{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:5IWNDXLBSCJG3W6XQDLP7AKQ5S","short_pith_number":"pith:5IWNDXLB","schema_version":"1.0","canonical_sha256":"ea2cd1dd6190926ddbd780d6ff8150ec966ee481b34843a3b649704e0aac13b7","source":{"kind":"arxiv","id":"0805.1152","version":1},"attestation_state":"computed","paper":{"title":"The real analytic Feigenbaum-Coullet-Tresser attractor in the disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"E. Catsigeras, H. Enrich, M. Cerminara","submitted_at":"2008-05-08T12:34:30Z","abstract_excerpt":"We consider a real analytic diffeomorphism $\\psi_0$ on a n-dimensional disk D, n >= 2, exhibiting a Feigenbaum-Coullet-Tresser (F.C.T.) attractor, being far, in the standard topology of the real analytic diffeomorphism space C(D), from the standard F.C.T. map $\\phi_0$ fixed by the double renormalization. We prove that $\\psi_0$ persists along a codimension-one manifold M \\subset C(D), and that it is the bifurcating map along any one-parameter family in $C(D)$ transversal to M, from diffeomorphisms attracted to sinks, to those which exhibit chaos. The main tool in the proofs is a theorem of Func"},"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":"0805.1152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-05-08T12:34:30Z","cross_cats_sorted":[],"title_canon_sha256":"20c63012dbc1147fb2b723a9e055096a896fc85351410203effd93657da047fb","abstract_canon_sha256":"dcb0096933d83d214bba03c145d0ff247f0e696f4da197d9254c515268d33437"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:51.310447Z","signature_b64":"def5mAy2wVhq0pAmgih4lYYnfBMIBNBlTrbvh6zrmdukXomWya/Jrlon5upSaeBv6ffOqGO4QafVTRU5pvTPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea2cd1dd6190926ddbd780d6ff8150ec966ee481b34843a3b649704e0aac13b7","last_reissued_at":"2026-05-18T04:31:51.309746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:51.309746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The real analytic Feigenbaum-Coullet-Tresser attractor in the disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"E. Catsigeras, H. Enrich, M. Cerminara","submitted_at":"2008-05-08T12:34:30Z","abstract_excerpt":"We consider a real analytic diffeomorphism $\\psi_0$ on a n-dimensional disk D, n >= 2, exhibiting a Feigenbaum-Coullet-Tresser (F.C.T.) attractor, being far, in the standard topology of the real analytic diffeomorphism space C(D), from the standard F.C.T. map $\\phi_0$ fixed by the double renormalization. We prove that $\\psi_0$ persists along a codimension-one manifold M \\subset C(D), and that it is the bifurcating map along any one-parameter family in $C(D)$ transversal to M, from diffeomorphisms attracted to sinks, to those which exhibit chaos. The main tool in the proofs is a theorem of Func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1152","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":"0805.1152","created_at":"2026-05-18T04:31:51.309871+00:00"},{"alias_kind":"arxiv_version","alias_value":"0805.1152v1","created_at":"2026-05-18T04:31:51.309871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.1152","created_at":"2026-05-18T04:31:51.309871+00:00"},{"alias_kind":"pith_short_12","alias_value":"5IWNDXLBSCJG","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"5IWNDXLBSCJG3W6X","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"5IWNDXLB","created_at":"2026-05-18T12:25:56.245647+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/5IWNDXLBSCJG3W6XQDLP7AKQ5S","json":"https://pith.science/pith/5IWNDXLBSCJG3W6XQDLP7AKQ5S.json","graph_json":"https://pith.science/api/pith-number/5IWNDXLBSCJG3W6XQDLP7AKQ5S/graph.json","events_json":"https://pith.science/api/pith-number/5IWNDXLBSCJG3W6XQDLP7AKQ5S/events.json","paper":"https://pith.science/paper/5IWNDXLB"},"agent_actions":{"view_html":"https://pith.science/pith/5IWNDXLBSCJG3W6XQDLP7AKQ5S","download_json":"https://pith.science/pith/5IWNDXLBSCJG3W6XQDLP7AKQ5S.json","view_paper":"https://pith.science/paper/5IWNDXLB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0805.1152&json=true","fetch_graph":"https://pith.science/api/pith-number/5IWNDXLBSCJG3W6XQDLP7AKQ5S/graph.json","fetch_events":"https://pith.science/api/pith-number/5IWNDXLBSCJG3W6XQDLP7AKQ5S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5IWNDXLBSCJG3W6XQDLP7AKQ5S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5IWNDXLBSCJG3W6XQDLP7AKQ5S/action/storage_attestation","attest_author":"https://pith.science/pith/5IWNDXLBSCJG3W6XQDLP7AKQ5S/action/author_attestation","sign_citation":"https://pith.science/pith/5IWNDXLBSCJG3W6XQDLP7AKQ5S/action/citation_signature","submit_replication":"https://pith.science/pith/5IWNDXLBSCJG3W6XQDLP7AKQ5S/action/replication_record"}},"created_at":"2026-05-18T04:31:51.309871+00:00","updated_at":"2026-05-18T04:31:51.309871+00:00"}