{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IHQNZMFISUA4LDZUMNZ2ZEFUZO","short_pith_number":"pith:IHQNZMFI","canonical_record":{"source":{"id":"1510.07096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-24T01:13:35Z","cross_cats_sorted":[],"title_canon_sha256":"1f438527e128f2c115733c13fe1638808e237616d9c587ecb8013aa3d9e4cebb","abstract_canon_sha256":"a589370e8628724ad935c5e55a3a12de3e61fd84b5394f4ec0de97e4e33b1b4e"},"schema_version":"1.0"},"canonical_sha256":"41e0dcb0a89501c58f346373ac90b4cba0658c2894be51ad6ff9e52586ba4309","source":{"kind":"arxiv","id":"1510.07096","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07096","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07096v1","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07096","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"IHQNZMFISUA4","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IHQNZMFISUA4LDZU","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IHQNZMFI","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IHQNZMFISUA4LDZUMNZ2ZEFUZO","target":"record","payload":{"canonical_record":{"source":{"id":"1510.07096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-24T01:13:35Z","cross_cats_sorted":[],"title_canon_sha256":"1f438527e128f2c115733c13fe1638808e237616d9c587ecb8013aa3d9e4cebb","abstract_canon_sha256":"a589370e8628724ad935c5e55a3a12de3e61fd84b5394f4ec0de97e4e33b1b4e"},"schema_version":"1.0"},"canonical_sha256":"41e0dcb0a89501c58f346373ac90b4cba0658c2894be51ad6ff9e52586ba4309","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:42.189373Z","signature_b64":"NE6u6wgVvpI8qPI4M+gGSJdBUWJntsambQy1+lScP0HBXFNHWePefp9NkGYpSc/npQb0sOWUjaEpp1tiLkaAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41e0dcb0a89501c58f346373ac90b4cba0658c2894be51ad6ff9e52586ba4309","last_reissued_at":"2026-05-18T00:41:42.188824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:42.188824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.07096","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6NZX6Ko6+vFpECsnuo2vCKpN6o9p+MUp2V77u8KuhdvNGhMRNKf+8UjcxZXxMQWgVICAkC/JqAQwvYmqLsdsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:31:21.609237Z"},"content_sha256":"1a4a3991877d06440b46d2c34a759f04814beed59d2ca9900cb1c5dc2a5f17e7","schema_version":"1.0","event_id":"sha256:1a4a3991877d06440b46d2c34a759f04814beed59d2ca9900cb1c5dc2a5f17e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IHQNZMFISUA4LDZUMNZ2ZEFUZO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the maximum running time in graph bootstrap percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"B\\'ela Bollob\\'as, Julian Sahasrabudhe, Micha{\\l} Przykucki, Oliver Riordan","submitted_at":"2015-10-24T01:13:35Z","abstract_excerpt":"Graph bootstrap percolation is a simple cellular automaton introduced by Bollob\\'as in 1968. Given a graph $H$ and a set $G \\subseteq E(K_n)$ we initially \"infect\" all edges in $G$ and then, in consecutive steps, we infect every $e \\in K_n$ that completes a new infected copy of $H$ in $K_n$. We say that $G$ percolates if eventually every edge in $K_n$ is infected. The extremal question about the size of the smallest percolating sets when $H = K_r$ was answered independently by Alon, Kalai and Frankl. Here we consider a different question raised more recently by Bollob\\'as: what is the maximum "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07096","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4yWlCSzVCgF46SlWmbd0pT2cfwtaKzHONRAAj1gZKBgEfzSCnWQAHB+RB54XzjqM3B2nZeUSAcRIA89HcCq1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:31:21.609596Z"},"content_sha256":"f2d05764be471c00da3a4002c17cc4a712def24e3f4330801107ec8e1bc8b9b5","schema_version":"1.0","event_id":"sha256:f2d05764be471c00da3a4002c17cc4a712def24e3f4330801107ec8e1bc8b9b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IHQNZMFISUA4LDZUMNZ2ZEFUZO/bundle.json","state_url":"https://pith.science/pith/IHQNZMFISUA4LDZUMNZ2ZEFUZO