{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TCD2MBMZJJVPOH5I4EI4VZA32B","short_pith_number":"pith:TCD2MBMZ","canonical_record":{"source":{"id":"1701.04345","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-16T16:13:57Z","cross_cats_sorted":[],"title_canon_sha256":"cf95f2e65b840cc123db38136e00364768aa2a07886f13b5a130d0ff5658e607","abstract_canon_sha256":"6dbd40f4624c54ac2f59cba8ff6c4d60a6e18399f6ebbdcdb46bab4fa6d8085c"},"schema_version":"1.0"},"canonical_sha256":"9887a605994a6af71fa8e111cae41bd06283f56b177cdcad1bcc1d2f19d1431b","source":{"kind":"arxiv","id":"1701.04345","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04345","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04345v2","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04345","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"pith_short_12","alias_value":"TCD2MBMZJJVP","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TCD2MBMZJJVPOH5I","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TCD2MBMZ","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TCD2MBMZJJVPOH5I4EI4VZA32B","target":"record","payload":{"canonical_record":{"source":{"id":"1701.04345","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-16T16:13:57Z","cross_cats_sorted":[],"title_canon_sha256":"cf95f2e65b840cc123db38136e00364768aa2a07886f13b5a130d0ff5658e607","abstract_canon_sha256":"6dbd40f4624c54ac2f59cba8ff6c4d60a6e18399f6ebbdcdb46bab4fa6d8085c"},"schema_version":"1.0"},"canonical_sha256":"9887a605994a6af71fa8e111cae41bd06283f56b177cdcad1bcc1d2f19d1431b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:24.742728Z","signature_b64":"PuI8AXBMmwAQsDS4Ov77y1hwx1shSc4VFUNkpwC9AfPDQJNiff1753MM0oguzCdMRC4aN7+utmpPfpz3jqr5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9887a605994a6af71fa8e111cae41bd06283f56b177cdcad1bcc1d2f19d1431b","last_reissued_at":"2026-05-17T23:52:24.742047Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:24.742047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.04345","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z7G6YlJUwvnNpSNscUps7mpyTa5efMrGpnYGVIpCQ2oB6G6/HwCc/CWTARdMsHF7Km0nPy8BrOVJ6cMZW3MKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:53:26.242223Z"},"content_sha256":"072344e3e21ce500e654f611b9e13b0f65617c5299dab56c118c2407a9b200e1","schema_version":"1.0","event_id":"sha256:072344e3e21ce500e654f611b9e13b0f65617c5299dab56c118c2407a9b200e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TCD2MBMZJJVPOH5I4EI4VZA32B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Over Recurrence for Mixing Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Terrence Adams","submitted_at":"2017-01-16T16:13:57Z","abstract_excerpt":"We show that every invertible strong mixing transformation on a Lebesgue space has strictly over-recurrent sets. Also, we give an explicit procedure for constructing strong mixing transformations with no under-recurrent sets. This answers both parts of a question of V. Bergelson.\n  We define $\\epsilon$-over-recurrence and show that given $\\epsilon > 0$, any ergodic measure preserving invertible transformation (including discrete spectrum) has $\\epsilon$-over-recurrent sets of arbitrarily small measure. Discrete spectrum transformations and rotations do not have over-recurrent sets, but we cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04345","kind":"arxiv","version":2},"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":"2026-05-17T23:52:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HljB1Gnbqnjh12pP41t4Hj8HBNy9UHe8MW5sy20dIEx27JgEU7zBugN/DrPtvb7vBj2JjICVQ4euh/Co7sECDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:53:26.242904Z"},"content_sha256":"d2e8b59fbcdefc0beae749b3edce60249c2d4ddd1ed807c42783e9863942494d","schema_version":"1.0","event_id":"sha256:d2e8b59fbcdefc0beae749b3edce60249c2d4ddd1ed807c42783e9863942494d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TCD2MBMZJJVPOH5I4EI4VZA32B/bundle.json","state_url":"https://pith.science/pith/TCD2MBMZJJVPOH5I4EI4VZA32B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TCD2MBMZJJVPOH5I4EI4VZA32B/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":"2026-06-04T20:53:26Z","links":{"resolver":"https://pith.science/pith/TCD2MBMZJJVPOH5I4EI4VZA32B","bundle":"https://pith.science/pith/TCD2MBMZJJVPOH5I4EI4VZA32B/bundle.json","state":"https://pith.science/pith/TCD2MBMZJJVPOH5I4EI4VZA32B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TCD2MBMZJJVPOH5I4EI4VZA32B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TCD2MBMZJJVPOH5I4EI4VZA32B","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":"6dbd40f4624c54ac2f59cba8ff6c4d60a6e18399f6ebbdcdb46bab4fa6d8085c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-16T16:13:57Z","title_canon_sha256":"cf95f2e65b840cc123db38136e00364768aa2a07886f13b5a130d0ff5658e607"},"schema_version":"1.0","source":{"id":"1701.04345","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04345","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04345v2","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04345","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"pith_short_12","alias_value":"TCD2MBMZJJVP","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TCD2MBMZJJVPOH5I","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TCD2MBMZ","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:d2e8b59fbcdefc0beae749b3edce60249c2d4ddd1ed807c42783e9863942494d","target":"graph","created_at":"2026-05-17T23:52:24Z","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 show that every invertible strong mixing transformation on a Lebesgue space has strictly over-recurrent sets. Also, we give an explicit procedure for constructing strong mixing transformations with no under-recurrent sets. This answers both parts of a question of V. Bergelson.\n  We define $\\epsilon$-over-recurrence and show that given $\\epsilon > 0$, any ergodic measure preserving invertible transformation (including discrete spectrum) has $\\epsilon$-over-recurrent sets of arbitrarily small measure. Discrete spectrum transformations and rotations do not have over-recurrent sets, but we cons","authors_text":"Terrence Adams","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-16T16:13:57Z","title":"Over Recurrence for Mixing Transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04345","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":"sha256:072344e3e21ce500e654f611b9e13b0f65617c5299dab56c118c2407a9b200e1","target":"record","created_at":"2026-05-17T23:52:24Z","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":"6dbd40f4624c54ac2f59cba8ff6c4d60a6e18399f6ebbdcdb46bab4fa6d8085c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-16T16:13:57Z","title_canon_sha256":"cf95f2e65b840cc123db38136e00364768aa2a07886f13b5a130d0ff5658e607"},"schema_version":"1.0","source":{"id":"1701.04345","kind":"arxiv","version":2}},"canonical_sha256":"9887a605994a6af71fa8e111cae41bd06283f56b177cdcad1bcc1d2f19d1431b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9887a605994a6af71fa8e111cae41bd06283f56b177cdcad1bcc1d2f19d1431b","first_computed_at":"2026-05-17T23:52:24.742047Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:24.742047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PuI8AXBMmwAQsDS4Ov77y1hwx1shSc4VFUNkpwC9AfPDQJNiff1753MM0oguzCdMRC4aN7+utmpPfpz3jqr5Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:24.742728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04345","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:072344e3e21ce500e654f611b9e13b0f65617c5299dab56c118c2407a9b200e1","sha256:d2e8b59fbcdefc0beae749b3edce60249c2d4ddd1ed807c42783e9863942494d"],"state_sha256":"3499f608b5d1fa1f98db33799e1ba90e274f097d48d1e9eaa1aac6f84787c786"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LI8eP54+GAXn6NixwF6LTWPi/gVLPVUygb5BQ2jrT3TQ9rWsGWmekQEjhD/vBUkX/CpsyrHyiDP4Bb748svCCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:53:26.246512Z","bundle_sha256":"d7ea74e51b8b064a3b703b932b8495a0c09a2cad30741afb680879bd0e01f034"}}