{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HNBFFA2ODGZ7ASOOJBLRJZQCSS","short_pith_number":"pith:HNBFFA2O","canonical_record":{"source":{"id":"1609.04070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-13T22:58:08Z","cross_cats_sorted":[],"title_canon_sha256":"2b40f5b468f8be55267f9e97638949afd4eb8a1e923cb20cacb310d4fc2bfa2b","abstract_canon_sha256":"c1fd3cd10e9e3d7d1404d0f6bb8a168fe5e957ebc7c589880bc5749f484d48f8"},"schema_version":"1.0"},"canonical_sha256":"3b4252834e19b3f049ce485714e60294be30d3eee2e7a6ff336efabdda1a6370","source":{"kind":"arxiv","id":"1609.04070","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04070","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04070v2","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04070","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"pith_short_12","alias_value":"HNBFFA2ODGZ7","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HNBFFA2ODGZ7ASOO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HNBFFA2O","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HNBFFA2ODGZ7ASOOJBLRJZQCSS","target":"record","payload":{"canonical_record":{"source":{"id":"1609.04070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-13T22:58:08Z","cross_cats_sorted":[],"title_canon_sha256":"2b40f5b468f8be55267f9e97638949afd4eb8a1e923cb20cacb310d4fc2bfa2b","abstract_canon_sha256":"c1fd3cd10e9e3d7d1404d0f6bb8a168fe5e957ebc7c589880bc5749f484d48f8"},"schema_version":"1.0"},"canonical_sha256":"3b4252834e19b3f049ce485714e60294be30d3eee2e7a6ff336efabdda1a6370","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:37.148697Z","signature_b64":"DhZhocK+xBx/Vx6RbHpDSmhbG2JD2gxeK4qtdBFWolqGE6stytoXtruqVVusDV/gdSzc8NzlfAgsAsFMGI/OAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b4252834e19b3f049ce485714e60294be30d3eee2e7a6ff336efabdda1a6370","last_reissued_at":"2026-05-18T00:18:37.148158Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:37.148158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.04070","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":"2026-05-18T00:18:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aqqT8eNaHFMpMNTV2vMPYDANjqS669QK6z587b4FgcaHYzJcwFYidt0sUCgjdbdl1zD+vdDaSYZinOdQ0bTvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:35:42.707095Z"},"content_sha256":"d446e30b0ee7334242fd69cb08fbf4aa9b5b59b5f122b6c7b4541e029d0ba032","schema_version":"1.0","event_id":"sha256:d446e30b0ee7334242fd69cb08fbf4aa9b5b59b5f122b6c7b4541e029d0ba032"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HNBFFA2ODGZ7ASOOJBLRJZQCSS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luca Di Persio, Mykola Lebid, Tomasz O\\.za\\'nski, Tyll Krueger, Viktor Bezborodov","submitted_at":"2016-09-13T22:58:08Z","abstract_excerpt":"We formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similarly to the classical lattice growth models the proof makes use of the subadditive ergodic theorem. A precise expression for the speed of propagation is given in the case of a truncated free branching birth rate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04070","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":"2026-05-18T00:18:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ufpyuBwxUZ8JkYPFfR0YxYA1AKe3mXJd00Iynjpso5ZLFrE346VdQArWFMUclc0DAieYA5gCYzgQHKY+6n5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:35:42.707448Z"},"content_sha256":"2abe1eb1645fb62e772715cedc4dc39cf8cdcd42bd6ef9b431a2d624445b4259","schema_version":"1.0","event_id":"sha256:2abe1eb1645fb62e772715cedc4dc39cf8cdcd42bd6ef9b431a2d624445b4259"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNBFFA2ODGZ7ASOOJBLRJZQCSS/bundle.json","state_url":"https://pith.science/pith/HNBFFA2ODGZ7ASOOJBLRJZQCSS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNBFFA2ODGZ7ASOOJBLRJZQCSS/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":"2026-06-22T11:35:42Z","links":{"resolver":"https://pith.science/pith/HNBFFA2ODGZ7ASOOJBLRJZQCSS","bundle":"https://pith.science/pith/HNBFFA2ODGZ7ASOOJBLRJZQCSS/bundle.json","state":"https://pith.science/pith/HNBFFA2ODGZ7ASOOJBLRJZQCSS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNBFFA2ODGZ7ASOOJBLRJZQCSS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HNBFFA2ODGZ7ASOOJBLRJZQCSS","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":"c1fd3cd10e9e3d7d1404d0f6bb8a168fe5e957ebc7c589880bc5749f484d48f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-13T22:58:08Z","title_canon_sha256":"2b40f5b468f8be55267f9e97638949afd4eb8a1e923cb20cacb310d4fc2bfa2b"},"schema_version":"1.0","source":{"id":"1609.04070","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04070","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04070v2","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04070","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"pith_short_12","alias_value":"HNBFFA2ODGZ7","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HNBFFA2ODGZ7ASOO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HNBFFA2O","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:2abe1eb1645fb62e772715cedc4dc39cf8cdcd42bd6ef9b431a2d624445b4259","target":"graph","created_at":"2026-05-18T00:18:37Z","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 formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similarly to the classical lattice growth models the proof makes use of the subadditive ergodic theorem. A precise expression for the speed of propagation is given in the case of a truncated free branching birth rate.","authors_text":"Luca Di Persio, Mykola Lebid, Tomasz O\\.za\\'nski, Tyll Krueger, Viktor Bezborodov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-13T22:58:08Z","title":"Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04070","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:d446e30b0ee7334242fd69cb08fbf4aa9b5b59b5f122b6c7b4541e029d0ba032","target":"record","created_at":"2026-05-18T00:18:37Z","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":"c1fd3cd10e9e3d7d1404d0f6bb8a168fe5e957ebc7c589880bc5749f484d48f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-13T22:58:08Z","title_canon_sha256":"2b40f5b468f8be55267f9e97638949afd4eb8a1e923cb20cacb310d4fc2bfa2b"},"schema_version":"1.0","source":{"id":"1609.04070","kind":"arxiv","version":2}},"canonical_sha256":"3b4252834e19b3f049ce485714e60294be30d3eee2e7a6ff336efabdda1a6370","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b4252834e19b3f049ce485714e60294be30d3eee2e7a6ff336efabdda1a6370","first_computed_at":"2026-05-18T00:18:37.148158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:37.148158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DhZhocK+xBx/Vx6RbHpDSmhbG2JD2gxeK4qtdBFWolqGE6stytoXtruqVVusDV/gdSzc8NzlfAgsAsFMGI/OAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:37.148697Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04070","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d446e30b0ee7334242fd69cb08fbf4aa9b5b59b5f122b6c7b4541e029d0ba032","sha256:2abe1eb1645fb62e772715cedc4dc39cf8cdcd42bd6ef9b431a2d624445b4259"],"state_sha256":"3004f831403b556ecd029c206ab4d9daa3c7b7b3ce4f02473358d0374f991a7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UOHiXDs08YAFKEa1thlFz8FD9ZIYzJbHe2qpXpM+botiUp0ni2tXBKPLVjOVTmLzxUBSn/rx8FMp6U9ZYos+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:35:42.709508Z","bundle_sha256":"2e477462b533d70d00e3d47efc5f4b3caa61622465ed9822ef06c3d12cd66d8a"}}