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IHQNZMFISUA4LDZUMNZ2ZEFUZO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T10:31:21Z","links":{"resolver":"https://pith.science/pith/IHQNZMFISUA4LDZUMNZ2ZEFUZO","bundle":"https://pith.science/pith/IHQNZMFISUA4LDZUMNZ2ZEFUZO/bundle.json","state":"https://pith.science/pith/IHQNZMFISUA4LDZUMNZ2ZEFUZO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IHQNZMFISUA4LDZUMNZ2ZEFUZO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IHQNZMFISUA4LDZUMNZ2ZEFUZO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a589370e8628724ad935c5e55a3a12de3e61fd84b5394f4ec0de97e4e33b1b4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-24T01:13:35Z","title_canon_sha256":"1f438527e128f2c115733c13fe1638808e237616d9c587ecb8013aa3d9e4cebb"},"schema_version":"1.0","source":{"id":"1510.07096","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07096","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07096v1","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07096","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"IHQNZMFISUA4","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IHQNZMFISUA4LDZU","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IHQNZMFI","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:f2d05764be471c00da3a4002c17cc4a712def24e3f4330801107ec8e1bc8b9b5","target":"graph","created_at":"2026-05-18T00:41:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Graph bootstrap percolation is a simple cellular automaton introduced by Bollob\\'as in 1968. Given a graph $H$ and a set $G \\subseteq E(K_n)$ we initially \"infect\" all edges in $G$ and then, in consecutive steps, we infect every $e \\in K_n$ that completes a new infected copy of $H$ in $K_n$. We say that $G$ percolates if eventually every edge in $K_n$ is infected. The extremal question about the size of the smallest percolating sets when $H = K_r$ was answered independently by Alon, Kalai and Frankl. Here we consider a different question raised more recently by Bollob\\'as: what is the maximum ","authors_text":"B\\'ela Bollob\\'as, Julian Sahasrabudhe, Micha{\\l} Przykucki, Oliver Riordan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-24T01:13:35Z","title":"On the maximum running time in graph bootstrap percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07096","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1a4a3991877d06440b46d2c34a759f04814beed59d2ca9900cb1c5dc2a5f17e7","target":"record","created_at":"2026-05-18T00:41:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a589370e8628724ad935c5e55a3a12de3e61fd84b5394f4ec0de97e4e33b1b4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-24T01:13:35Z","title_canon_sha256":"1f438527e128f2c115733c13fe1638808e237616d9c587ecb8013aa3d9e4cebb"},"schema_version":"1.0","source":{"id":"1510.07096","kind":"arxiv","version":1}},"canonical_sha256":"41e0dcb0a89501c58f346373ac90b4cba0658c2894be51ad6ff9e52586ba4309","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41e0dcb0a89501c58f346373ac90b4cba0658c2894be51ad6ff9e52586ba4309","first_computed_at":"2026-05-18T00:41:42.188824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:42.188824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NE6u6wgVvpI8qPI4M+gGSJdBUWJntsambQy1+lScP0HBXFNHWePefp9NkGYpSc/npQb0sOWUjaEpp1tiLkaAAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:42.189373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07096","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a4a3991877d06440b46d2c34a759f04814beed59d2ca9900cb1c5dc2a5f17e7","sha256:f2d05764be471c00da3a4002c17cc4a712def24e3f4330801107ec8e1bc8b9b5"],"state_sha256":"75e33f7f78d2717be60ee9deecb876c09162f59ab9a379de64a78cf8c306bd18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LXDLIWAYQacneQ1sC9OsdV5dmaWCYMcyQPvXQTXhKmXOp0x3KKoMCpZe9P63RWeEwu6icIIiwWJt/jPSWpElCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T10:31:21.611518Z","bundle_sha256":"eae8bf0e2df3dd024cde571950d5d650c1cbe68aa965f2bad80dca07f22d98ae"}}