{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QU5PUC5HIQLCJUQP2POIJSO7PL","short_pith_number":"pith:QU5PUC5H","schema_version":"1.0","canonical_sha256":"853afa0ba7441624d20fd3dc84c9df7aedc954796005faa9bc8b3eb0a1a397cb","source":{"kind":"arxiv","id":"1412.8041","version":1},"attestation_state":"computed","paper":{"title":"Physical Measures for Infinitely Renormalizable Lorenz Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bj\\\"orn Winckler, Marco Martens","submitted_at":"2014-12-27T13:19:07Z","abstract_excerpt":"A physical measure on the attractor of a system describes the statistical behavior of typical orbits. An example occurs in unimodal dynamics. Namely, all infinitely renormalizable unimodal maps have a physical measure. For Lorenz dynamics, even in the simple case of infinitely renormalizable systems, the existence of physical measures is more delicate. In this article we construct examples of infinitely renormalizable Lorenz maps which do not have a physical measure. A priori bounds on the geometry play a crucial role in (unimodal) dynamics. There are infinitely renormalizable Lorenz maps whic"},"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":"1412.8041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-27T13:19:07Z","cross_cats_sorted":[],"title_canon_sha256":"24010967ab10c174b668803d57cb578655f361969de3db64b2be5eee4805f9bd","abstract_canon_sha256":"9ba58a41dc504ce13942592a66a064f51479b8ba476c9ff7684ae104388a8da1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:45.255425Z","signature_b64":"YS5Um2A9TOHfPFTIewi8ffuudf+I5kV7fX4VYdCdUlGYIGrauINIFknNxjwRRjDtTYCwPtT9gNXWOp1PwiySBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"853afa0ba7441624d20fd3dc84c9df7aedc954796005faa9bc8b3eb0a1a397cb","last_reissued_at":"2026-05-18T01:03:45.255009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:45.255009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Physical Measures for Infinitely Renormalizable Lorenz Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bj\\\"orn Winckler, Marco Martens","submitted_at":"2014-12-27T13:19:07Z","abstract_excerpt":"A physical measure on the attractor of a system describes the statistical behavior of typical orbits. An example occurs in unimodal dynamics. Namely, all infinitely renormalizable unimodal maps have a physical measure. For Lorenz dynamics, even in the simple case of infinitely renormalizable systems, the existence of physical measures is more delicate. In this article we construct examples of infinitely renormalizable Lorenz maps which do not have a physical measure. A priori bounds on the geometry play a crucial role in (unimodal) dynamics. There are infinitely renormalizable Lorenz maps whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8041","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":"1412.8041","created_at":"2026-05-18T01:03:45.255073+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.8041v1","created_at":"2026-05-18T01:03:45.255073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8041","created_at":"2026-05-18T01:03:45.255073+00:00"},{"alias_kind":"pith_short_12","alias_value":"QU5PUC5HIQLC","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QU5PUC5HIQLCJUQP","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QU5PUC5H","created_at":"2026-05-18T12:28:46.137349+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/QU5PUC5HIQLCJUQP2POIJSO7PL","json":"https://pith.science/pith/QU5PUC5HIQLCJUQP2POIJSO7PL.json","graph_json":"https://pith.science/api/pith-number/QU5PUC5HIQLCJUQP2POIJSO7PL/graph.json","events_json":"https://pith.science/api/pith-number/QU5PUC5HIQLCJUQP2POIJSO7PL/events.json","paper":"https://pith.science/paper/QU5PUC5H"},"agent_actions":{"view_html":"https://pith.science/pith/QU5PUC5HIQLCJUQP2POIJSO7PL","download_json":"https://pith.science/pith/QU5PUC5HIQLCJUQP2POIJSO7PL.json","view_paper":"https://pith.science/paper/QU5PUC5H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.8041&json=true","fetch_graph":"https://pith.science/api/pith-number/QU5PUC5HIQLCJUQP2POIJSO7PL/graph.json","fetch_events":"https://pith.science/api/pith-number/QU5PUC5HIQLCJUQP2POIJSO7PL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QU5PUC5HIQLCJUQP2POIJSO7PL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QU5PUC5HIQLCJUQP2POIJSO7PL/action/storage_attestation","attest_author":"https://pith.science/pith/QU5PUC5HIQLCJUQP2POIJSO7PL/action/author_attestation","sign_citation":"https://pith.science/pith/QU5PUC5HIQLCJUQP2POIJSO7PL/action/citation_signature","submit_replication":"https://pith.science/pith/QU5PUC5HIQLCJUQP2POIJSO7PL/action/replication_record"}},"created_at":"2026-05-18T01:03:45.255073+00:00","updated_at":"2026-05-18T01:03:45.255073+00:00"}