{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3H2IVFUK3QJSKSLA4RIJ4X4NHE","short_pith_number":"pith:3H2IVFUK","canonical_record":{"source":{"id":"1408.6346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-27T08:41:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b6b2d14c8d950c988daa8d71ec656a4afb0d61b052d067b3792cb1d3a617ae44","abstract_canon_sha256":"876432503c01cb04c4f0cc1f6102a3245c41b28b180509fbbab14d87a0d0e60a"},"schema_version":"1.0"},"canonical_sha256":"d9f48a968adc13254960e4509e5f8d39329698111cf635102cae19637cceec19","source":{"kind":"arxiv","id":"1408.6346","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6346","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6346v1","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6346","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"3H2IVFUK3QJS","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3H2IVFUK3QJSKSLA","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3H2IVFUK","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3H2IVFUK3QJSKSLA4RIJ4X4NHE","target":"record","payload":{"canonical_record":{"source":{"id":"1408.6346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-27T08:41:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b6b2d14c8d950c988daa8d71ec656a4afb0d61b052d067b3792cb1d3a617ae44","abstract_canon_sha256":"876432503c01cb04c4f0cc1f6102a3245c41b28b180509fbbab14d87a0d0e60a"},"schema_version":"1.0"},"canonical_sha256":"d9f48a968adc13254960e4509e5f8d39329698111cf635102cae19637cceec19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:07.705605Z","signature_b64":"Vzk5m1Ob8eZ4yE1yp06C2lBhKnnvZj5eVyirZdZZQvoTb1MUcbGXPSngSKc0EPKoejgSz6Xo3mlAt0PEkbh5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9f48a968adc13254960e4509e5f8d39329698111cf635102cae19637cceec19","last_reissued_at":"2026-05-18T02:44:07.705063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:07.705063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.6346","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":"2026-05-18T02:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6NkWQJxfa3GgqHQoFPGVGBu5Q1jFPYWx5T0C4eTWsU5Nz9HBttXOwzS/82Xd8IKFKXpdY0nJsOCJ7nplsvTwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:33:45.211069Z"},"content_sha256":"e559d56987a119526da9aaa02f5b5376bcc15712f6c749652487b64677cad6b5","schema_version":"1.0","event_id":"sha256:e559d56987a119526da9aaa02f5b5376bcc15712f6c749652487b64677cad6b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3H2IVFUK3QJSKSLA4RIJ4X4NHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free Jump Dynamics in Continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Joanna Baranska, Yuri Kozitsky","submitted_at":"2014-08-27T08:41:05Z","abstract_excerpt":"The evolution is described of an infinite system of hopping point particles in $\\mathbb{R}^d$. The states of the system are probability measures on the space of configurations of particles. Under the condition that the initial state $\\mu_0$ has correlation functions of all orders which are: (a) $k_{\\mu_0}^{(n)} \\in L^\\infty ((\\mathbb{R}^d)^n)$ (essentially bounded); (b) $\\|k_{\\mu_0}^{(n)}\\|_{ L^\\infty ((\\mathbb{R}^d)^n)} \\leq C^n$, $n\\in \\mathbb{N}$ (sub-Poissonian), the evolution $\\mu_0 \\mapsto \\mu_t$, $t>0$, is obtained as a continuously differentiable map $k_{\\mu_0} \\mapsto k_t$, $k_t =(k_t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6346","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":"2026-05-18T02:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KeRacj6n8NpdjoOMuaA1lg7GLSIkgMR5f9eTSzRcKqeoOIAdkEYScErvIl2FjlLr1o1PyNJsgdkQTlHN7lj8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:33:45.211732Z"},"content_sha256":"75544fb21129c908c5e8c902ce7d5d3392f4cd0f18ee19361570575491893ea4","schema_version":"1.0","event_id":"sha256:75544fb21129c908c5e8c902ce7d5d3392f4cd0f18ee19361570575491893ea4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3H2IVFUK3QJSKSLA4RIJ4X4NHE/bundle.json","state