{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:WVBVPITNR6H5HE2V7YI7WAE5UP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4ea7d45309568f296ecba33b4f0980e72c4a5ec60d61ac7f0778ac531dbd4176","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2006-12-17T04:00:35Z","title_canon_sha256":"9a1c889fef7b6dcabc5428e7eb6f1c371261f3860acaec4f49b835cb2d4be57e"},"schema_version":"1.0","source":{"id":"math/0612480","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612480","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612480v2","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612480","created_at":"2026-05-18T04:22:32Z"},{"alias_kind":"pith_short_12","alias_value":"WVBVPITNR6H5","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"WVBVPITNR6H5HE2V","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"WVBVPITN","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:1589351bb361aee8ccd1dd18c6e8adf89de9d399f00b9eadc307d84bbf24656c","target":"graph","created_at":"2026-05-18T04:22:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Cesar E. Silva, Jennifer James, Kathryn Lindsey, Peter Speh, Thomas Koberda","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2006-12-17T04:00:35Z","title":"Measurable Sensitivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612480","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6bd3b895aa4fd591b315a86911b9825c4fda3cb61152e95fd60f1243361a3ff1","target":"record","created_at":"2026-05-18T04:22:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4ea7d45309568f296ecba33b4f0980e72c4a5ec60d61ac7f0778ac531dbd4176","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2006-12-17T04:00:35Z","title_canon_sha256":"9a1c889fef7b6dcabc5428e7eb6f1c371261f3860acaec4f49b835cb2d4be57e"},"schema_version":"1.0","source":{"id":"math/0612480","kind":"arxiv","version":2}},"canonical_sha256":"b54357a26d8f8fd39355fe11fb009da3cd9962ba7b1308c2c5e8e2e101c0f319","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b54357a26d8f8fd39355fe11fb009da3cd9962ba7b1308c2c5e8e2e101c0f319","first_computed_at":"2026-05-18T04:22:32.123263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:32.123263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l4RtF5eVC3Ry0pZX/cNgSt0N5HS9B0r7b98bwmiwdSPPHSYvwyGxF1RXs2qME3D7y2chOzEpvNIfq39w1LnzDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:32.123767Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612480","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bd3b895aa4fd591b315a86911b9825c4fda3cb61152e95fd60f1243361a3ff1","sha256:1589351bb361aee8ccd1dd18c6e8adf89de9d399f00b9eadc307d84bbf24656c"],"state_sha256":"534919415119b20de034fe70cde0b3ec325d7c785660ed2a78050b8ee836b31f"}