{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ET6MQT2AWPKBCACTHVROPJRG77","short_pith_number":"pith:ET6MQT2A","canonical_record":{"source":{"id":"1109.5094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-23T14:49:43Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"7fdf3c176701d0d92c3a1c14b578914e1c0b12a99451dfa06a7af25e71afe703","abstract_canon_sha256":"196ee14ee43d493afad3b8f16475a3352e7d88610607e24d6f026e276316708a"},"schema_version":"1.0"},"canonical_sha256":"24fcc84f40b3d41100533d62e7a626fff3a3f3a19a833505f863b9bfb4b3900b","source":{"kind":"arxiv","id":"1109.5094","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5094","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5094v2","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5094","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"pith_short_12","alias_value":"ET6MQT2AWPKB","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"ET6MQT2AWPKBCACT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"ET6MQT2A","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ET6MQT2AWPKBCACTHVROPJRG77","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-23T14:49:43Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"7fdf3c176701d0d92c3a1c14b578914e1c0b12a99451dfa06a7af25e71afe703","abstract_canon_sha256":"196ee14ee43d493afad3b8f16475a3352e7d88610607e24d6f026e276316708a"},"schema_version":"1.0"},"canonical_sha256":"24fcc84f40b3d41100533d62e7a626fff3a3f3a19a833505f863b9bfb4b3900b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:48.549570Z","signature_b64":"fN4pA4LZ6qSOjYo1bo5cgVkib2U61QSId0vUXA7OfntdAUtlxunSzUxHjncwZuU2pfpVBiwhGk3Wyab1f5hJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24fcc84f40b3d41100533d62e7a626fff3a3f3a19a833505f863b9bfb4b3900b","last_reissued_at":"2026-05-18T02:28:48.549192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:48.549192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5094","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":"2026-05-18T02:28:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rzPWzn3HOGgGqmoHiKZiRAlt6BlbWfPmj5AOikPnsoloyA8E5cy/ECsY89E6ykm6VmhUO/vPazxWLlSc8av8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:58:37.912369Z"},"content_sha256":"7f022612204ca54b7b81fa8fa973878504e4efcbe20471fc2318d6905041d8d7","schema_version":"1.0","event_id":"sha256:7f022612204ca54b7b81fa8fa973878504e4efcbe20471fc2318d6905041d8d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ET6MQT2AWPKBCACTHVROPJRG77","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semigroup approach to birth-and-death stochastic dynamics in continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.FA","authors_text":"Dmitri Finkelshtein, Oleksandr Kutoviy, Yuri Kondratiev","submitted_at":"2011-09-23T14:49:43Z","abstract_excerpt":"We describe a general approach to the construction of a state evolution corresponding to the Markov generator of a spatial birth-and-death dynamics in $\\mathbb{R}^d$. We present conditions on the birth-and-death intensities which are sufficient for the existence of an evolution as a strongly continuous semigroup in a proper Banach space of correlation functions satisfying the Ruelle bound. The convergence of a Vlasov-type scaling for the corresponding stochastic dynamics is considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5094","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":"2026-05-18T02:28:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6mjmqtofwIdOtq7YB+0vpI3vmiH9bKhZZA91lZ4KuiXtBCKAWj8/VGA9/R3LQ7UmTe+isTfDctWQLs9zLLmDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:58:37.913073Z"},"content_sha256":"bb1924324235984d812015fa7625f447541bac216fe62bb3534ba6328404e348","schema_version":"1.0","event_id":"sha256:bb1924324235984d812015fa7625f447541bac216fe62bb3534ba6328404e348"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ET6MQT2AWPKBCACTHVROPJRG77/bundle.json","state_url":"https://pith.science/pith/ET6MQT2AWPKBCACTHVROPJRG77/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ET6MQT2AWPKBCACTHVROPJRG77/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":"2026-06-08T18:58:37Z","links":{"resolver":"https://pith.science/pith/ET6MQT2AWPKBCACTHVROPJRG77","bundle":"https://pith.science/pith/ET6MQT2AWPKBCACTHVROPJRG77/bundle.json","state":"https://pith.science/pith/ET6MQT2AWPKBCACTHVROPJRG77/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ET6MQT2AWPKBCACTHVROPJRG77/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ET6MQT2AWPKBCACTHVROPJRG77","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":"196ee14ee43d493afad3b8f16475a3352e7d88610607e24d6f026e276316708a","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-23T14:49:43Z","title_canon_sha256":"7fdf3c176701d0d92c3a1c14b578914e1c0b12a99451dfa06a7af25e71afe703"},"schema_version":"1.0","source":{"id":"1109.5094","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5094","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5094v2","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5094","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"pith_short_12","alias_value":"ET6MQT2AWPKB","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"ET6MQT2AWPKBCACT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"ET6MQT2A","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:bb1924324235984d812015fa7625f447541bac216fe62bb3534ba6328404e348","target":"graph","created_at":"2026-05-18T02:28:48Z","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 describe a general approach to the construction of a state evolution corresponding to the Markov generator of a spatial birth-and-death dynamics in $\\mathbb{R}^d$. We present conditions on the birth-and-death intensities which are sufficient for the existence of an evolution as a strongly continuous semigroup in a proper Banach space of correlation functions satisfying the Ruelle bound. The convergence of a Vlasov-type scaling for the corresponding stochastic dynamics is considered.","authors_text":"Dmitri Finkelshtein, Oleksandr Kutoviy, Yuri Kondratiev","cross_cats":["math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-23T14:49:43Z","title":"Semigroup approach to birth-and-death stochastic dynamics in continuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5094","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":"sha256:7f022612204ca54b7b81fa8fa973878504e4efcbe20471fc2318d6905041d8d7","target":"record","created_at":"2026-05-18T02:28:48Z","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":"196ee14ee43d493afad3b8f16475a3352e7d88610607e24d6f026e276316708a","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-23T14:49:43Z","title_canon_sha256":"7fdf3c176701d0d92c3a1c14b578914e1c0b12a99451dfa06a7af25e71afe703"},"schema_version":"1.0","source":{"id":"1109.5094","kind":"arxiv","version":2}},"canonical_sha256":"24fcc84f40b3d41100533d62e7a626fff3a3f3a19a833505f863b9bfb4b3900b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24fcc84f40b3d41100533d62e7a626fff3a3f3a19a833505f863b9bfb4b3900b","first_computed_at":"2026-05-18T02:28:48.549192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:48.549192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fN4pA4LZ6qSOjYo1bo5cgVkib2U61QSId0vUXA7OfntdAUtlxunSzUxHjncwZuU2pfpVBiwhGk3Wyab1f5hJCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:48.549570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5094","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f022612204ca54b7b81fa8fa973878504e4efcbe20471fc2318d6905041d8d7","sha256:bb1924324235984d812015fa7625f447541bac216fe62bb3534ba6328404e348"],"state_sha256":"341bcc2658619070ebc5b5945ec8bd167abacdae09650350add3efc981149a6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HOhgMemtRqR6YcLOcikKIyr0UuAOpYAwfwo5vzptj4ZR2vS8icxCS8S6Tmn362IWNjF7tAjq2c3RxnpGUVD6Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:58:37.916905Z","bundle_sha256":"677dcccfc9e44aa0fa204b8a2219d5f61094eaca582ec2a2fe2b7835bccfbde0"}}