{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:BVQ55S4N3T5KUFYTFD7MKV3ONW","short_pith_number":"pith:BVQ55S4N","canonical_record":{"source":{"id":"math/0512033","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.SP","submitted_at":"2005-12-01T16:40:06Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"6c19d6f39ac1c8552aede2af75b598da3611eef57748ef468749576dfd1b0f51","abstract_canon_sha256":"7bd68b6c90ee500ed390a799fb2a3180014724608f754019c84c887c2ea21f51"},"schema_version":"1.0"},"canonical_sha256":"0d61decb8ddcfaaa171328fec5576e6d917aefd03b45e58c85bd88eaa27fc275","source":{"kind":"arxiv","id":"math/0512033","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512033","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512033v1","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512033","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"BVQ55S4N3T5K","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"BVQ55S4N3T5KUFYT","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"BVQ55S4N","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:BVQ55S4N3T5KUFYTFD7MKV3ONW","target":"record","payload":{"canonical_record":{"source":{"id":"math/0512033","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.SP","submitted_at":"2005-12-01T16:40:06Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"6c19d6f39ac1c8552aede2af75b598da3611eef57748ef468749576dfd1b0f51","abstract_canon_sha256":"7bd68b6c90ee500ed390a799fb2a3180014724608f754019c84c887c2ea21f51"},"schema_version":"1.0"},"canonical_sha256":"0d61decb8ddcfaaa171328fec5576e6d917aefd03b45e58c85bd88eaa27fc275","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:23.121463Z","signature_b64":"oHf6+7EOyySIxxSw25GlgkM63AZetq3YGdZkKipXFa+KfRW9XsAiVhWBgKgwnwTos/QmpnXbvwQ0KDNS+FAKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d61decb8ddcfaaa171328fec5576e6d917aefd03b45e58c85bd88eaa27fc275","last_reissued_at":"2026-05-18T02:30:23.121006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:23.121006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0512033","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dawRDpWA+O4yb41QFJskIaA0uNb/FJqlGMMzBlNXZn8pq/xOpn3FIpa1vJP0DFp41iCevBi3LW2QvZc1aQPyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:01:50.059752Z"},"content_sha256":"d1e9fba1bf77572c313e7c698e17364f687994a081e4c4d91c3835032ea73144","schema_version":"1.0","event_id":"sha256:d1e9fba1bf77572c313e7c698e17364f687994a081e4c4d91c3835032ea73144"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:BVQ55S4N3T5KUFYTFD7MKV3ONW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform Szego Cocycles Over Strictly Ergodic Subshifts","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.SP","authors_text":"Daniel Lenz (TU Chemnitz), David Damanik (Caltech)","submitted_at":"2005-12-01T16:40:06Z","abstract_excerpt":"We consider ergodic families of Verblunsky coefficients generated by minimal aperiodic subshifts. Simon conjectured that the associated probability measures on the unit circle have essential support of zero Lebesgue measure. We prove this for a large class of subshifts, namely those satisfying Boshernitzan's condition. This is accomplished by relating the essential support to uniform convergence properties of the corresponding Szego cocycles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512033","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FK2Hk+jGmIPAWIqKExd0JhpwJ9QD69e4hKgVqWgu8341if/ymkfvCqDDANZgLDU1nShe9DX40q+3rX0oITD7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:01:50.060092Z"},"content_sha256":"f3dc42c3763f88a6b4aedaa403a103f4a54baedd345100c77e1a85361c96b044","schema_version":"1.0","event_id":"sha256:f3dc42c3763f88a6b4aedaa403a103f4a54baedd345100c77e1a85361c96b044"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BVQ55S4N3T5KUFYTFD7MKV3ONW/bundle.json","state_url":"https://pith.science/pith/BVQ55S4N3T5KUFYTFD7MKV3ONW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BVQ55S4N3T5KUFYTFD7MKV3ONW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T11:01:50Z","links":{"resolver":"https://pith.science/pith/BVQ55S4N3T5KUFYTFD7MKV3ONW","bundle":"https://pith.science/pith/BVQ55S4N3T5KUFYTFD7MKV3ONW/bundle.json","state":"https://pith.science/pith/BVQ55S4N3T5KUFYTFD7MKV3ONW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BVQ55S4N3T5KUFYTFD7MKV3ONW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:BVQ55S4N3T5KUFYTFD7MKV3ONW","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":"7bd68b6c90ee500ed390a799fb2a3180014724608f754019c84c887c2ea21f51","cross_cats_sorted":["math.CA"],"license":"","primary_cat":"math.SP","submitted_at":"2005-12-01T16:40:06Z","title_canon_sha256":"6c19d6f39ac1c8552aede2af75b598da3611eef57748ef468749576dfd1b0f51"},"schema_version":"1.0","source":{"id":"math/0512033","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512033","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512033v1","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512033","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"BVQ55S4N3T5K","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"BVQ55S4N3T5KUFYT","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"BVQ55S4N","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f3dc42c3763f88a6b4aedaa403a103f4a54baedd345100c77e1a85361c96b044","target":"graph","created_at":"2026-05-18T02:30:23Z","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 consider ergodic families of Verblunsky coefficients generated by minimal aperiodic subshifts. Simon conjectured that the associated probability measures on the unit circle have essential support of zero Lebesgue measure. We prove this for a large class of subshifts, namely those satisfying Boshernitzan's condition. This is accomplished by relating the essential support to uniform convergence properties of the corresponding Szego cocycles.","authors_text":"Daniel Lenz (TU Chemnitz), David Damanik (Caltech)","cross_cats":["math.CA"],"headline":"","license":"","primary_cat":"math.SP","submitted_at":"2005-12-01T16:40:06Z","title":"Uniform Szego Cocycles Over Strictly Ergodic Subshifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512033","kind":"arxiv","version":1},"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:d1e9fba1bf77572c313e7c698e17364f687994a081e4c4d91c3835032ea73144","target":"record","created_at":"2026-05-18T02:30:23Z","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":"7bd68b6c90ee500ed390a799fb2a3180014724608f754019c84c887c2ea21f51","cross_cats_sorted":["math.CA"],"license":"","primary_cat":"math.SP","submitted_at":"2005-12-01T16:40:06Z","title_canon_sha256":"6c19d6f39ac1c8552aede2af75b598da3611eef57748ef468749576dfd1b0f51"},"schema_version":"1.0","source":{"id":"math/0512033","kind":"arxiv","version":1}},"canonical_sha256":"0d61decb8ddcfaaa171328fec5576e6d917aefd03b45e58c85bd88eaa27fc275","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d61decb8ddcfaaa171328fec5576e6d917aefd03b45e58c85bd88eaa27fc275","first_computed_at":"2026-05-18T02:30:23.121006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:23.121006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oHf6+7EOyySIxxSw25GlgkM63AZetq3YGdZkKipXFa+KfRW9XsAiVhWBgKgwnwTos/QmpnXbvwQ0KDNS+FAKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:23.121463Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0512033","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1e9fba1bf77572c313e7c698e17364f687994a081e4c4d91c3835032ea73144","sha256:f3dc42c3763f88a6b4aedaa403a103f4a54baedd345100c77e1a85361c96b044"],"state_sha256":"ee9a40035812498b51f5f9d36dd51c1af03dfd608295365e740c5aad8c5e59a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RxYzydBDCmI19tGLLaGL99WUwivdBTa6ZRAU/DUEs9DLjh0onoufZxC+gppM3sfydrnWKhG3BvwST4HYTmqmAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T11:01:50.062222Z","bundle_sha256":"cecac30426980fb4d2cc98a86dc30240581044dd3eaf8359f53a750a63e87118"}}