{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZZTFKXFQ2BSSCIWQJNPLDSBTA3","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":"a8e62d0db1d155a46afebe5a9c2c83449976512eb83e2cba228132d9ac791cdd","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-23T20:13:49Z","title_canon_sha256":"2768fc44630d395bb88a78641c89ade1011153b3ccdd5b6f072b09c5693529e6"},"schema_version":"1.0","source":{"id":"2606.25145","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.25145","created_at":"2026-06-25T00:18:19Z"},{"alias_kind":"arxiv_version","alias_value":"2606.25145v1","created_at":"2026-06-25T00:18:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25145","created_at":"2026-06-25T00:18:19Z"},{"alias_kind":"pith_short_12","alias_value":"ZZTFKXFQ2BSS","created_at":"2026-06-25T00:18:19Z"},{"alias_kind":"pith_short_16","alias_value":"ZZTFKXFQ2BSSCIWQ","created_at":"2026-06-25T00:18:19Z"},{"alias_kind":"pith_short_8","alias_value":"ZZTFKXFQ","created_at":"2026-06-25T00:18:19Z"}],"graph_snapshots":[{"event_id":"sha256:d90fdf347b295f0efbc428ae4867d6ac43aa608f99c9a9e9aeafb168cddd3265","target":"graph","created_at":"2026-06-25T00:18:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.25145/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the geometry of classical trajectories generated by separable two-dimensional polynomial potentials of the form $V(x,y)=\\tfrac{1}{2}\\big(x^{2N}+A\\,y^{2N}\\big)$, where $N=1,2,\\ldots,$ and $A>0$. Special emphasis is placed on the emergence of nonlinear Lissajous figures and on the distinction between global and particular superintegrability in the Liouville sense. In the harmonic case ($N=1$) closed periodic orbits are a consequence of an additional \\emph{global} integral of motion whenever the frequency ratio is rational, rendering the system maximally superintegrable. In contras","authors_text":"A. M. Escobar-Ruiz, R. Azuaje","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-23T20:13:49Z","title":"Nonlinear Lissajous orbits and particular superintegrability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25145","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":"sha256:0fd7d8783c0fa8932ea28fe6a79db2e202daccd5c52286a1adeac9bafd3a0947","target":"record","created_at":"2026-06-25T00:18:19Z","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":"a8e62d0db1d155a46afebe5a9c2c83449976512eb83e2cba228132d9ac791cdd","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-23T20:13:49Z","title_canon_sha256":"2768fc44630d395bb88a78641c89ade1011153b3ccdd5b6f072b09c5693529e6"},"schema_version":"1.0","source":{"id":"2606.25145","kind":"arxiv","version":1}},"canonical_sha256":"ce66555cb0d0652122d04b5eb1c83306e10389d751c5ef4e070ef1f3c0c0cc85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce66555cb0d0652122d04b5eb1c83306e10389d751c5ef4e070ef1f3c0c0cc85","first_computed_at":"2026-06-25T00:18:19.241971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T00:18:19.241971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EpmlGFq0/MyJzy62utyVB7NDEHhN/MoeT/2qdjLVyKo0lQMCMQuajGuDUFFdvJMM3wHu/XgfXrLCcqEJEvYgBg==","signature_status":"signed_v1","signed_at":"2026-06-25T00:18:19.242310Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.25145","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fd7d8783c0fa8932ea28fe6a79db2e202daccd5c52286a1adeac9bafd3a0947","sha256:d90fdf347b295f0efbc428ae4867d6ac43aa608f99c9a9e9aeafb168cddd3265"],"state_sha256":"ead0fb788a4852a86b883970e3232a90d310bff1ebf4c006c14854363d5a2e57"}