{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GSK5QDVLQ3R5OCR6SUEBVBGSJC","short_pith_number":"pith:GSK5QDVL","schema_version":"1.0","canonical_sha256":"3495d80eab86e3d70a3e95081a84d248a3178a19bc8867e8c0eac14a3eae8d32","source":{"kind":"arxiv","id":"1112.0397","version":6},"attestation_state":"computed","paper":{"title":"A geometric path from zero Lyapunov exponents to rotation cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MG"],"primary_cat":"math.DS","authors_text":"Andr\\'es Navas, Jairo Bochi","submitted_at":"2011-12-02T07:21:01Z","abstract_excerpt":"We consider cocycles of isometries on spaces of nonpositive curvature $H$. We show that the supremum of the drift over all invariant ergodic probability measures equals the infimum of the displacements of continuous sections under the cocycle dynamics. In particular, if a cocycle has uniform sublinear drift, then there are almost invariant sections, that is, sections that move arbitrarily little under the cocycle dynamics. If, in addition, $H$ is a symmetric space, then we show that almost invariant sections can be made invariant by perturbing the cocycle."},"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":"1112.0397","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-02T07:21:01Z","cross_cats_sorted":["math.DG","math.MG"],"title_canon_sha256":"7f65573c85c4092cd7430eaeff03083b53611679fa0a3e8f6c19ec295ce9697c","abstract_canon_sha256":"185f5c817c091a8682dcd8664e4ce68ff6fe9f8fabebf998c6df7ee97d9bc505"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:19.095006Z","signature_b64":"dIsCyFnoLB/CN5ZK7Ocsqva4UwtjwT1mhRaElaiiCpJBE3UTj0C8itmFOO2UXyBA6+xLKAeBjfGHBjx+q1jHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3495d80eab86e3d70a3e95081a84d248a3178a19bc8867e8c0eac14a3eae8d32","last_reissued_at":"2026-05-17T23:53:19.094416Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:19.094416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A geometric path from zero Lyapunov exponents to rotation cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MG"],"primary_cat":"math.DS","authors_text":"Andr\\'es Navas, Jairo Bochi","submitted_at":"2011-12-02T07:21:01Z","abstract_excerpt":"We consider cocycles of isometries on spaces of nonpositive curvature $H$. We show that the supremum of the drift over all invariant ergodic probability measures equals the infimum of the displacements of continuous sections under the cocycle dynamics. In particular, if a cocycle has uniform sublinear drift, then there are almost invariant sections, that is, sections that move arbitrarily little under the cocycle dynamics. If, in addition, $H$ is a symmetric space, then we show that almost invariant sections can be made invariant by perturbing the cocycle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0397","kind":"arxiv","version":6},"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":"1112.0397","created_at":"2026-05-17T23:53:19.094496+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0397v6","created_at":"2026-05-17T23:53:19.094496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0397","created_at":"2026-05-17T23:53:19.094496+00:00"},{"alias_kind":"pith_short_12","alias_value":"GSK5QDVLQ3R5","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"GSK5QDVLQ3R5OCR6","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"GSK5QDVL","created_at":"2026-05-18T12:26:30.835961+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/GSK5QDVLQ3R5OCR6SUEBVBGSJC","json":"https://pith.science/pith/GSK5QDVLQ3R5OCR6SUEBVBGSJC.json","graph_json":"https://pith.science/api/pith-number/GSK5QDVLQ3R5OCR6SUEBVBGSJC/graph.json","events_json":"https://pith.science/api/pith-number/GSK5QDVLQ3R5OCR6SUEBVBGSJC/events.json","paper":"https://pith.science/paper/GSK5QDVL"},"agent_actions":{"view_html":"https://pith.science/pith/GSK5QDVLQ3R5OCR6SUEBVBGSJC","download_json":"https://pith.science/pith/GSK5QDVLQ3R5OCR6SUEBVBGSJC.json","view_paper":"https://pith.science/paper/GSK5QDVL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0397&json=true","fetch_graph":"https://pith.science/api/pith-number/GSK5QDVLQ3R5OCR6SUEBVBGSJC/graph.json","fetch_events":"https://pith.science/api/pith-number/GSK5QDVLQ3R5OCR6SUEBVBGSJC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GSK5QDVLQ3R5OCR6SUEBVBGSJC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GSK5QDVLQ3R5OCR6SUEBVBGSJC/action/storage_attestation","attest_author":"https://pith.science/pith/GSK5QDVLQ3R5OCR6SUEBVBGSJC/action/author_attestation","sign_citation":"https://pith.science/pith/GSK5QDVLQ3R5OCR6SUEBVBGSJC/action/citation_signature","submit_replication":"https://pith.science/pith/GSK5QDVLQ3R5OCR6SUEBVBGSJC/action/replication_record"}},"created_at":"2026-05-17T23:53:19.094496+00:00","updated_at":"2026-05-17T23:53:19.094496+00:00"}