{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:6SLKVWXRNDBUUEGGOZRMX3RMS6","short_pith_number":"pith:6SLKVWXR","schema_version":"1.0","canonical_sha256":"f496aadaf168c34a10c67662cbee2c9791353c33044fe09d7052c4ae13c25a69","source":{"kind":"arxiv","id":"math-ph/0610069","version":2},"attestation_state":"computed","paper":{"title":"Invariant varieties of periodic points for some higher dimensional integrable maps","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Noriko Saitoh, Satoru Saito","submitted_at":"2006-10-25T19:49:44Z","abstract_excerpt":"By studying various rational integrable maps on $\\mathbf{\\hat C}^d$ with $p$ invariants, we show that periodic points form an invariant variety of dimension $\\ge p$ for each period, in contrast to the case of nonintegrable maps in which they are isolated. We prove the theorem: {\\it `If there is an invariant variety of periodic points of some period, there is no set of isolated periodic points of other period in the map.'}"},"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":"math-ph/0610069","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-10-25T19:49:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"97bb0884e246c5023d31f3d439b2d8748771fa0f0c5d5d93dd1d43964efa49e7","abstract_canon_sha256":"8d603d3a695502e3b170b20902efc5dea4604e59ba9c165f65f52c774dc038fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:32.574802Z","signature_b64":"F3fC2DG6RP6n4rTyCMyxuX368meLP1eVh7ot91Dg6e/ODSFVnnteZ3rmIGEcwk/ou+7Uvwj4M7F+KMb7MiTBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f496aadaf168c34a10c67662cbee2c9791353c33044fe09d7052c4ae13c25a69","last_reissued_at":"2026-05-18T01:38:32.574139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:32.574139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant varieties of periodic points for some higher dimensional integrable maps","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Noriko Saitoh, Satoru Saito","submitted_at":"2006-10-25T19:49:44Z","abstract_excerpt":"By studying various rational integrable maps on $\\mathbf{\\hat C}^d$ with $p$ invariants, we show that periodic points form an invariant variety of dimension $\\ge p$ for each period, in contrast to the case of nonintegrable maps in which they are isolated. We prove the theorem: {\\it `If there is an invariant variety of periodic points of some period, there is no set of isolated periodic points of other period in the map.'}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0610069","kind":"arxiv","version":2},"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":"math-ph/0610069","created_at":"2026-05-18T01:38:32.574258+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0610069v2","created_at":"2026-05-18T01:38:32.574258+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0610069","created_at":"2026-05-18T01:38:32.574258+00:00"},{"alias_kind":"pith_short_12","alias_value":"6SLKVWXRNDBU","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"6SLKVWXRNDBUUEGG","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"6SLKVWXR","created_at":"2026-05-18T12:25:53.939244+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/6SLKVWXRNDBUUEGGOZRMX3RMS6","json":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6.json","graph_json":"https://pith.science/api/pith-number/6SLKVWXRNDBUUEGGOZRMX3RMS6/graph.json","events_json":"https://pith.science/api/pith-number/6SLKVWXRNDBUUEGGOZRMX3RMS6/events.json","paper":"https://pith.science/paper/6SLKVWXR"},"agent_actions":{"view_html":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6","download_json":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6.json","view_paper":"https://pith.science/paper/6SLKVWXR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0610069&json=true","fetch_graph":"https://pith.science/api/pith-number/6SLKVWXRNDBUUEGGOZRMX3RMS6/graph.json","fetch_events":"https://pith.science/api/pith-number/6SLKVWXRNDBUUEGGOZRMX3RMS6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6/action/storage_attestation","attest_author":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6/action/author_attestation","sign_citation":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6/action/citation_signature","submit_replication":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6/action/replication_record"}},"created_at":"2026-05-18T01:38:32.574258+00:00","updated_at":"2026-05-18T01:38:32.574258+00:00"}