{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2DG6RQYCKRC6TJTBSO7F55UHSG","short_pith_number":"pith:2DG6RQYC","canonical_record":{"source":{"id":"1301.1637","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-08T19:04:17Z","cross_cats_sorted":[],"title_canon_sha256":"08f58a2224c0a858acdd0417b021b3e82e33edca45f843c4337c55c8174001f4","abstract_canon_sha256":"d1e72c3e9fb5cb83e71323f4cca850b3984bc3b62ee487d06e6c7c5cd56d3bc3"},"schema_version":"1.0"},"canonical_sha256":"d0cde8c3025445e9a66193be5ef68791b67592d166de830e58e7b02b2e8b7174","source":{"kind":"arxiv","id":"1301.1637","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1637","created_at":"2026-05-18T03:27:11Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1637v4","created_at":"2026-05-18T03:27:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1637","created_at":"2026-05-18T03:27:11Z"},{"alias_kind":"pith_short_12","alias_value":"2DG6RQYCKRC6","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2DG6RQYCKRC6TJTB","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2DG6RQYC","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2DG6RQYCKRC6TJTBSO7F55UHSG","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1637","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-08T19:04:17Z","cross_cats_sorted":[],"title_canon_sha256":"08f58a2224c0a858acdd0417b021b3e82e33edca45f843c4337c55c8174001f4","abstract_canon_sha256":"d1e72c3e9fb5cb83e71323f4cca850b3984bc3b62ee487d06e6c7c5cd56d3bc3"},"schema_version":"1.0"},"canonical_sha256":"d0cde8c3025445e9a66193be5ef68791b67592d166de830e58e7b02b2e8b7174","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:11.255614Z","signature_b64":"AKIq2o7bzHHjd88g0mitdxl44Jtd3KuAUNBDRTLxOPbo/HAXNL4oUapDRhD/swS0FWHHc9ZiStYYX2nMFVkKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0cde8c3025445e9a66193be5ef68791b67592d166de830e58e7b02b2e8b7174","last_reissued_at":"2026-05-18T03:27:11.254813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:11.254813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1637","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YhYpsjQDM7mSJktbwzpfUdbEekncALO37/g0+xQjB3UcNSRm8q2nX2hsVgCEOkMVlZ+lVcsgcI7R20Cu806qBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:09:02.698936Z"},"content_sha256":"e161f590b24a066afa0b7f7a27674d4da7c2e42ba3b83c19fdcdbb38b4c97ceb","schema_version":"1.0","event_id":"sha256:e161f590b24a066afa0b7f7a27674d4da7c2e42ba3b83c19fdcdbb38b4c97ceb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2DG6RQYCKRC6TJTBSO7F55UHSG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodic bounded constructions, Disjointness and Weak Limits of Powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"V. V. Ryzhikov","submitted_at":"2013-01-08T19:04:17Z","abstract_excerpt":"In connection with some recent results by J. Bourgain and H. Abdalaoui, M. Lemanczyk, T. De La Rue (ALR) we present a short proof of Bourgain's theorem on Mobius orthogonality property for bounded rank-one constructions. The proof of the fact (due to ALR) that bounded-recurrent constructions with Markov self-similarity have to be flat-recurrent is simplified as well.(v4 in Russian)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1637","kind":"arxiv","version":4},"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":"2026-05-18T03:27:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lU/1qCS7H0o1vSVHJRQ700ojSgN29c99YOeserJHCdo+iLiLjGHzKu5LG5ckbWrh5/LXY3o3Xtf2p9J63Xo2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:09:02.699703Z"},"content_sha256":"edf6e1a8c88d892f3e8aab75cfb4fb687cb696950b9995e56db44f52ba446220","schema_version":"1.0","event_id":"sha256:edf6e1a8c88d892f3e8aab75cfb4fb687cb696950b9995e56db44f52ba446220"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2DG6RQYCKRC6TJTBSO7F55UHSG/bundle.json","state_url":"https://pith.science/pith/2DG6RQYCKRC6TJTBSO7F55UHSG