6-9ec2-c98f6dfff0cb · outbound
When does a tree activate the random graph? Gravner, A.E
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 933412b4-c333-449f-9bcf-4d0b9320321f · outbound
When does a tree activate the random graph? Gravner, B
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f7f80b03-9a7c-4c29-bb0a-d34f6c8fd811 · outbound
When does a tree activate the random graph? Gravner, E
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ec02a631-1051-4a9a-bdc6-5bb693834bbb · outbound
When does a tree activate the random graph? Gromov, Hyperbolic groups, in Essays in group theory, ed
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 272624b4-b353-48cf-bd1f-145415b95bec · outbound
When does a tree activate the random graph? Simonovits's theorem in random graphs
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ed3fd181-f5b2-43cd-a6eb-28a9299d9b16 · outbound
When does a tree activate the random graph? Stability of large cuts in random graphs
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 8558b6eb-4674-45ba-af24-90ec2c44970d · outbound
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 70cd6e39-11ee-4503-bb02-2e7df0dffd45 · outbound
When does a tree activate the random graph? Kahle, Topology of random clique complexes , Discrete Math., 309:6 (2009) 1658–1671
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 58a106c0-1e41-494c-a443-ffd78bcf7bcc · outbound
When does a tree activate the random graph? Kalai, Hyperconnectivity of graphs, Graphs Combin., 1 (1985) 65–79
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation cab788ce-b904-4095-82e4-e7e0477ac7f5 · outbound
When does a tree activate the random graph? Kalai, Weakly saturated graphs are rigid, in: Convexity and graph theory (Jerusalem, 1981), North-Holland Math
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 1800d65e-c99a-4bc4-b250-c2410dc2b3d0 · outbound
When does a tree activate the random graph? Weak saturation numbers in random graphs
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 6ed682d5-147e-4b5b-b664-3430ada4e4a8 · outbound
When does a tree activate the random graph? Kalinichenko, M
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 592f01a3-4e4e-4e17-97eb-e8300f388bbe · outbound
When does a tree activate the random graph? Koml´ os, E
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 2c1c89f3-43aa-4739-8228-1f0434f694b7 · outbound
When does a tree activate the random graph? Kor´ andi, Y
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4dd2d87f-bfa5-4d32-b6e7-68537e9dc1f9 · outbound
When does a tree activate the random graph? Kor´ andi, B
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 8a24bcff-67a3-45bb-b03f-b96df245f302 · outbound
When does a tree activate the random graph? Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d6f1318c-0aa2-47b8-ba3c-d69a2c691159 · outbound
When does a tree activate the random graph? Krivelevich, G
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d7dc59a5-3143-4a15-8092-12876043ca5b · outbound
When does a tree activate the random graph? Kronenberg, T
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0ba8adc2-9e13-456e-a0df-22cf0ccd5509 · outbound
When does a tree activate the random graph? Morris, Bootstrap percolation, and other automata, European Journal of Combinatorics, 66 (2017) 250–263
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 53b74345-7607-4ffa-8995-11e45df3183f · outbound
When does a tree activate the random graph? Morris, Zero-temperature Glauber dynamics on Zd, Probab
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation bd810cae-70ea-44f6-91bf-78a9da045d28 · outbound
When does a tree activate the random graph? Morrison, J
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 09db5ef4-66f9-4d94-b725-49b9945ca65c · outbound
When does a tree activate the random graph? Morrison, J
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation bc1c9ba1-3bd4-4ca6-bd49-ccaa8c7a9610 · outbound
When does a tree activate the random graph? Moshkovitz, A
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f03b07cc-2dca-48b9-92d6-076e37554210 · outbound
When does a tree activate the random graph? O’Connell, Some large deviation results for sparse random graphs , Probab
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 6d72bc03-395a-4c2f-8955-977f8cabdd63 · outbound
When does a tree activate the random graph? Pikhurko, Extremal hypergraphs, PhD thesis, University of Cambridge, 1999
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4a082663-88c4-493c-92cc-48278ccad138 · outbound
When does a tree activate the random graph? Pikhurko, Weakly saturated hypergraphs and exterior algebra , Combin
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 202b2f9c-5661-43dd-a8b7-2d0acb3731cc · outbound
When does a tree activate the random graph? Schacht, Extremal results for random discrete structures , Annals of Mathematics, 184:2 (2016) 333–365
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 8c8d6181-c915-408c-94ad-1b818665ef71 · outbound
When does a tree activate the random graph? Shapira, M
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0f84e7f1-7c6a-48fa-9e25-e681356116d9 · outbound
When does a tree activate the random graph? Spencer, Counting extensions, Journal of Combinatorial Theory, Series A, 55:2 (1990) 247– 255
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d208afee-2e1b-401d-8d5a-6bf3bd9b7c43 · outbound
When does a tree activate the random graph? A short proof of Tuza's conjecture for weak saturation in hypergraphs
Reference 61
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ba7bec13-6ff2-4b9f-a70d-6f8e38e478a7 · outbound
When does a tree activate the random graph? Terekhov, M
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7689d68e-0a16-42b2-821b-9ff286ad17e6 · outbound
When does a tree activate the random graph? Weak saturation rank: a failure of linear algebraic approach to weak saturation
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 2d54cca2-0da8-4d60-baa1-0ad861120c2a · outbound
When does a tree activate the random graph? Unresolved cited work
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 477b3d3a-e46e-4a43-93f5-c104b5317554 · outbound
When does a tree activate the random graph? von Neumann, Theory of Self-Reproducing Automata , Univ
Reference 65
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 389eaf59-8111-44e5-a982-d190dac2f17c · outbound
When does a tree activate the random graph? Tuza, Asymptotic growth of sparse saturated structures is locally determined, Discrete Math- ematics, 108:1-3 (1992) 397–402
Reference 66
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ad1a21f4-da51-4978-9986-5d15932e9ebf · outbound
When does a tree activate the random graph? Ulam, Random processes and transformations, Proc
Reference 67
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4ed526f0-d3c2-4496-ba56-b60cca3e0f66 · inbound
Weak saturation numbers of large complete bipartite graphs When does a tree activate the random graph?
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.