{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BHN3CAU6GGB3C4SP3EOIUREB3Y","short_pith_number":"pith:BHN3CAU6","canonical_record":{"source":{"id":"1610.06479","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-20T16:12:28Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"34a4cc87134e2b7ca49568c803bb996d2d5e518207781ece543162ef44a92e86","abstract_canon_sha256":"8b790ff86bddf40c8cfe05ec6593b109b8854fc08fc3940e0cc87624005cd66d"},"schema_version":"1.0"},"canonical_sha256":"09dbb1029e3183b1724fd91c8a4481de1d0b62267aa2a891e781068bfe9a8a31","source":{"kind":"arxiv","id":"1610.06479","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06479","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06479v2","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06479","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"BHN3CAU6GGB3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BHN3CAU6GGB3C4SP","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BHN3CAU6","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BHN3CAU6GGB3C4SP3EOIUREB3Y","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06479","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-20T16:12:28Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"34a4cc87134e2b7ca49568c803bb996d2d5e518207781ece543162ef44a92e86","abstract_canon_sha256":"8b790ff86bddf40c8cfe05ec6593b109b8854fc08fc3940e0cc87624005cd66d"},"schema_version":"1.0"},"canonical_sha256":"09dbb1029e3183b1724fd91c8a4481de1d0b62267aa2a891e781068bfe9a8a31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:59.760997Z","signature_b64":"lHuyEh7C8eybESbU7bx5V2vj6DIOkHBWxHgBIohJ3AFVDTdEy5MP0TwQro3OA6p5Oz4FEkq3pz4nc4Sq+o9SCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09dbb1029e3183b1724fd91c8a4481de1d0b62267aa2a891e781068bfe9a8a31","last_reissued_at":"2026-05-18T00:33:59.760397Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:59.760397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06479","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pRTsa4Gz5mvmqYrZnCi3KSdb/x/bDYEvzCFak2qo/CP+WbK332BzCTOdwfVNo5LaVjqzMVtRbA7Ku6oJbr++DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:46:49.817807Z"},"content_sha256":"c64983de9b677cf6650ea4d4cb84005fe828ca46a4aa53617da2521a594ead4a","schema_version":"1.0","event_id":"sha256:c64983de9b677cf6650ea4d4cb84005fe828ca46a4aa53617da2521a594ead4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BHN3CAU6GGB3C4SP3EOIUREB3Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Competition in growth and urns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Daniel Ahlberg, Robert Morris, Simon Griffiths, Svante Janson","submitted_at":"2016-10-20T16:12:28Z","abstract_excerpt":"We study survival among two competing types in two settings: a planar growth model related to two-neighbour bootstrap percolation, and a system of urns with graph-based interactions. In the planar growth model, uncoloured sites are given a colour at rate $0$, $1$ or $\\infty$, depending on whether they have zero, one, or at least two neighbours of that colour. In the urn scheme, each vertex of a graph $G$ has an associated urn containing some number of either blue or red balls (but not both). At each time step, a ball is chosen uniformly at random from all those currently present in the system,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06479","kind":"arxiv","version":2},"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":"2026-05-18T00:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DftKtC3zQfS4xX8izxqrmGkbonl+hz4XhcQqjle+/2Ss/5S4XUFssjTTamXS5GW7Fs6kNrHdxlM363aZSgaGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:46:49.818159Z"},"content_sha256":"2783d27cdbaf6886930420d726c45098a1d49d0d297539fec16b2824463fe377","schema_version":"1.0","event_id":"sha256:2783d27cdbaf6886930420d726c45098a1d49d0d297539fec16b2824463fe377"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BHN3CAU6GGB3C4SP3EOIUREB3Y/bundle.json","state_url":"https://pith.science/pith/BHN3CAU6GGB3C4SP3EOIUREB3Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BHN3CAU6GGB3C4SP3EOIUREB3Y/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":"2026-05-30T14:46:49Z","links":{"resolver":"https://pith.science/pith/BHN3CAU6GGB3C4SP3EOIUREB3Y","bundle":"https://pith.science/pith/BHN3CAU6GGB3C4SP3EOIUREB3Y/bundle.json","state":"https://pith.science/pith/BHN3CAU6GGB3C4SP3EOIUREB3Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BHN3CAU6GGB3C4SP3EOIUREB3Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BHN3CAU6GGB3C4SP3EOIUREB3Y","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":"8b790ff86bddf40c8cfe05ec6593b109b8854fc08fc3940e0cc87624005cd66d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-20T16:12:28Z","title_canon_sha256":"34a4cc87134e2b7ca49568c803bb996d2d5e518207781ece543162ef44a92e86"},"schema_version":"1.0","source":{"id":"1610.06479","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06479","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06479v2","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06479","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"BHN3CAU6GGB3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BHN3CAU6GGB3C4SP","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BHN3CAU6","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:2783d27cdbaf6886930420d726c45098a1d49d0d297539fec16b2824463fe377","target":"graph","created_at":"2026-05-18T00:33:59Z","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":"We study survival among two competing types in two settings: a planar growth model related to two-neighbour bootstrap percolation, and a system of urns with graph-based interactions. In the planar growth model, uncoloured sites are given a colour at rate $0$, $1$ or $\\infty$, depending on whether they have zero, one, or at least two neighbours of that colour. In the urn scheme, each vertex of a graph $G$ has an associated urn containing some number of either blue or red balls (but not both). At each time step, a ball is chosen uniformly at random from all those currently present in the system,","authors_text":"Daniel Ahlberg, Robert Morris, Simon Griffiths, Svante Janson","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-20T16:12:28Z","title":"Competition in growth and urns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06479","kind":"arxiv","version":2},"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:c64983de9b677cf6650ea4d4cb84005fe828ca46a4aa53617da2521a594ead4a","target":"record","created_at":"2026-05-18T00:33:59Z","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":"8b790ff86bddf40c8cfe05ec6593b109b8854fc08fc3940e0cc87624005cd66d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-20T16:12:28Z","title_canon_sha256":"34a4cc87134e2b7ca49568c803bb996d2d5e518207781ece543162ef44a92e86"},"schema_version":"1.0","source":{"id":"1610.06479","kind":"arxiv","version":2}},"canonical_sha256":"09dbb1029e3183b1724fd91c8a4481de1d0b62267aa2a891e781068bfe9a8a31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09dbb1029e3183b1724fd91c8a4481de1d0b62267aa2a891e781068bfe9a8a31","first_computed_at":"2026-05-18T00:33:59.760397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:59.760397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lHuyEh7C8eybESbU7bx5V2vj6DIOkHBWxHgBIohJ3AFVDTdEy5MP0TwQro3OA6p5Oz4FEkq3pz4nc4Sq+o9SCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:59.760997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06479","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c64983de9b677cf6650ea4d4cb84005fe828ca46a4aa53617da2521a594ead4a","sha256:2783d27cdbaf6886930420d726c45098a1d49d0d297539fec16b2824463fe377"],"state_sha256":"7c822bbf0a2a05a71f68135fde785729d0911917ef98ad0b0eb1971ee5b8f22d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M5uLDiKXRQCM0oAIyJMvpHbMCpj8Ztpj/wKQf6Fe73HHMYgU0a5fcNXkSY7TszQVmUox/ByT9qjuGaWCkjqJCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:46:49.820762Z","bundle_sha256":"704cf67d30b851921747c1b2ba14711362a32025bf7ac1b0b7261ff34a149c89"}}