{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:E3QOFQN2MGPNCS6R547AGG3UWC","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":"e9c16434a375548c96aeaba6293793f9755b06b049680001f808264872de1dfa","cross_cats_sorted":["cond-mat.other","math.DS","math.MP","nlin.CD","physics.class-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2007-02-18T20:13:57Z","title_canon_sha256":"57bb341542a2deef5fc9becaf3b096ae3d2a9213e7445edc00759949faf46b36"},"schema_version":"1.0","source":{"id":"math-ph/0702065","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0702065","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0702065v1","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0702065","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"E3QOFQN2MGPN","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"E3QOFQN2MGPNCS6R","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"E3QOFQN2","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:46281bbaa31cfe6c2442a43bc6026916c3708a0dcbf10eef79953a2f22346ce9","target":"graph","created_at":"2026-05-18T02:25:12Z","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":"Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a fractional generalization of the Ginzburg-Landau and nonlinear Schrodinger equations. As another example, dynamical equations for particles chain with power-law interaction and memory are considered in the continuous limit. The obtained fractional equations can be applied to complex media with/without random parameters or processes.","authors_text":"George M. Zaslavsky, Vasily E. Tarasov","cross_cats":["cond-mat.other","math.DS","math.MP","nlin.CD","physics.class-ph"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2007-02-18T20:13:57Z","title":"Fractional Dynamics of Systems with Long-Range Space Interaction and Temporal Memory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0702065","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:d826cf8596489cc04ded895e3f54848f198b17959acd58c246d6598ebe36d386","target":"record","created_at":"2026-05-18T02:25:12Z","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":"e9c16434a375548c96aeaba6293793f9755b06b049680001f808264872de1dfa","cross_cats_sorted":["cond-mat.other","math.DS","math.MP","nlin.CD","physics.class-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2007-02-18T20:13:57Z","title_canon_sha256":"57bb341542a2deef5fc9becaf3b096ae3d2a9213e7445edc00759949faf46b36"},"schema_version":"1.0","source":{"id":"math-ph/0702065","kind":"arxiv","version":1}},"canonical_sha256":"26e0e2c1ba619ed14bd1ef3e031b74b0b28a6d4ef0ec13bb6eb4b34bf6b5c37f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26e0e2c1ba619ed14bd1ef3e031b74b0b28a6d4ef0ec13bb6eb4b34bf6b5c37f","first_computed_at":"2026-05-18T02:25:12.478130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:12.478130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gmycp3pnJyI19/aPSk7wB/fGXQUSnSxIXKYKs1fNqT7a5zk8f9r6Iei7htWe0M0niTyDsC0ExjgHxBeZu34kDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:12.478705Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0702065","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d826cf8596489cc04ded895e3f54848f198b17959acd58c246d6598ebe36d386","sha256:46281bbaa31cfe6c2442a43bc6026916c3708a0dcbf10eef79953a2f22346ce9"],"state_sha256":"4830f71b03df79b451543e4cfa881016e9f8e4710c4bf10373f23dbe73109b54"}