{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZKYCLKL3WFN6U45XYWMXYNGXRG","short_pith_number":"pith:ZKYCLKL3","schema_version":"1.0","canonical_sha256":"cab025a97bb15bea73b7c5997c34d789af640eefe9362d537bc2efce4a39bb4e","source":{"kind":"arxiv","id":"1510.04312","version":1},"attestation_state":"computed","paper":{"title":"Entropy, volume growth and SRB measures for Banach space mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Blumenthal, Lai-Sang Young","submitted_at":"2015-10-14T20:58:34Z","abstract_excerpt":"We consider $C^2$ Fr\\'echet differentiable mappings of Banach spaces leaving invariant compactly supported Borel probability measures, and study the relation between entropy and volume growth for a natural notion of volume defined on finite dimensional subspaces. SRB measures are characterized as exactly those measures for which entropy is equal to volume growth on unstable manifolds, equivalently the sum of positive Lyapunov exponents of the map. In addition to numerous difficulties incurred by our infinite-dimensional setting, a crucial aspect to the proof is the technical point that the vol"},"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":"1510.04312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-14T20:58:34Z","cross_cats_sorted":[],"title_canon_sha256":"d4df5b974bfc631ab5a6b059e35b1df500bf643c1f8d8b2addd22088d0cf32e5","abstract_canon_sha256":"9fe7f50886489b75ec3612b74f5c574eee5056ce1feb6196acaac4643b6f32b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:07.512738Z","signature_b64":"hDyEwAEs5ZMXDNC56Nvg7RmDhuOeHJnaJDwA4P0Nsf1AE/hXac7zfj+lapugaNvIV1yyw71Nx16SGfJ4zeroBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cab025a97bb15bea73b7c5997c34d789af640eefe9362d537bc2efce4a39bb4e","last_reissued_at":"2026-05-18T01:30:07.512065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:07.512065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy, volume growth and SRB measures for Banach space mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Blumenthal, Lai-Sang Young","submitted_at":"2015-10-14T20:58:34Z","abstract_excerpt":"We consider $C^2$ Fr\\'echet differentiable mappings of Banach spaces leaving invariant compactly supported Borel probability measures, and study the relation between entropy and volume growth for a natural notion of volume defined on finite dimensional subspaces. SRB measures are characterized as exactly those measures for which entropy is equal to volume growth on unstable manifolds, equivalently the sum of positive Lyapunov exponents of the map. In addition to numerous difficulties incurred by our infinite-dimensional setting, a crucial aspect to the proof is the technical point that the vol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04312","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":"1510.04312","created_at":"2026-05-18T01:30:07.512173+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.04312v1","created_at":"2026-05-18T01:30:07.512173+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04312","created_at":"2026-05-18T01:30:07.512173+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZKYCLKL3WFN6","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZKYCLKL3WFN6U45X","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZKYCLKL3","created_at":"2026-05-18T12:29:52.810259+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/ZKYCLKL3WFN6U45XYWMXYNGXRG","json":"https://pith.science/pith/ZKYCLKL3WFN6U45XYWMXYNGXRG.json","graph_json":"https://pith.science/api/pith-number/ZKYCLKL3WFN6U45XYWMXYNGXRG/graph.json","events_json":"https://pith.science/api/pith-number/ZKYCLKL3WFN6U45XYWMXYNGXRG/events.json","paper":"https://pith.science/paper/ZKYCLKL3"},"agent_actions":{"view_html":"https://pith.science/pith/ZKYCLKL3WFN6U45XYWMXYNGXRG","download_json":"https://pith.science/pith/ZKYCLKL3WFN6U45XYWMXYNGXRG.json","view_paper":"https://pith.science/paper/ZKYCLKL3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.04312&json=true","fetch_graph":"https://pith.science/api/pith-number/ZKYCLKL3WFN6U45XYWMXYNGXRG/graph.json","fetch_events":"https://pith.science/api/pith-number/ZKYCLKL3WFN6U45XYWMXYNGXRG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZKYCLKL3WFN6U45XYWMXYNGXRG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZKYCLKL3WFN6U45XYWMXYNGXRG/action/storage_attestation","attest_author":"https://pith.science/pith/ZKYCLKL3WFN6U45XYWMXYNGXRG/action/author_attestation","sign_citation":"https://pith.science/pith/ZKYCLKL3WFN6U45XYWMXYNGXRG/action/citation_signature","submit_replication":"https://pith.science/pith/ZKYCLKL3WFN6U45XYWMXYNGXRG/action/replication_record"}},"created_at":"2026-05-18T01:30:07.512173+00:00","updated_at":"2026-05-18T01:30:07.512173+00:00"}