{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:2EAORBUAE6WHWMMWFMQP35TNAK","short_pith_number":"pith:2EAORBUA","schema_version":"1.0","canonical_sha256":"d100e8868027ac7b31962b20fdf66d028f934f211ba64f6ef7b9d8057ad1617a","source":{"kind":"arxiv","id":"0905.0088","version":1},"attestation_state":"computed","paper":{"title":"Indices of the iterates of ({\\Bbb R}^3)-homeomorphisms at fixed points which are isolated invariant sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Francisco R. Ruiz del Portal, Jos\\'e M. Salazar, Patrice Le Calvez","submitted_at":"2009-05-01T13:16:46Z","abstract_excerpt":"Let (U \\subset {\\mathbb R}^3) be an open set and (f:U \\to f(U) \\subset {\\mathbb R}^3) be a homeomorphism. Let (p \\in U) be a fixed point. It is known that, if (\\{p\\}) is not an isolated invariant set, the sequence of the fixed point indices of the iterates of (f) at (p), ((i(f^n,p))_{n\\geq 1}), is, in general, unbounded. The main goal of this paper is to show that when (\\{p\\}) is an isolated invariant set, the sequence ((i(f^n,p))_{n\\geq 1}) is periodic. Conversely, we show that for any periodic sequence of integers ((I_n)_{n \\geq1}) satisfying Dold's necessary congruences, there exists an ori"},"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":"0905.0088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-05-01T13:16:46Z","cross_cats_sorted":[],"title_canon_sha256":"9db83b4cf07412c088186d8ffc2b35fe85d66f41c51ff26b959baf4f64a19785","abstract_canon_sha256":"f3cf32d3a7abc75753d8c3dbc0c2324b39d1017f6e6f969178ec55cf0b6e9f1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:03.311643Z","signature_b64":"yHS0yaQ7Nfcb252uTpzIwQ+VizLyM5IKyaGfPkqNRbQkdk134HNvDXs7l8IHHp/qVg6yBCBNXmlE/mZVbZVmCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d100e8868027ac7b31962b20fdf66d028f934f211ba64f6ef7b9d8057ad1617a","last_reissued_at":"2026-05-18T02:58:03.310928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:03.310928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Indices of the iterates of ({\\Bbb R}^3)-homeomorphisms at fixed points which are isolated invariant sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Francisco R. Ruiz del Portal, Jos\\'e M. Salazar, Patrice Le Calvez","submitted_at":"2009-05-01T13:16:46Z","abstract_excerpt":"Let (U \\subset {\\mathbb R}^3) be an open set and (f:U \\to f(U) \\subset {\\mathbb R}^3) be a homeomorphism. Let (p \\in U) be a fixed point. It is known that, if (\\{p\\}) is not an isolated invariant set, the sequence of the fixed point indices of the iterates of (f) at (p), ((i(f^n,p))_{n\\geq 1}), is, in general, unbounded. The main goal of this paper is to show that when (\\{p\\}) is an isolated invariant set, the sequence ((i(f^n,p))_{n\\geq 1}) is periodic. Conversely, we show that for any periodic sequence of integers ((I_n)_{n \\geq1}) satisfying Dold's necessary congruences, there exists an ori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0088","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":"0905.0088","created_at":"2026-05-18T02:58:03.311049+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.0088v1","created_at":"2026-05-18T02:58:03.311049+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0088","created_at":"2026-05-18T02:58:03.311049+00:00"},{"alias_kind":"pith_short_12","alias_value":"2EAORBUAE6WH","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"2EAORBUAE6WHWMMW","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"2EAORBUA","created_at":"2026-05-18T12:25:58.018023+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/2EAORBUAE6WHWMMWFMQP35TNAK","json":"https://pith.science/pith/2EAORBUAE6WHWMMWFMQP35TNAK.json","graph_json":"https://pith.science/api/pith-number/2EAORBUAE6WHWMMWFMQP35TNAK/graph.json","events_json":"https://pith.science/api/pith-number/2EAORBUAE6WHWMMWFMQP35TNAK/events.json","paper":"https://pith.science/paper/2EAORBUA"},"agent_actions":{"view_html":"https://pith.science/pith/2EAORBUAE6WHWMMWFMQP35TNAK","download_json":"https://pith.science/pith/2EAORBUAE6WHWMMWFMQP35TNAK.json","view_paper":"https://pith.science/paper/2EAORBUA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.0088&json=true","fetch_graph":"https://pith.science/api/pith-number/2EAORBUAE6WHWMMWFMQP35TNAK/graph.json","fetch_events":"https://pith.science/api/pith-number/2EAORBUAE6WHWMMWFMQP35TNAK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2EAORBUAE6WHWMMWFMQP35TNAK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2EAORBUAE6WHWMMWFMQP35TNAK/action/storage_attestation","attest_author":"https://pith.science/pith/2EAORBUAE6WHWMMWFMQP35TNAK/action/author_attestation","sign_citation":"https://pith.science/pith/2EAORBUAE6WHWMMWFMQP35TNAK/action/citation_signature","submit_replication":"https://pith.science/pith/2EAORBUAE6WHWMMWFMQP35TNAK/action/replication_record"}},"created_at":"2026-05-18T02:58:03.311049+00:00","updated_at":"2026-05-18T02:58:03.311049+00:00"}