{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:WVBVPITNR6H5HE2V7YI7WAE5UP","short_pith_number":"pith:WVBVPITN","schema_version":"1.0","canonical_sha256":"b54357a26d8f8fd39355fe11fb009da3cd9962ba7b1308c2c5e8e2e101c0f319","source":{"kind":"arxiv","id":"math/0612480","version":2},"attestation_state":"computed","paper":{"title":"Measurable Sensitivity","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Cesar E. Silva, Jennifer James, Kathryn Lindsey, Peter Speh, Thomas Koberda","submitted_at":"2006-12-17T04:00:35Z","abstract_excerpt":"We introduce the notion of measurable sensitivity, a measure-theoretic version of the condition of sensitive dependence on initial conditions. It is a consequence of light mixing, implies a transformation has only finitely many eigenvalues, and does not exist in the infinite measure-preserving case. Unlike the traditional notion of sensitive dependence, measurable sensitivity carries up to measure-theoretic isomorphism, thus ignoring the behavior of the function on null sets and eliminating dependence on the choice of metric."},"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":"math/0612480","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2006-12-17T04:00:35Z","cross_cats_sorted":[],"title_canon_sha256":"9a1c889fef7b6dcabc5428e7eb6f1c371261f3860acaec4f49b835cb2d4be57e","abstract_canon_sha256":"4ea7d45309568f296ecba33b4f0980e72c4a5ec60d61ac7f0778ac531dbd4176"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:32.123767Z","signature_b64":"l4RtF5eVC3Ry0pZX/cNgSt0N5HS9B0r7b98bwmiwdSPPHSYvwyGxF1RXs2qME3D7y2chOzEpvNIfq39w1LnzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b54357a26d8f8fd39355fe11fb009da3cd9962ba7b1308c2c5e8e2e101c0f319","last_reissued_at":"2026-05-18T04:22:32.123263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:32.123263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Measurable Sensitivity","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Cesar E. Silva, Jennifer James, Kathryn Lindsey, Peter Speh, Thomas Koberda","submitted_at":"2006-12-17T04:00:35Z","abstract_excerpt":"We introduce the notion of measurable sensitivity, a measure-theoretic version of the condition of sensitive dependence on initial conditions. It is a consequence of light mixing, implies a transformation has only finitely many eigenvalues, and does not exist in the infinite measure-preserving case. Unlike the traditional notion of sensitive dependence, measurable sensitivity carries up to measure-theoretic isomorphism, thus ignoring the behavior of the function on null sets and eliminating dependence on the choice of metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612480","kind":"arxiv","version":2},"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":"math/0612480","created_at":"2026-05-18T04:22:32.123345+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0612480v2","created_at":"2026-05-18T04:22:32.123345+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612480","created_at":"2026-05-18T04:22:32.123345+00:00"},{"alias_kind":"pith_short_12","alias_value":"WVBVPITNR6H5","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"WVBVPITNR6H5HE2V","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"WVBVPITN","created_at":"2026-05-18T12:25:54.717736+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/WVBVPITNR6H5HE2V7YI7WAE5UP","json":"https://pith.science/pith/WVBVPITNR6H5HE2V7YI7WAE5UP.json","graph_json":"https://pith.science/api/pith-number/WVBVPITNR6H5HE2V7YI7WAE5UP/graph.json","events_json":"https://pith.science/api/pith-number/WVBVPITNR6H5HE2V7YI7WAE5UP/events.json","paper":"https://pith.science/paper/WVBVPITN"},"agent_actions":{"view_html":"https://pith.science/pith/WVBVPITNR6H5HE2V7YI7WAE5UP","download_json":"https://pith.science/pith/WVBVPITNR6H5HE2V7YI7WAE5UP.json","view_paper":"https://pith.science/paper/WVBVPITN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0612480&json=true","fetch_graph":"https://pith.science/api/pith-number/WVBVPITNR6H5HE2V7YI7WAE5UP/graph.json","fetch_events":"https://pith.science/api/pith-number/WVBVPITNR6H5HE2V7YI7WAE5UP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WVBVPITNR6H5HE2V7YI7WAE5UP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WVBVPITNR6H5HE2V7YI7WAE5UP/action/storage_attestation","attest_author":"https://pith.science/pith/WVBVPITNR6H5HE2V7YI7WAE5UP/action/author_attestation","sign_citation":"https://pith.science/pith/WVBVPITNR6H5HE2V7YI7WAE5UP/action/citation_signature","submit_replication":"https://pith.science/pith/WVBVPITNR6H5HE2V7YI7WAE5UP/action/replication_record"}},"created_at":"2026-05-18T04:22:32.123345+00:00","updated_at":"2026-05-18T04:22:32.123345+00:00"}