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2DG6RQYCKRC6TJTBSO7F55UHSG/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":"2026-06-10T13:09:02Z","links":{"resolver":"https://pith.science/pith/2DG6RQYCKRC6TJTBSO7F55UHSG","bundle":"https://pith.science/pith/2DG6RQYCKRC6TJTBSO7F55UHSG/bundle.json","state":"https://pith.science/pith/2DG6RQYCKRC6TJTBSO7F55UHSG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2DG6RQYCKRC6TJTBSO7F55UHSG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2DG6RQYCKRC6TJTBSO7F55UHSG","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":"d1e72c3e9fb5cb83e71323f4cca850b3984bc3b62ee487d06e6c7c5cd56d3bc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-08T19:04:17Z","title_canon_sha256":"08f58a2224c0a858acdd0417b021b3e82e33edca45f843c4337c55c8174001f4"},"schema_version":"1.0","source":{"id":"1301.1637","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1637","created_at":"2026-05-18T03:27:11Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1637v4","created_at":"2026-05-18T03:27:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1637","created_at":"2026-05-18T03:27:11Z"},{"alias_kind":"pith_short_12","alias_value":"2DG6RQYCKRC6","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2DG6RQYCKRC6TJTB","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2DG6RQYC","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:edf6e1a8c88d892f3e8aab75cfb4fb687cb696950b9995e56db44f52ba446220","target":"graph","created_at":"2026-05-18T03:27:11Z","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":"In connection with some recent results by J. Bourgain and H. Abdalaoui, M. Lemanczyk, T. De La Rue (ALR) we present a short proof of Bourgain's theorem on Mobius orthogonality property for bounded rank-one constructions. The proof of the fact (due to ALR) that bounded-recurrent constructions with Markov self-similarity have to be flat-recurrent is simplified as well.(v4 in Russian)","authors_text":"V. V. Ryzhikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-08T19:04:17Z","title":"Ergodic bounded constructions, Disjointness and Weak Limits of Powers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1637","kind":"arxiv","version":4},"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:e161f590b24a066afa0b7f7a27674d4da7c2e42ba3b83c19fdcdbb38b4c97ceb","target":"record","created_at":"2026-05-18T03:27:11Z","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":"d1e72c3e9fb5cb83e71323f4cca850b3984bc3b62ee487d06e6c7c5cd56d3bc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-08T19:04:17Z","title_canon_sha256":"08f58a2224c0a858acdd0417b021b3e82e33edca45f843c4337c55c8174001f4"},"schema_version":"1.0","source":{"id":"1301.1637","kind":"arxiv","version":4}},"canonical_sha256":"d0cde8c3025445e9a66193be5ef68791b67592d166de830e58e7b02b2e8b7174","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0cde8c3025445e9a66193be5ef68791b67592d166de830e58e7b02b2e8b7174","first_computed_at":"2026-05-18T03:27:11.254813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:11.254813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AKIq2o7bzHHjd88g0mitdxl44Jtd3KuAUNBDRTLxOPbo/HAXNL4oUapDRhD/swS0FWHHc9ZiStYYX2nMFVkKAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:11.255614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1637","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e161f590b24a066afa0b7f7a27674d4da7c2e42ba3b83c19fdcdbb38b4c97ceb","sha256:edf6e1a8c88d892f3e8aab75cfb4fb687cb696950b9995e56db44f52ba446220"],"state_sha256":"560be8552b1f5b6698d0d78bd0c13429402edb3e6b0c91621237929a681422f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8QivtCmbHom2zO8W/6ecS7TzXQc2fSwAJ0yXeMsXRonkJIfSFWlTFspBFax5QduvZ9xMT1Zhl9ma0Wrg3a7/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T13:09:02.704210Z","bundle_sha256":"d12cf4a4e0dbe556fc92d57a29a138b311fca03b8a05231aa2569c44c13616c5"}}