{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PVXUTT5VSAVUTEL2775RLOPQ4S","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":"7f3c3c27210f93e4e0e56a3f1301e5f1ba9f6dc1c0f2f1c9bfa87219e6f4d0d1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-03-14T21:28:55Z","title_canon_sha256":"542c76e08582e9fe93560e1ea6130a73d50a510f9afca13e8722b44deb382fe0"},"schema_version":"1.0","source":{"id":"1503.04351","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04351","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04351v1","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04351","created_at":"2026-05-18T02:23:25Z"},{"alias_kind":"pith_short_12","alias_value":"PVXUTT5VSAVU","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PVXUTT5VSAVUTEL2","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PVXUTT5V","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:2ac305f153d0423fd1ce5ebe28808ed7ae90011eec264bb87765ba4b8ea1d937","target":"graph","created_at":"2026-05-18T02:23:25Z","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":"In this paper we propose a lattice analog of phase-space fractional Liouville equation. The Liouville equation for phase-space lattice with long-range jumps of power-law types is suggested. We prove that the continuum limit transforms this lattice equation into Liouville equation with conjugate Riesz fractional derivatives of non-integer orders with respect to coordinates of continuum phase-space. An application of the fractional Liouville equation with these Riesz fractional derivatives to describe properties of plasma-like nonlocal media is considered.","authors_text":"Vasily E. Tarasov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-03-14T21:28:55Z","title":"Fractional Liouville Equation on Lattice Phase-Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04351","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:bf358305c86476b3a82b107e52abc6dcf50635909ce4e3d8f113cf5e168ad2cb","target":"record","created_at":"2026-05-18T02:23:25Z","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":"7f3c3c27210f93e4e0e56a3f1301e5f1ba9f6dc1c0f2f1c9bfa87219e6f4d0d1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-03-14T21:28:55Z","title_canon_sha256":"542c76e08582e9fe93560e1ea6130a73d50a510f9afca13e8722b44deb382fe0"},"schema_version":"1.0","source":{"id":"1503.04351","kind":"arxiv","version":1}},"canonical_sha256":"7d6f49cfb5902b49917afffb15b9f0e4988b7c936517fa68b869a3ba6b30ea1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d6f49cfb5902b49917afffb15b9f0e4988b7c936517fa68b869a3ba6b30ea1e","first_computed_at":"2026-05-18T02:23:25.378867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:25.378867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E+mdeMgWtXuaH4956bcKOuU8/yf7RoUQfTR6gBYUcojIZIBe6FbUbqGil8WXpl9Jwg/IDGh/+qou41KAW+AUDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:25.379398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04351","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf358305c86476b3a82b107e52abc6dcf50635909ce4e3d8f113cf5e168ad2cb","sha256:2ac305f153d0423fd1ce5ebe28808ed7ae90011eec264bb87765ba4b8ea1d937"],"state_sha256":"71c5d24c9f43d45453c3c8d930179e9c431e3672f204d4a27bbd9efbb7693591"}