{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3WIQGC2HVDK5FIAWGPTQ6J5NUM","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":"7abce53bf8d2291bcc01650bbcb7c23f5c86fa9113dd4cd929a266ad99a94c1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-15T20:07:56Z","title_canon_sha256":"74304ef69cd657e2101aafeb777e98c87d4ae9a969143c7b51e807d0173e5ce8"},"schema_version":"1.0","source":{"id":"1606.04962","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04962","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04962v3","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04962","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"3WIQGC2HVDK5","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"3WIQGC2HVDK5FIAW","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"3WIQGC2H","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:fe8af0db6d632b6326d8fc67f719752d3cea224b616eddc966fee73f1e887953","target":"graph","created_at":"2026-05-18T00:33:23Z","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 provide an abstract framework for the study of certain spectral properties of parabolic systems; specifically, we determine under which general conditions to expect the presence of absolutely continuous spectral measures. We use these general conditions to derive results for spectral properties of time-changes of unipotent flows on homogeneous spaces of semisimple groups regarding absolutely continuous spectrum as well as maximal spectral type; the time-changes of the horocycle flow are special cases of this general category of flows. In addition we use the general conditions to derive spec","authors_text":"Lucia D. Simonelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-15T20:07:56Z","title":"Absolutely Continuous Spectrum for Parabolic Flows/Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04962","kind":"arxiv","version":3},"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:f13a5a80351e947b7c860d79651159ea5488eb69b927345d4f2d7563a65fe1dc","target":"record","created_at":"2026-05-18T00:33:23Z","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":"7abce53bf8d2291bcc01650bbcb7c23f5c86fa9113dd4cd929a266ad99a94c1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-15T20:07:56Z","title_canon_sha256":"74304ef69cd657e2101aafeb777e98c87d4ae9a969143c7b51e807d0173e5ce8"},"schema_version":"1.0","source":{"id":"1606.04962","kind":"arxiv","version":3}},"canonical_sha256":"dd91030b47a8d5d2a01633e70f27ada314dba625c3257020699cf17b29afa3ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd91030b47a8d5d2a01633e70f27ada314dba625c3257020699cf17b29afa3ec","first_computed_at":"2026-05-18T00:33:23.584180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:23.584180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DD274NwA+gRWNGPiuDjS0+a5LU1TxZlCoTeIICgMNtqFlGumufneN+UIls6vp3w7X4O+ZraQF7eAMgiM4cmMBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:23.584918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04962","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f13a5a80351e947b7c860d79651159ea5488eb69b927345d4f2d7563a65fe1dc","sha256:fe8af0db6d632b6326d8fc67f719752d3cea224b616eddc966fee73f1e887953"],"state_sha256":"a83e745c299a7474ad798887fb5c9b15ec72217e7dd2be08cf61255630d32f03"}