{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:6SLKVWXRNDBUUEGGOZRMX3RMS6","short_pith_number":"pith:6SLKVWXR","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"},"canonical_sha256":"f496aadaf168c34a10c67662cbee2c9791353c33044fe09d7052c4ae13c25a69","source":{"kind":"arxiv","id":"math-ph/0610069","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0610069","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0610069v2","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0610069","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"6SLKVWXRNDBU","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6SLKVWXRNDBUUEGG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6SLKVWXR","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:6SLKVWXRNDBUUEGGOZRMX3RMS6","target":"record","payload":{"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"},"canonical_sha256":"f496aadaf168c34a10c67662cbee2c9791353c33044fe09d7052c4ae13c25a69","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"},"source_kind":"arxiv","source_id":"math-ph/0610069","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/sR+VTRlU/hz8RBtiQYX2MVNrmG+mYiYw18aJ2/zXFDApc5yKU18GXggW7FOiEZiJbdVSr7bna//9AVfa3IoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:22:42.458532Z"},"content_sha256":"9c04aa96be788ae7acb6f861569b9f29b7c31a1b6b69b51ac472ebe93d53d797","schema_version":"1.0","event_id":"sha256:9c04aa96be788ae7acb6f861569b9f29b7c31a1b6b69b51ac472ebe93d53d797"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:6SLKVWXRNDBUUEGGOZRMX3RMS6","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkdpuPh/Up4SpL9z8w6zmDPVerxWnliBfw279CNSTiyilhMzikhJfaNqmKYPVRGW1WrkBNmxa3JPbAyw25lwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:22:42.459176Z"},"content_sha256":"ee5e992641db7ed81083d6b16c7edb93385c5ad3cbfbca84c7f24320c7c7ed0a","schema_version":"1.0","event_id":"sha256:ee5e992641db7ed81083d6b16c7edb93385c5ad3cbfbca84c7f24320c7c7ed0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6/bundle.json","state_url":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6/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":"2026-05-29T18:22:42Z","links":{"resolver":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6","bundle":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6/bundle.json","state":"https://pith.science/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6SLKVWXRNDBUUEGGOZRMX3RMS6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:6SLKVWXRNDBUUEGGOZRMX3RMS6","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":"8d603d3a695502e3b170b20902efc5dea4604e59ba9c165f65f52c774dc038fc","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-10-25T19:49:44Z","title_canon_sha256":"97bb0884e246c5023d31f3d439b2d8748771fa0f0c5d5d93dd1d43964efa49e7"},"schema_version":"1.0","source":{"id":"math-ph/0610069","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0610069","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0610069v2","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0610069","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"6SLKVWXRNDBU","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6SLKVWXRNDBUUEGG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6SLKVWXR","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:ee5e992641db7ed81083d6b16c7edb93385c5ad3cbfbca84c7f24320c7c7ed0a","target":"graph","created_at":"2026-05-18T01:38:32Z","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":"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.'}","authors_text":"Noriko Saitoh, Satoru Saito","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-10-25T19:49:44Z","title":"Invariant varieties of periodic points for some higher dimensional integrable maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0610069","kind":"arxiv","version":2},"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":"sha256:9c04aa96be788ae7acb6f861569b9f29b7c31a1b6b69b51ac472ebe93d53d797","target":"record","created_at":"2026-05-18T01:38:32Z","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":"8d603d3a695502e3b170b20902efc5dea4604e59ba9c165f65f52c774dc038fc","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-10-25T19:49:44Z","title_canon_sha256":"97bb0884e246c5023d31f3d439b2d8748771fa0f0c5d5d93dd1d43964efa49e7"},"schema_version":"1.0","source":{"id":"math-ph/0610069","kind":"arxiv","version":2}},"canonical_sha256":"f496aadaf168c34a10c67662cbee2c9791353c33044fe09d7052c4ae13c25a69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f496aadaf168c34a10c67662cbee2c9791353c33044fe09d7052c4ae13c25a69","first_computed_at":"2026-05-18T01:38:32.574139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:32.574139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F3fC2DG6RP6n4rTyCMyxuX368meLP1eVh7ot91Dg6e/ODSFVnnteZ3rmIGEcwk/ou+7Uvwj4M7F+KMb7MiTBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:32.574802Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0610069","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c04aa96be788ae7acb6f861569b9f29b7c31a1b6b69b51ac472ebe93d53d797","sha256:ee5e992641db7ed81083d6b16c7edb93385c5ad3cbfbca84c7f24320c7c7ed0a"],"state_sha256":"5f935a45e12a405a41096f72c9321c74d6fb24dd346d4b74a85e29ba071529b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H87wuUB9pyi5luGVRLEwWhCWs4Vcgf60ByoSx2egjeb7xhQ68Yt5hz8bY8i1ZK4bPw1x80nhSx05URiN6GuJCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:22:42.462975Z","bundle_sha256":"35eab68344628210279383a9eff291e90cd600c814feecc75e81872e22ad06ef"}}