{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KAP2AJWAWVPLBSYD4LHSW4JVFO","short_pith_number":"pith:KAP2AJWA","schema_version":"1.0","canonical_sha256":"501fa026c0b55eb0cb03e2cf2b71352b9d0583e23bd42f7c2840ca0be591c004","source":{"kind":"arxiv","id":"1004.5029","version":3},"attestation_state":"computed","paper":{"title":"Perturbation of the Lyapunov spectra of periodic orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Bonatti, Jairo Bochi","submitted_at":"2010-04-28T13:42:23Z","abstract_excerpt":"We describe all Lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism. The description is expressed in terms of the finest dominated splitting and Lyapunov exponents that appear in the limit of a sequence of periodic orbits, and involves the majorization partial order. Among the applications, we give a simple criterion for the occurrence of universal dynamics."},"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":"1004.5029","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-04-28T13:42:23Z","cross_cats_sorted":[],"title_canon_sha256":"f97cd1b5c884bcd82a391ba6d5d18b9c9a7dbc4a2d200b941e6f0187ad27fcd0","abstract_canon_sha256":"a682a415edd4bb1ffa526042a5c6e638988b53ee91667ea82bf1e20cdb2dd811"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:15.443807Z","signature_b64":"Ott1bCznsnQCtVBJIIKmWzcVLlE1BLMqmIxOYn+ubW4GesyOhzMfu4PIZGkJgPCN1QCinAJgJclBtKEudPC/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"501fa026c0b55eb0cb03e2cf2b71352b9d0583e23bd42f7c2840ca0be591c004","last_reissued_at":"2026-05-18T02:24:15.443135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:15.443135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perturbation of the Lyapunov spectra of periodic orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Bonatti, Jairo Bochi","submitted_at":"2010-04-28T13:42:23Z","abstract_excerpt":"We describe all Lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism. The description is expressed in terms of the finest dominated splitting and Lyapunov exponents that appear in the limit of a sequence of periodic orbits, and involves the majorization partial order. Among the applications, we give a simple criterion for the occurrence of universal dynamics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5029","kind":"arxiv","version":3},"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":"1004.5029","created_at":"2026-05-18T02:24:15.443231+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.5029v3","created_at":"2026-05-18T02:24:15.443231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5029","created_at":"2026-05-18T02:24:15.443231+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAP2AJWAWVPL","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAP2AJWAWVPLBSYD","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAP2AJWA","created_at":"2026-05-18T12:26:09.077623+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/KAP2AJWAWVPLBSYD4LHSW4JVFO","json":"https://pith.science/pith/KAP2AJWAWVPLBSYD4LHSW4JVFO.json","graph_json":"https://pith.science/api/pith-number/KAP2AJWAWVPLBSYD4LHSW4JVFO/graph.json","events_json":"https://pith.science/api/pith-number/KAP2AJWAWVPLBSYD4LHSW4JVFO/events.json","paper":"https://pith.science/paper/KAP2AJWA"},"agent_actions":{"view_html":"https://pith.science/pith/KAP2AJWAWVPLBSYD4LHSW4JVFO","download_json":"https://pith.science/pith/KAP2AJWAWVPLBSYD4LHSW4JVFO.json","view_paper":"https://pith.science/paper/KAP2AJWA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.5029&json=true","fetch_graph":"https://pith.science/api/pith-number/KAP2AJWAWVPLBSYD4LHSW4JVFO/graph.json","fetch_events":"https://pith.science/api/pith-number/KAP2AJWAWVPLBSYD4LHSW4JVFO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAP2AJWAWVPLBSYD4LHSW4JVFO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAP2AJWAWVPLBSYD4LHSW4JVFO/action/storage_attestation","attest_author":"https://pith.science/pith/KAP2AJWAWVPLBSYD4LHSW4JVFO/action/author_attestation","sign_citation":"https://pith.science/pith/KAP2AJWAWVPLBSYD4LHSW4JVFO/action/citation_signature","submit_replication":"https://pith.science/pith/KAP2AJWAWVPLBSYD4LHSW4JVFO/action/replication_record"}},"created_at":"2026-05-18T02:24:15.443231+00:00","updated_at":"2026-05-18T02:24:15.443231+00:00"}