{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:X7DC7O47YNHFJURDSPASRUPYVK","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":"0724ba47cdec9896eda171725e22bed853a965ae712ce832f5e1459c854ca222","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-07-27T08:14:12Z","title_canon_sha256":"01ca120a48a74ed307a6ef712f0107350c4b71d28af123a123d2140262aa16a7"},"schema_version":"1.0","source":{"id":"1807.10480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10480","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10480v1","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10480","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"X7DC7O47YNHF","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"X7DC7O47YNHFJURD","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"X7DC7O47","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:73e61986e699ed65297a8f29775395e3393b0d8ee6bcfcc444673b424606299e","target":"graph","created_at":"2026-05-18T00:09:40Z","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 statistical counterpart of the formalism of hamiltonian systems with convex dissipation arXiv:0810.1419 , arXiv:1408.3102 is a completely open subject. Here are described a stochastic version of the SBEN principle and a Liouville type theorem which uses a minimal dissipation cost functional.","authors_text":"Marius Buliga","cross_cats":["math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-07-27T08:14:12Z","title":"A stochastic version and a Liouville theorem for hamiltonian inclusions with convex dissipation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10480","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:b4d62e12fa66dfdd1e6e729c48c31d6096f40213235ba60b4ed15ba1bc7284dc","target":"record","created_at":"2026-05-18T00:09:40Z","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":"0724ba47cdec9896eda171725e22bed853a965ae712ce832f5e1459c854ca222","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-07-27T08:14:12Z","title_canon_sha256":"01ca120a48a74ed307a6ef712f0107350c4b71d28af123a123d2140262aa16a7"},"schema_version":"1.0","source":{"id":"1807.10480","kind":"arxiv","version":1}},"canonical_sha256":"bfc62fbb9fc34e54d22393c128d1f8aaa819450f7d8a5af58fc7684823e46cba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfc62fbb9fc34e54d22393c128d1f8aaa819450f7d8a5af58fc7684823e46cba","first_computed_at":"2026-05-18T00:09:40.467787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:40.467787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9IbD6nczCvxx9XnI0AJAivhgiQnZXZ0H4v09qTDNtR6lOXLtAs2stvltYfDW11gwJtfDcp7Fp2jxr0YUi9NDBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:40.468306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.10480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4d62e12fa66dfdd1e6e729c48c31d6096f40213235ba60b4ed15ba1bc7284dc","sha256:73e61986e699ed65297a8f29775395e3393b0d8ee6bcfcc444673b424606299e"],"state_sha256":"d23e696b3d17f9baf65f35fd787478c159a595a51466ca22b3b4dc40da70ee27"}