_url":"https://pith.science/pith/3H2IVFUK3QJSKSLA4RIJ4X4NHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3H2IVFUK3QJSKSLA4RIJ4X4NHE/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":"2026-05-31T23:33:45Z","links":{"resolver":"https://pith.science/pith/3H2IVFUK3QJSKSLA4RIJ4X4NHE","bundle":"https://pith.science/pith/3H2IVFUK3QJSKSLA4RIJ4X4NHE/bundle.json","state":"https://pith.science/pith/3H2IVFUK3QJSKSLA4RIJ4X4NHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3H2IVFUK3QJSKSLA4RIJ4X4NHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3H2IVFUK3QJSKSLA4RIJ4X4NHE","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":"876432503c01cb04c4f0cc1f6102a3245c41b28b180509fbbab14d87a0d0e60a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-27T08:41:05Z","title_canon_sha256":"b6b2d14c8d950c988daa8d71ec656a4afb0d61b052d067b3792cb1d3a617ae44"},"schema_version":"1.0","source":{"id":"1408.6346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6346","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6346v1","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6346","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"3H2IVFUK3QJS","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3H2IVFUK3QJSKSLA","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3H2IVFUK","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:75544fb21129c908c5e8c902ce7d5d3392f4cd0f18ee19361570575491893ea4","target":"graph","created_at":"2026-05-18T02:44:07Z","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":"The evolution is described of an infinite system of hopping point particles in $\\mathbb{R}^d$. The states of the system are probability measures on the space of configurations of particles. Under the condition that the initial state $\\mu_0$ has correlation functions of all orders which are: (a) $k_{\\mu_0}^{(n)} \\in L^\\infty ((\\mathbb{R}^d)^n)$ (essentially bounded); (b) $\\|k_{\\mu_0}^{(n)}\\|_{ L^\\infty ((\\mathbb{R}^d)^n)} \\leq C^n$, $n\\in \\mathbb{N}$ (sub-Poissonian), the evolution $\\mu_0 \\mapsto \\mu_t$, $t>0$, is obtained as a continuously differentiable map $k_{\\mu_0} \\mapsto k_t$, $k_t =(k_t","authors_text":"Joanna Baranska, Yuri Kozitsky","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-27T08:41:05Z","title":"Free Jump Dynamics in Continuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6346","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:e559d56987a119526da9aaa02f5b5376bcc15712f6c749652487b64677cad6b5","target":"record","created_at":"2026-05-18T02:44:07Z","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":"876432503c01cb04c4f0cc1f6102a3245c41b28b180509fbbab14d87a0d0e60a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-27T08:41:05Z","title_canon_sha256":"b6b2d14c8d950c988daa8d71ec656a4afb0d61b052d067b3792cb1d3a617ae44"},"schema_version":"1.0","source":{"id":"1408.6346","kind":"arxiv","version":1}},"canonical_sha256":"d9f48a968adc13254960e4509e5f8d39329698111cf635102cae19637cceec19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9f48a968adc13254960e4509e5f8d39329698111cf635102cae19637cceec19","first_computed_at":"2026-05-18T02:44:07.705063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:07.705063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vzk5m1Ob8eZ4yE1yp06C2lBhKnnvZj5eVyirZdZZQvoTb1MUcbGXPSngSKc0EPKoejgSz6Xo3mlAt0PEkbh5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:07.705605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e559d56987a119526da9aaa02f5b5376bcc15712f6c749652487b64677cad6b5","sha256:75544fb21129c908c5e8c902ce7d5d3392f4cd0f18ee19361570575491893ea4"],"state_sha256":"d981abadb82ff9e3051b95c661026280f2814e98a6bda4cbeb24dabfcd167264"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UBsfYAs/UNomDqdXCnlosdoYxxs/0cZmvFSAPEA852k4xRK41JNxdnAeSlOzIyMckBRFvUsFPXWDC3S5SCSYCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:33:45.215021Z","bundle_sha256":"026af8cc04937142fbcea711b25d7a6cd613a236aeb7e92ed272a616b7a0f82b"}}