{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GN2H3V7ZNCZDYBDMVNMNYFMEL4","short_pith_number":"pith:GN2H3V7Z","schema_version":"1.0","canonical_sha256":"33747dd7f968b23c046cab58dc15845f35e5793807527b29dec35bc547ef082b","source":{"kind":"arxiv","id":"1907.04559","version":1},"attestation_state":"computed","paper":{"title":"The maximum length of $K_r$-Bootstrap Percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexey Pokrovskiy, Gal Kronenberg, J\\'ozsef Balogh, Tibor Szab\\'o","submitted_at":"2019-07-10T08:05:49Z","abstract_excerpt":"Graph-bootstrap percolation, also known as weak saturation, was introduced by Bollob\\'as in 1968. In this process, we start with initial \"infected\" set of edges $E_0$, and we infect new edges according to a predetermined rule. Given a graph $H$ and a set of previously infected edges $E_t\\subseteq E(K_n)$, we infect a non-infected edge $e$ if it completes a new copy of $H$ in $G=([n],E_t\\cup e)$. A question raised by Bollob\\'as asks for the maximum time the process can run before it stabilizes. Bollob\\'as, Przykucki, Riordan, and Sahasrabudhe considered this problem for the most natural case wh"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1907.04559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-10T08:05:49Z","cross_cats_sorted":[],"title_canon_sha256":"09428d17f5b2ad0c7e22de0af7fb72a4fa9caec493c3b1584ed270b8b5aacf17","abstract_canon_sha256":"2bd8a040908df7426bec6b26c1b24f15e10a3293906738a24d3a22d19f1d3ec5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:59.886296Z","signature_b64":"qpZPC0kTO4Z5cyf6NZHc9SPlv0V/OPFvGVlJImWOsWWhHxl7ZTNv9YbNqt1lidhtTVrOkx9f8JJycbPcmaqXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33747dd7f968b23c046cab58dc15845f35e5793807527b29dec35bc547ef082b","last_reissued_at":"2026-05-17T23:40:59.885826Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:59.885826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The maximum length of $K_r$-Bootstrap Percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexey Pokrovskiy, Gal Kronenberg, J\\'ozsef Balogh, Tibor Szab\\'o","submitted_at":"2019-07-10T08:05:49Z","abstract_excerpt":"Graph-bootstrap percolation, also known as weak saturation, was introduced by Bollob\\'as in 1968. In this process, we start with initial \"infected\" set of edges $E_0$, and we infect new edges according to a predetermined rule. Given a graph $H$ and a set of previously infected edges $E_t\\subseteq E(K_n)$, we infect a non-infected edge $e$ if it completes a new copy of $H$ in $G=([n],E_t\\cup e)$. A question raised by Bollob\\'as asks for the maximum time the process can run before it stabilizes. Bollob\\'as, Przykucki, Riordan, and Sahasrabudhe considered this problem for the most natural case wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04559","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.04559","created_at":"2026-05-17T23:40:59.885893+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.04559v1","created_at":"2026-05-17T23:40:59.885893+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04559","created_at":"2026-05-17T23:40:59.885893+00:00"},{"alias_kind":"pith_short_12","alias_value":"GN2H3V7ZNCZD","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GN2H3V7ZNCZDYBDM","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GN2H3V7Z","created_at":"2026-05-18T12:33:18.533446+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.22630","citing_title":"Upper bounds on the running time of bootstrap percolation","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2604.04607","citing_title":"Bootstrap percolation of extension hypergraphs","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GN2H3V7ZNCZDYBDMVNMNYFMEL4","json":"https://pith.science/pith/GN2H3V7ZNCZDYBDMVNMNYFMEL4.json","graph_json":"https://pith.science/api/pith-number/GN2H3V7ZNCZDYBDMVNMNYFMEL4/graph.json","events_json":"https://pith.science/api/pith-number/GN2H3V7ZNCZDYBDMVNMNYFMEL4/events.json","paper":"https://pith.science/paper/GN2H3V7Z"},"agent_actions":{"view_html":"https://pith.science/pith/GN2H3V7ZNCZDYBDMVNMNYFMEL4","download_json":"https://pith.science/pith/GN2H3V7ZNCZDYBDMVNMNYFMEL4.json","view_paper":"https://pith.science/paper/GN2H3V7Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.04559&json=true","fetch_graph":"https://pith.science/api/pith-number/GN2H3V7ZNCZDYBDMVNMNYFMEL4/graph.json","fetch_events":"https://pith.science/api/pith-number/GN2H3V7ZNCZDYBDMVNMNYFMEL4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GN2H3V7ZNCZDYBDMVNMNYFMEL4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GN2H3V7ZNCZDYBDMVNMNYFMEL4/action/storage_attestation","attest_author":"https://pith.science/pith/GN2H3V7ZNCZDYBDMVNMNYFMEL4/action/author_attestation","sign_citation":"https://pith.science/pith/GN2H3V7ZNCZDYBDMVNMNYFMEL4/action/citation_signature","submit_replication":"https://pith.science/pith/GN2H3V7ZNCZDYBDMVNMNYFMEL4/action/replication_record"}},"created_at":"2026-05-17T23:40:59.885893+00:00","updated_at":"2026-05-17T23:40:59.885893+00:00"}