{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3JNP2HOYS2S2LNRY3VM32YIVOS","short_pith_number":"pith:3JNP2HOY","schema_version":"1.0","canonical_sha256":"da5afd1dd896a5a5b638dd59bd61157480e73b40cf73fac427446c1b1f59eaef","source":{"kind":"arxiv","id":"1402.7249","version":1},"attestation_state":"computed","paper":{"title":"Canonical methods of constructing invariant tori by phase-space sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Mikko Kaasalainen, Teemu Laakso","submitted_at":"2014-02-28T14:09:35Z","abstract_excerpt":"Invariant tori in phase space can be constructed via a nonperturbative canonical transformation applied to a known integrable Hamiltonian H. Hitherto, this process has been carried through with H corresponding to the isochrone potential and the harmonic oscillator. In this paper, we expand the applicability regime of the torus construction method by demonstrating that H can be based on a St\\\"ackel potential, the most general known form of an integrable potential. Also, we present a simple scheme, based on phase space sampling, for recovering the angle variables on the constructed torus. Numeri"},"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":"1402.7249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-28T14:09:35Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d92b9f82d5368833f30a46a6fc048a6dfd163ea5f3215c67f3e699b3f877b485","abstract_canon_sha256":"63f890dbd6e4ae6f06456c8d698fbe315ea7a9751cddca40809ba8675fe1c3c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:25.930122Z","signature_b64":"YQUM3tKkA6OXuYJxCI75I4pR5j18LX2rxHWsvfFR+fHselyp7y1/Uvel8e3Zg4f6AKZL0TFiL0HUIkWtJi9pCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da5afd1dd896a5a5b638dd59bd61157480e73b40cf73fac427446c1b1f59eaef","last_reissued_at":"2026-05-18T02:57:25.929444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:25.929444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Canonical methods of constructing invariant tori by phase-space sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Mikko Kaasalainen, Teemu Laakso","submitted_at":"2014-02-28T14:09:35Z","abstract_excerpt":"Invariant tori in phase space can be constructed via a nonperturbative canonical transformation applied to a known integrable Hamiltonian H. Hitherto, this process has been carried through with H corresponding to the isochrone potential and the harmonic oscillator. In this paper, we expand the applicability regime of the torus construction method by demonstrating that H can be based on a St\\\"ackel potential, the most general known form of an integrable potential. Also, we present a simple scheme, based on phase space sampling, for recovering the angle variables on the constructed torus. Numeri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7249","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":"1402.7249","created_at":"2026-05-18T02:57:25.929568+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.7249v1","created_at":"2026-05-18T02:57:25.929568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.7249","created_at":"2026-05-18T02:57:25.929568+00:00"},{"alias_kind":"pith_short_12","alias_value":"3JNP2HOYS2S2","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3JNP2HOYS2S2LNRY","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3JNP2HOY","created_at":"2026-05-18T12:28:11.866339+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/3JNP2HOYS2S2LNRY3VM32YIVOS","json":"https://pith.science/pith/3JNP2HOYS2S2LNRY3VM32YIVOS.json","graph_json":"https://pith.science/api/pith-number/3JNP2HOYS2S2LNRY3VM32YIVOS/graph.json","events_json":"https://pith.science/api/pith-number/3JNP2HOYS2S2LNRY3VM32YIVOS/events.json","paper":"https://pith.science/paper/3JNP2HOY"},"agent_actions":{"view_html":"https://pith.science/pith/3JNP2HOYS2S2LNRY3VM32YIVOS","download_json":"https://pith.science/pith/3JNP2HOYS2S2LNRY3VM32YIVOS.json","view_paper":"https://pith.science/paper/3JNP2HOY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.7249&json=true","fetch_graph":"https://pith.science/api/pith-number/3JNP2HOYS2S2LNRY3VM32YIVOS/graph.json","fetch_events":"https://pith.science/api/pith-number/3JNP2HOYS2S2LNRY3VM32YIVOS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3JNP2HOYS2S2LNRY3VM32YIVOS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3JNP2HOYS2S2LNRY3VM32YIVOS/action/storage_attestation","attest_author":"https://pith.science/pith/3JNP2HOYS2S2LNRY3VM32YIVOS/action/author_attestation","sign_citation":"https://pith.science/pith/3JNP2HOYS2S2LNRY3VM32YIVOS/action/citation_signature","submit_replication":"https://pith.science/pith/3JNP2HOYS2S2LNRY3VM32YIVOS/action/replication_record"}},"created_at":"2026-05-18T02:57:25.929568+00:00","updated_at":"2026-05-18T02:57:25.929568+00:00"}