{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:2VNGW35HHUMJZUXLFWE7VA323B","short_pith_number":"pith:2VNGW35H","schema_version":"1.0","canonical_sha256":"d55a6b6fa73d189cd2eb2d89fa837ad8580df784400b36a54b161f925e8cf92b","source":{"kind":"arxiv","id":"nlin/0512013","version":1},"attestation_state":"computed","paper":{"title":"Fractional dynamics of coupled oscillators with long-range interaction","license":"","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","nlin.CD","physics.class-ph"],"primary_cat":"nlin.PS","authors_text":"George M. Zaslavsky, Vasily E. Tarasov","submitted_at":"2005-12-06T21:00:33Z","abstract_excerpt":"We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range power-wise interaction. The corresponding term in dynamical equations is proportional to $1/|n-m|^{\\alpha+1}$. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order $\\alpha$, when $0<\\alpha<2$. We consider few models of coupled oscillators and show how their synchronization can appear as a result of bifurcation, and how the corresponding solutions depend on $\\alpha$. The presence of fractional derivative "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"nlin/0512013","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.PS","submitted_at":"2005-12-06T21:00:33Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","nlin.CD","physics.class-ph"],"title_canon_sha256":"9abf4ad409a3e26fe9a3e7014eb29d6a777fdf6c64ae05e96f2f592156133439","abstract_canon_sha256":"dd5fd1b70b28c92014947069abddba1ac82b4474a73a9d84e07341a7d0f79112"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:51.434311Z","signature_b64":"LQLCS+afJOdmT6B1f5muZVbJNPLmgHg4dj93IR18WtzhCuoGwUvjC4+PBAeMpDlrlKoYMU898n+M1lIyTw4wBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d55a6b6fa73d189cd2eb2d89fa837ad8580df784400b36a54b161f925e8cf92b","last_reissued_at":"2026-05-18T02:27:51.433772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:51.433772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional dynamics of coupled oscillators with long-range interaction","license":"","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","nlin.CD","physics.class-ph"],"primary_cat":"nlin.PS","authors_text":"George M. Zaslavsky, Vasily E. Tarasov","submitted_at":"2005-12-06T21:00:33Z","abstract_excerpt":"We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range power-wise interaction. The corresponding term in dynamical equations is proportional to $1/|n-m|^{\\alpha+1}$. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order $\\alpha$, when $0<\\alpha<2$. We consider few models of coupled oscillators and show how their synchronization can appear as a result of bifurcation, and how the corresponding solutions depend on $\\alpha$. The presence of fractional derivative "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0512013","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0512013","created_at":"2026-05-18T02:27:51.433847+00:00"},{"alias_kind":"arxiv_version","alias_value":"nlin/0512013v1","created_at":"2026-05-18T02:27:51.433847+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0512013","created_at":"2026-05-18T02:27:51.433847+00:00"},{"alias_kind":"pith_short_12","alias_value":"2VNGW35HHUMJ","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"2VNGW35HHUMJZUXL","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"2VNGW35H","created_at":"2026-05-18T12:25:52.687210+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B","json":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B.json","graph_json":"https://pith.science/api/pith-number/2VNGW35HHUMJZUXLFWE7VA323B/graph.json","events_json":"https://pith.science/api/pith-number/2VNGW35HHUMJZUXLFWE7VA323B/events.json","paper":"https://pith.science/paper/2VNGW35H"},"agent_actions":{"view_html":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B","download_json":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B.json","view_paper":"https://pith.science/paper/2VNGW35H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=nlin/0512013&json=true","fetch_graph":"https://pith.science/api/pith-number/2VNGW35HHUMJZUXLFWE7VA323B/graph.json","fetch_events":"https://pith.science/api/pith-number/2VNGW35HHUMJZUXLFWE7VA323B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B/action/storage_attestation","attest_author":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B/action/author_attestation","sign_citation":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B/action/citation_signature","submit_replication":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B/action/replication_record"}},"created_at":"2026-05-18T02:27:51.433847+00:00","updated_at":"2026-05-18T02:27:51.433847+00:00"}