{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YFZ3NZPJNJRCUULJW6SQBSCCYA","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":"2d371f1facde641b652e2c3a4fe1e64614896e00b6867cdd41f7492fd161fb0c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-08T13:42:57Z","title_canon_sha256":"1104844cef12192668319787e49a34539a9e499c084a2cdb2bd3d11fac89d6c3"},"schema_version":"1.0","source":{"id":"1407.2080","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2080","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2080v1","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2080","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"pith_short_12","alias_value":"YFZ3NZPJNJRC","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YFZ3NZPJNJRCUULJ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YFZ3NZPJ","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:9e755d0e9a9e56605109594291ff609f41c2bceb36f41e2fa2e7234bb1bc1250","target":"graph","created_at":"2026-05-18T02:48:08Z","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":"Various many-body models are treated, which describe $N$ points confined to move on a plane circle. Their Newtonian equations of motion (\"accelerations equal forces\") are integrable, i. e. they allow the explicit exhibition of $N$ constants of motion in terms of the dependent variables and their time-derivatives. Some of these models are moreover solvable by purely algebraic operations, by (explicitly performable) quadratures and, finally, by functional inversions. The techniques to manufacture these models are not new; some of these models are themselves new; others are reinterpretations of k","authors_text":"Francesco Calogero, Oksana Bihun","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-08T13:42:57Z","title":"Solvable and/or integrable many-body models on a circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2080","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:f68c4ca713bddad786ec41b2a76df5b2b5e8dc270c50f1f5da07a24151737b3e","target":"record","created_at":"2026-05-18T02:48:08Z","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":"2d371f1facde641b652e2c3a4fe1e64614896e00b6867cdd41f7492fd161fb0c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-08T13:42:57Z","title_canon_sha256":"1104844cef12192668319787e49a34539a9e499c084a2cdb2bd3d11fac89d6c3"},"schema_version":"1.0","source":{"id":"1407.2080","kind":"arxiv","version":1}},"canonical_sha256":"c173b6e5e96a622a5169b7a500c842c029c4f0dfe28b63791445b865c9f8e92f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c173b6e5e96a622a5169b7a500c842c029c4f0dfe28b63791445b865c9f8e92f","first_computed_at":"2026-05-18T02:48:08.496156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:08.496156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BxylpHQmASfuEp/din3aYR12D8Wi5bj8Hr94e4kAnn5L7o4TSoc0mNIqkh09FHXJqkD4p0UWapoGN+pljvzNCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:08.496708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2080","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f68c4ca713bddad786ec41b2a76df5b2b5e8dc270c50f1f5da07a24151737b3e","sha256:9e755d0e9a9e56605109594291ff609f41c2bceb36f41e2fa2e7234bb1bc1250"],"state_sha256":"0ec8674719ef91cd368aae3413273c68ad68449f5d3c851df198056fceecf9cf"}