{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:2VNGW35HHUMJZUXLFWE7VA323B","short_pith_number":"pith:2VNGW35H","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"},"canonical_sha256":"d55a6b6fa73d189cd2eb2d89fa837ad8580df784400b36a54b161f925e8cf92b","source":{"kind":"arxiv","id":"nlin/0512013","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0512013","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0512013v1","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0512013","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"pith_short_12","alias_value":"2VNGW35HHUMJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"2VNGW35HHUMJZUXL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"2VNGW35H","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:2VNGW35HHUMJZUXLFWE7VA323B","target":"record","payload":{"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"},"canonical_sha256":"d55a6b6fa73d189cd2eb2d89fa837ad8580df784400b36a54b161f925e8cf92b","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"},"source_kind":"arxiv","source_id":"nlin/0512013","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":"2026-05-18T02:27:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6hxIOeqvWU1+GcDuBYmEDuUjpUNDqKRXMXJxEE7FrNmfHgSPUNEo4WXrFszj1yI6gDGFZExpdutf3VkkktwcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:12:44.076004Z"},"content_sha256":"b820877c87bab384015b63394ead584b9de74938acf01529aec22d65fc156649","schema_version":"1.0","event_id":"sha256:b820877c87bab384015b63394ead584b9de74938acf01529aec22d65fc156649"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:2VNGW35HHUMJZUXLFWE7VA323B","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HxVgO/Z8npDDCu0eIQG6J7vXXptIIh2YZJ33CdRyx1anKeuiw19UNhKYoTolSYTZ27oUB9ZmCYKGkZn4R4V8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:12:44.076358Z"},"content_sha256":"73b03ebb04819fca34453578bd9b1c0f7371a0d2a7dd158fa89dacb4b7fa8c92","schema_version":"1.0","event_id":"sha256:73b03ebb04819fca34453578bd9b1c0f7371a0d2a7dd158fa89dacb4b7fa8c92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B/bundle.json","state_url":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2VNGW35HHUMJZUXLFWE7VA323B/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":"2026-06-01T19:12:44Z","links":{"resolver":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B","bundle":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B/bundle.json","state":"https://pith.science/pith/2VNGW35HHUMJZUXLFWE7VA323B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2VNGW35HHUMJZUXLFWE7VA323B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:2VNGW35HHUMJZUXLFWE7VA323B","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":"dd5fd1b70b28c92014947069abddba1ac82b4474a73a9d84e07341a7d0f79112","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","nlin.CD","physics.class-ph"],"license":"","primary_cat":"nlin.PS","submitted_at":"2005-12-06T21:00:33Z","title_canon_sha256":"9abf4ad409a3e26fe9a3e7014eb29d6a777fdf6c64ae05e96f2f592156133439"},"schema_version":"1.0","source":{"id":"nlin/0512013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0512013","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0512013v1","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0512013","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"pith_short_12","alias_value":"2VNGW35HHUMJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"2VNGW35HHUMJZUXL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"2VNGW35H","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:73b03ebb04819fca34453578bd9b1c0f7371a0d2a7dd158fa89dacb4b7fa8c92","target":"graph","created_at":"2026-05-18T02:27:51Z","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":"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 ","authors_text":"George M. Zaslavsky, Vasily E. Tarasov","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","nlin.CD","physics.class-ph"],"headline":"","license":"","primary_cat":"nlin.PS","submitted_at":"2005-12-06T21:00:33Z","title":"Fractional dynamics of coupled oscillators with long-range interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0512013","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:b820877c87bab384015b63394ead584b9de74938acf01529aec22d65fc156649","target":"record","created_at":"2026-05-18T02:27:51Z","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":"dd5fd1b70b28c92014947069abddba1ac82b4474a73a9d84e07341a7d0f79112","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","nlin.CD","physics.class-ph"],"license":"","primary_cat":"nlin.PS","submitted_at":"2005-12-06T21:00:33Z","title_canon_sha256":"9abf4ad409a3e26fe9a3e7014eb29d6a777fdf6c64ae05e96f2f592156133439"},"schema_version":"1.0","source":{"id":"nlin/0512013","kind":"arxiv","version":1}},"canonical_sha256":"d55a6b6fa73d189cd2eb2d89fa837ad8580df784400b36a54b161f925e8cf92b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d55a6b6fa73d189cd2eb2d89fa837ad8580df784400b36a54b161f925e8cf92b","first_computed_at":"2026-05-18T02:27:51.433772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:51.433772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LQLCS+afJOdmT6B1f5muZVbJNPLmgHg4dj93IR18WtzhCuoGwUvjC4+PBAeMpDlrlKoYMU898n+M1lIyTw4wBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:51.434311Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0512013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b820877c87bab384015b63394ead584b9de74938acf01529aec22d65fc156649","sha256:73b03ebb04819fca34453578bd9b1c0f7371a0d2a7dd158fa89dacb4b7fa8c92"],"state_sha256":"5c6003f2b3c3ad99fee069d2470a43e65ef8ffc2d858bb1dedb73980d21e5f4c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QRsib7jabXlZjg6HU9sozFSqjnlVSxrWab4NIUfP0yx/zlZFOKtF7hLDlgfipquOnK167GHI3EcJAkC4ofTIDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:12:44.078359Z","bundle_sha256":"9dca4e4cb58d8cf87d17c7a66272db1e7e0cf1430530d49d3daec02bb4875eac"}}