{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:DOSQV7GCATM7DRKBI7BQ3VX6ZF","short_pith_number":"pith:DOSQV7GC","schema_version":"1.0","canonical_sha256":"1ba50afcc204d9f1c54147c30dd6fec97d066ebdeb455eea908fe3178bdcd89a","source":{"kind":"arxiv","id":"0803.0849","version":1},"attestation_state":"computed","paper":{"title":"The Universal Cardinal Ordering of Fixed Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"A. Gonzalez Gomez, Jesus San Martin, M. Jose Moscoso","submitted_at":"2008-03-06T12:55:48Z","abstract_excerpt":"We present the theorem which determines, by a permutation, the cardinal ordering of fixed points for any orbit of a period doubling cascade. The inverse permutation generates the orbit and the symbolic sequence of the orbit is obtained as a corollary. The problem present in the symbolic sequences is solved. There, repeated symbols appear, for example, the R (right), which cannot be distinguished among them as it is not known which R is the rightmost of them all. Therefore, there is a lack of information about the dynamical system. Interestingly enough, it is important to point that this theore"},"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":"0803.0849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2008-03-06T12:55:48Z","cross_cats_sorted":[],"title_canon_sha256":"f4c5811781eea693da152890ec080346a8e1ccab5ec22cfcaf5681559c1412ea","abstract_canon_sha256":"170c0d883a68d16bf83fac1dfc50b159da266f766fb8371ce43e1c3d2fca863d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:00.509993Z","signature_b64":"Uc5BCEpwfhc1kd1uKiBB0LXZ0D8/jS4f2WRL9p0NFlZU7HdMbpi5Y+uTprsRBBfFtACeT4SvwxIq0XVFO3+9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ba50afcc204d9f1c54147c30dd6fec97d066ebdeb455eea908fe3178bdcd89a","last_reissued_at":"2026-05-18T02:16:00.509429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:00.509429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Universal Cardinal Ordering of Fixed Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"A. Gonzalez Gomez, Jesus San Martin, M. Jose Moscoso","submitted_at":"2008-03-06T12:55:48Z","abstract_excerpt":"We present the theorem which determines, by a permutation, the cardinal ordering of fixed points for any orbit of a period doubling cascade. The inverse permutation generates the orbit and the symbolic sequence of the orbit is obtained as a corollary. The problem present in the symbolic sequences is solved. There, repeated symbols appear, for example, the R (right), which cannot be distinguished among them as it is not known which R is the rightmost of them all. Therefore, there is a lack of information about the dynamical system. Interestingly enough, it is important to point that this theore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.0849","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":"0803.0849","created_at":"2026-05-18T02:16:00.509517+00:00"},{"alias_kind":"arxiv_version","alias_value":"0803.0849v1","created_at":"2026-05-18T02:16:00.509517+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.0849","created_at":"2026-05-18T02:16:00.509517+00:00"},{"alias_kind":"pith_short_12","alias_value":"DOSQV7GCATM7","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"DOSQV7GCATM7DRKB","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"DOSQV7GC","created_at":"2026-05-18T12:25:57.157939+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/DOSQV7GCATM7DRKBI7BQ3VX6ZF","json":"https://pith.science/pith/DOSQV7GCATM7DRKBI7BQ3VX6ZF.json","graph_json":"https://pith.science/api/pith-number/DOSQV7GCATM7DRKBI7BQ3VX6ZF/graph.json","events_json":"https://pith.science/api/pith-number/DOSQV7GCATM7DRKBI7BQ3VX6ZF/events.json","paper":"https://pith.science/paper/DOSQV7GC"},"agent_actions":{"view_html":"https://pith.science/pith/DOSQV7GCATM7DRKBI7BQ3VX6ZF","download_json":"https://pith.science/pith/DOSQV7GCATM7DRKBI7BQ3VX6ZF.json","view_paper":"https://pith.science/paper/DOSQV7GC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0803.0849&json=true","fetch_graph":"https://pith.science/api/pith-number/DOSQV7GCATM7DRKBI7BQ3VX6ZF/graph.json","fetch_events":"https://pith.science/api/pith-number/DOSQV7GCATM7DRKBI7BQ3VX6ZF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DOSQV7GCATM7DRKBI7BQ3VX6ZF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DOSQV7GCATM7DRKBI7BQ3VX6ZF/action/storage_attestation","attest_author":"https://pith.science/pith/DOSQV7GCATM7DRKBI7BQ3VX6ZF/action/author_attestation","sign_citation":"https://pith.science/pith/DOSQV7GCATM7DRKBI7BQ3VX6ZF/action/citation_signature","submit_replication":"https://pith.science/pith/DOSQV7GCATM7DRKBI7BQ3VX6ZF/action/replication_record"}},"created_at":"2026-05-18T02:16:00.509517+00:00","updated_at":"2026-05-18T02:16:00.509517+00:00"}