{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GUWZ67ZMF2LH3KYDLVEF7JEF3Z","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":"86fc0c047f9217ef3ddd11a6af451268726cd2bdf8120748c6101e5fb7eaf825","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-29T04:02:13Z","title_canon_sha256":"e410a41cf0a6334a387c5b25b8ebc0357a5ff1efed13c0965e66a801a6bcf76e"},"schema_version":"1.0","source":{"id":"1908.11040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.11040","created_at":"2026-07-05T02:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1908.11040v2","created_at":"2026-07-05T02:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.11040","created_at":"2026-07-05T02:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"GUWZ67ZMF2LH","created_at":"2026-07-05T02:58:02Z"},{"alias_kind":"pith_short_16","alias_value":"GUWZ67ZMF2LH3KYD","created_at":"2026-07-05T02:58:02Z"},{"alias_kind":"pith_short_8","alias_value":"GUWZ67ZM","created_at":"2026-07-05T02:58:02Z"}],"graph_snapshots":[{"event_id":"sha256:44711057167eabfb80df691a0484361cd922215f1c114584beb08e71578bca68","target":"graph","created_at":"2026-07-05T02:58:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.11040/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a twisted cohomology cocycle over the Teichmueller flow and prove a \"spectral gap\" for its Lyapunov spectrum with respect to the Masur-Veech measures. We then derive Hoelder estimates on spectral measures and bounds on the speed of weak mixing for almost all translation flows in every stratum of Abelian differentials on Riemann surfaces, as well as bounds on the deviation of ergodic averages for product translation flows on the product of a translation surface with a circle.","authors_text":"Giovanni Forni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-29T04:02:13Z","title":"Twisted Translation Flows and Effective Weak Mixing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.11040","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":"sha256:5fdeba1408b091aebd87af6bf75b2b4f5ce9168050bb59ccd7dc6cf1be315b72","target":"record","created_at":"2026-07-05T02:58:02Z","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":"86fc0c047f9217ef3ddd11a6af451268726cd2bdf8120748c6101e5fb7eaf825","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-29T04:02:13Z","title_canon_sha256":"e410a41cf0a6334a387c5b25b8ebc0357a5ff1efed13c0965e66a801a6bcf76e"},"schema_version":"1.0","source":{"id":"1908.11040","kind":"arxiv","version":2}},"canonical_sha256":"352d9f7f2c2e967dab035d485fa485de5356b51d7a2f096ecc5c75b253f29580","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"352d9f7f2c2e967dab035d485fa485de5356b51d7a2f096ecc5c75b253f29580","first_computed_at":"2026-07-05T02:58:02.985179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:58:02.985179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1V2h6icD2D9P4Y8HSdkgh5W93pygXGQmYi6C6t3RW/3al25kGq3aaSh5PwCAEst2iu2Gp0HoFel6/np+E38dDg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:58:02.985535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.11040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fdeba1408b091aebd87af6bf75b2b4f5ce9168050bb59ccd7dc6cf1be315b72","sha256:44711057167eabfb80df691a0484361cd922215f1c114584beb08e71578bca68"],"state_sha256":"070cafe3011ad2782f6fa808f3950792195d5980567a770b8e0db1a2020f8eb0"}