{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YB4KFZJFFNNTQZGGIEH4WOWADE","short_pith_number":"pith:YB4KFZJF","canonical_record":{"source":{"id":"1107.4005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-20T15:36:07Z","cross_cats_sorted":[],"title_canon_sha256":"9205001e03d561ef518cd8a9775d9ae91edf914f6d1ca7ff6271f69502942535","abstract_canon_sha256":"bc9425dcbce8b234a7c74f5b50b8cd1b5cd0b8d8f23ffafc1e7eb1f7270a7474"},"schema_version":"1.0"},"canonical_sha256":"c078a2e5252b5b3864c6410fcb3ac0190806ad3469e358959b21d9bbdf66b972","source":{"kind":"arxiv","id":"1107.4005","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4005","created_at":"2026-05-18T02:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4005v1","created_at":"2026-05-18T02:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4005","created_at":"2026-05-18T02:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"YB4KFZJFFNNT","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YB4KFZJFFNNTQZGG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YB4KFZJF","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YB4KFZJFFNNTQZGGIEH4WOWADE","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-20T15:36:07Z","cross_cats_sorted":[],"title_canon_sha256":"9205001e03d561ef518cd8a9775d9ae91edf914f6d1ca7ff6271f69502942535","abstract_canon_sha256":"bc9425dcbce8b234a7c74f5b50b8cd1b5cd0b8d8f23ffafc1e7eb1f7270a7474"},"schema_version":"1.0"},"canonical_sha256":"c078a2e5252b5b3864c6410fcb3ac0190806ad3469e358959b21d9bbdf66b972","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:14.212635Z","signature_b64":"rAAMLjGp22VclINWMg11xC1fnp3OJvqPBloovgg/z0gi8QJen3kC8jI9897gRiXms3kAuOoyEMioOKBFPdRrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c078a2e5252b5b3864c6410fcb3ac0190806ad3469e358959b21d9bbdf66b972","last_reissued_at":"2026-05-18T02:01:14.212143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:14.212143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4005","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":"2026-05-18T02:01:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BO880lefHWDPYZiXDYMMnl1LUKvTabYMRkVd+iBw8xBmNFyP9CwBZhWS1HaxntJLWfRyg45gvqsje9Qt9NJkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:56:44.354774Z"},"content_sha256":"f858d421251f0a02d5bb29ca37b9645906a5ace23bae1f34b106fa044e9285b4","schema_version":"1.0","event_id":"sha256:f858d421251f0a02d5bb29ca37b9645906a5ace23bae1f34b106fa044e9285b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YB4KFZJFFNNTQZGGIEH4WOWADE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dmitri Finkelshtein, Eugene Lytvynov, Oleksandr Kutoviy, Yuri Kondratiev","submitted_at":"2011-07-20T15:36:07Z","abstract_excerpt":"Let $\\Gamma$ denote the space of all locally finite subsets (configurations) in $\\mathbb R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\\Gamma$ in which pairs of particles simultaneously hop over $\\mathbb R^d$. We discuss a non-equilibrium dynamics of binary jumps. We prove the existence of an evolution of correlation functions on a finite time interval. We also show that a Vlasov-type mesoscopic scaling for such a dynamics leads to a generalized Boltzmann non-linear equation for the particle density."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4005","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":"2026-05-18T02:01:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lgrS0n+PN2rRcO1OfE7xzP27zU9a1hpUdThF/IH3yQDP1RnzevlljtVrTfqGC8P9qJX6748DTTpMiFXE/WOhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:56:44.355444Z"},"content_sha256":"e0f4d4f7558dff7911231959a9f7f69037c30fc89743f57dd5ca13258f18723a","schema_version":"1.0","event_id":"sha256:e0f4d4f7558dff7911231959a9f7f69037c30fc89743f57dd5ca13258f18723a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YB4KFZJFFNNTQZGGIEH4WOWADE/bundle.json","state_url":"https://pith.science/pith/YB4KFZJFFNNTQZGGIEH4WOWADE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YB4KFZJFFNNTQZGGIEH4WOWADE/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":"2026-06-09T01:56:44Z","links":{"resolver":"https://pith.science/pith/YB4KFZJFFNNTQZGGIEH4WOWADE","bundle":"https://pith.science/pith/YB4KFZJFFNNTQZGGIEH4WOWADE/bundle.json","state":"https://pith.science/pith/YB4KFZJFFNNTQZGGIEH4WOWADE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YB4KFZJFFNNTQZGGIEH4WOWADE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YB4KFZJFFNNTQZGGIEH4WOWADE","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":"bc9425dcbce8b234a7c74f5b50b8cd1b5cd0b8d8f23ffafc1e7eb1f7270a7474","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-20T15:36:07Z","title_canon_sha256":"9205001e03d561ef518cd8a9775d9ae91edf914f6d1ca7ff6271f69502942535"},"schema_version":"1.0","source":{"id":"1107.4005","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4005","created_at":"2026-05-18T02:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4005v1","created_at":"2026-05-18T02:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4005","created_at":"2026-05-18T02:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"YB4KFZJFFNNT","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YB4KFZJFFNNTQZGG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YB4KFZJF","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:e0f4d4f7558dff7911231959a9f7f69037c30fc89743f57dd5ca13258f18723a","target":"graph","created_at":"2026-05-18T02:01:14Z","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":"Let $\\Gamma$ denote the space of all locally finite subsets (configurations) in $\\mathbb R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\\Gamma$ in which pairs of particles simultaneously hop over $\\mathbb R^d$. We discuss a non-equilibrium dynamics of binary jumps. We prove the existence of an evolution of correlation functions on a finite time interval. We also show that a Vlasov-type mesoscopic scaling for such a dynamics leads to a generalized Boltzmann non-linear equation for the particle density.","authors_text":"Dmitri Finkelshtein, Eugene Lytvynov, Oleksandr Kutoviy, Yuri Kondratiev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-20T15:36:07Z","title":"Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4005","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:f858d421251f0a02d5bb29ca37b9645906a5ace23bae1f34b106fa044e9285b4","target":"record","created_at":"2026-05-18T02:01:14Z","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":"bc9425dcbce8b234a7c74f5b50b8cd1b5cd0b8d8f23ffafc1e7eb1f7270a7474","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-20T15:36:07Z","title_canon_sha256":"9205001e03d561ef518cd8a9775d9ae91edf914f6d1ca7ff6271f69502942535"},"schema_version":"1.0","source":{"id":"1107.4005","kind":"arxiv","version":1}},"canonical_sha256":"c078a2e5252b5b3864c6410fcb3ac0190806ad3469e358959b21d9bbdf66b972","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c078a2e5252b5b3864c6410fcb3ac0190806ad3469e358959b21d9bbdf66b972","first_computed_at":"2026-05-18T02:01:14.212143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:14.212143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rAAMLjGp22VclINWMg11xC1fnp3OJvqPBloovgg/z0gi8QJen3kC8jI9897gRiXms3kAuOoyEMioOKBFPdRrAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:14.212635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4005","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f858d421251f0a02d5bb29ca37b9645906a5ace23bae1f34b106fa044e9285b4","sha256:e0f4d4f7558dff7911231959a9f7f69037c30fc89743f57dd5ca13258f18723a"],"state_sha256":"59b85749ac6d4e6431c0de07d4c1b8a4a9beb9944e174ed1f279e807cef8ba30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5XG9Unb7bxBwbAHqVqHK2E6K6Kb9P3C4wEei4z/JvxIUDecRIWaXBdVKQ2yJjhGt36/Ud88ukqRX7dMaE6fMBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T01:56:44.361143Z","bundle_sha256":"3f2683dbd4c3d017c2714aee1a60a02502009ff9bc81ab6cb8906b099376aaf8"}}