{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:B23A7G4SXC5SLKTP77RZPMYZ42","short_pith_number":"pith:B23A7G4S","canonical_record":{"source":{"id":"1407.1641","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-07-07T09:33:46Z","cross_cats_sorted":[],"title_canon_sha256":"92e334a0a27d7fd270054c6f7a77c155ac0079c83ee45539f2cefa7e3c964bdb","abstract_canon_sha256":"9c27be13f2e9ff61f896475f171131e87f83c6cae9c815ab203875d174906dcc"},"schema_version":"1.0"},"canonical_sha256":"0eb60f9b92b8bb25aa6fffe397b319e691395b37b2f43018f9a8ba52a67f25f5","source":{"kind":"arxiv","id":"1407.1641","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1641","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1641v1","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1641","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"pith_short_12","alias_value":"B23A7G4SXC5S","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B23A7G4SXC5SLKTP","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B23A7G4S","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:B23A7G4SXC5SLKTP77RZPMYZ42","target":"record","payload":{"canonical_record":{"source":{"id":"1407.1641","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-07-07T09:33:46Z","cross_cats_sorted":[],"title_canon_sha256":"92e334a0a27d7fd270054c6f7a77c155ac0079c83ee45539f2cefa7e3c964bdb","abstract_canon_sha256":"9c27be13f2e9ff61f896475f171131e87f83c6cae9c815ab203875d174906dcc"},"schema_version":"1.0"},"canonical_sha256":"0eb60f9b92b8bb25aa6fffe397b319e691395b37b2f43018f9a8ba52a67f25f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:10.833203Z","signature_b64":"/4SRmb6k+jH+srrbJfEqqs24D46LpkMO7hIOiTey3W9GaC5+ptioia5I8y9/MhGTnsbxZYd9SvD6Pq5j5t0ZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0eb60f9b92b8bb25aa6fffe397b319e691395b37b2f43018f9a8ba52a67f25f5","last_reissued_at":"2026-05-18T02:48:10.832738Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:10.832738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.1641","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":"2026-05-18T02:48:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uYn9jaj4DbO6a3eQU9EP1rS3H5YgM0JjWw4mgb/gvIrv0SQb1d58BiakTiTIW9HURRG8RtOJnlp+PoBhs89WCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:54:04.665277Z"},"content_sha256":"a1807da94a541254e4a12351f1cdf7712e8bd7bcbd6e26b98f4ce6d77df28b57","schema_version":"1.0","event_id":"sha256:a1807da94a541254e4a12351f1cdf7712e8bd7bcbd6e26b98f4ce6d77df28b57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:B23A7G4SXC5SLKTP77RZPMYZ42","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-particle dynamical systems and polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Maria V. Demina, Nikolai A. Kudryashov","submitted_at":"2014-07-07T09:33:46Z","abstract_excerpt":"Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is described. The method enables one to integrate a wide class of polynomial multi--particle dynamical systems. The general solutions of certain dynamical systems related to linear second--order partial differential equations are found. As a by-product of our results, new families of orthogonal polynomials are derived. Our approach is also applicable to dynamica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1641","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":"2026-05-18T02:48:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"volUynkZqn1VwG84nAorXLyLggMesRAvVTzyURiDYK1+siU8r99udRCLLAw+VEw1OcusJLk7/F8fY36FtxKPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:54:04.665648Z"},"content_sha256":"815aaf9e2f4b4f0089a2cb156fc60363f7fe0af7bbb60582ec4d176d9a191d18","schema_version":"1.0","event_id":"sha256:815aaf9e2f4b4f0089a2cb156fc60363f7fe0af7bbb60582ec4d176d9a191d18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B23A7G4SXC5SLKTP77RZPMYZ42/bundle.json","state_url":"https://pith.science/pith/B23A7G4SXC5SLKTP77RZPMYZ42/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B23A7G4SXC5SLKTP77RZPMYZ42/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":"2026-06-02T04:54:04Z","links":{"resolver":"https://pith.science/pith/B23A7G4SXC5SLKTP77RZPMYZ42","bundle":"https://pith.science/pith/B23A7G4SXC5SLKTP77RZPMYZ42/bundle.json","state":"https://pith.science/pith/B23A7G4SXC5SLKTP77RZPMYZ42/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B23A7G4SXC5SLKTP77RZPMYZ42/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B23A7G4SXC5SLKTP77RZPMYZ42","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":"9c27be13f2e9ff61f896475f171131e87f83c6cae9c815ab203875d174906dcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-07-07T09:33:46Z","title_canon_sha256":"92e334a0a27d7fd270054c6f7a77c155ac0079c83ee45539f2cefa7e3c964bdb"},"schema_version":"1.0","source":{"id":"1407.1641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1641","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1641v1","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1641","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"pith_short_12","alias_value":"B23A7G4SXC5S","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B23A7G4SXC5SLKTP","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B23A7G4S","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:815aaf9e2f4b4f0089a2cb156fc60363f7fe0af7bbb60582ec4d176d9a191d18","target":"graph","created_at":"2026-05-18T02:48:10Z","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":"Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is described. The method enables one to integrate a wide class of polynomial multi--particle dynamical systems. The general solutions of certain dynamical systems related to linear second--order partial differential equations are found. As a by-product of our results, new families of orthogonal polynomials are derived. Our approach is also applicable to dynamica","authors_text":"Maria V. Demina, Nikolai A. Kudryashov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-07-07T09:33:46Z","title":"Multi-particle dynamical systems and polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1641","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:a1807da94a541254e4a12351f1cdf7712e8bd7bcbd6e26b98f4ce6d77df28b57","target":"record","created_at":"2026-05-18T02:48:10Z","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":"9c27be13f2e9ff61f896475f171131e87f83c6cae9c815ab203875d174906dcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-07-07T09:33:46Z","title_canon_sha256":"92e334a0a27d7fd270054c6f7a77c155ac0079c83ee45539f2cefa7e3c964bdb"},"schema_version":"1.0","source":{"id":"1407.1641","kind":"arxiv","version":1}},"canonical_sha256":"0eb60f9b92b8bb25aa6fffe397b319e691395b37b2f43018f9a8ba52a67f25f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0eb60f9b92b8bb25aa6fffe397b319e691395b37b2f43018f9a8ba52a67f25f5","first_computed_at":"2026-05-18T02:48:10.832738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:10.832738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/4SRmb6k+jH+srrbJfEqqs24D46LpkMO7hIOiTey3W9GaC5+ptioia5I8y9/MhGTnsbxZYd9SvD6Pq5j5t0ZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:10.833203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1807da94a541254e4a12351f1cdf7712e8bd7bcbd6e26b98f4ce6d77df28b57","sha256:815aaf9e2f4b4f0089a2cb156fc60363f7fe0af7bbb60582ec4d176d9a191d18"],"state_sha256":"2a668ec9df3f9a1678291edb37d2e662c193680ff8d8ce71616deaa1686d70b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mgLlye2oKZwoqCLNnEW13pFeTpe29ieP0DkMz5isEN+uhtG0pUisFXGCXzuDN0DZZ8q6uRYj2pKg4ZINQ/BtCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:54:04.668826Z","bundle_sha256":"f94bd385c4d9a0a5a9ab6096df4fd3187f145fdab37708692cc788f6efc2fefa"}}