{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:272E2CFKO5G3Z3E2LPFRYYA4MO","short_pith_number":"pith:272E2CFK","canonical_record":{"source":{"id":"1812.08027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-19T15:37:46Z","cross_cats_sorted":[],"title_canon_sha256":"05dba94999046f175f6fb873e1c54323d2d7c718e4bc7dd34ef156b4345a928d","abstract_canon_sha256":"4f90dbeb5ece016c13154ea5162eec59383138f528d03948a2d2658547ef64b4"},"schema_version":"1.0"},"canonical_sha256":"d7f44d08aa774dbcec9a5bcb1c601c63a243aec53ac9dfdb6b53eee718d3d6c6","source":{"kind":"arxiv","id":"1812.08027","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08027","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08027v1","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08027","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"pith_short_12","alias_value":"272E2CFKO5G3","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"272E2CFKO5G3Z3E2","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"272E2CFK","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:272E2CFKO5G3Z3E2LPFRYYA4MO","target":"record","payload":{"canonical_record":{"source":{"id":"1812.08027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-19T15:37:46Z","cross_cats_sorted":[],"title_canon_sha256":"05dba94999046f175f6fb873e1c54323d2d7c718e4bc7dd34ef156b4345a928d","abstract_canon_sha256":"4f90dbeb5ece016c13154ea5162eec59383138f528d03948a2d2658547ef64b4"},"schema_version":"1.0"},"canonical_sha256":"d7f44d08aa774dbcec9a5bcb1c601c63a243aec53ac9dfdb6b53eee718d3d6c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:55.125375Z","signature_b64":"/NibLUrN7reQVcj9pR2zFuo5t9yB1DwwRVZVWJv+jfexWnHmVh61Luh7cIYeh8LnLE2J624HeXce9vLXTd1rDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7f44d08aa774dbcec9a5bcb1c601c63a243aec53ac9dfdb6b53eee718d3d6c6","last_reissued_at":"2026-05-17T23:57:55.124808Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:55.124808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.08027","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":"2026-05-17T23:57:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47LuSV4b8sHIT7p9nFWfskZ6hTvJxyRFsbmPQZNy2w2fmzFjeutIvgE6UyIIr6LuIJIXqaom+pmWI/Oegb0rCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:24:20.650908Z"},"content_sha256":"2a510ac88c4339d9b0dd627eec1597bb766fc2fab89c86eb7959c70c042e4c40","schema_version":"1.0","event_id":"sha256:2a510ac88c4339d9b0dd627eec1597bb766fc2fab89c86eb7959c70c042e4c40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:272E2CFKO5G3Z3E2LPFRYYA4MO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Product of two staircase rank one transformations that is not loosely Bernoulli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Kanigowski, Thierry de la Rue (LMRS)","submitted_at":"2018-12-19T15:37:46Z","abstract_excerpt":"We construct two staircase rank one transformations whose Cartesian product is not loosely Bernoulli."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08027","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":"2026-05-17T23:57:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bnE4QbkPiWvSyiwk+ZQwVzaQ+FKYL23bdqAxAqVyfT1u1BiZ6n48XtiL940oHRO3HyIKdWzVrEeJ5i9WJhWEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:24:20.651245Z"},"content_sha256":"be211b691af98a3aafb46554b8c9f5df0b9eb9bb3da4e1d812b060f136f8f23e","schema_version":"1.0","event_id":"sha256:be211b691af98a3aafb46554b8c9f5df0b9eb9bb3da4e1d812b060f136f8f23e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/272E2CFKO5G3Z3E2LPFRYYA4MO/bundle.json","state_url":"https://pith.science/pith/272E2CFKO5G3Z3E2LPFRYYA4MO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/272E2CFKO5G3Z3E2LPFRYYA4MO/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":"2026-06-23T12:24:20Z","links":{"resolver":"https://pith.science/pith/272E2CFKO5G3Z3E2LPFRYYA4MO","bundle":"https://pith.science/pith/272E2CFKO5G3Z3E2LPFRYYA4MO/bundle.json","state":"https://pith.science/pith/272E2CFKO5G3Z3E2LPFRYYA4MO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/272E2CFKO5G3Z3E2LPFRYYA4MO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:272E2CFKO5G3Z3E2LPFRYYA4MO","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":"4f90dbeb5ece016c13154ea5162eec59383138f528d03948a2d2658547ef64b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-19T15:37:46Z","title_canon_sha256":"05dba94999046f175f6fb873e1c54323d2d7c718e4bc7dd34ef156b4345a928d"},"schema_version":"1.0","source":{"id":"1812.08027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08027","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08027v1","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08027","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"pith_short_12","alias_value":"272E2CFKO5G3","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"272E2CFKO5G3Z3E2","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"272E2CFK","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:be211b691af98a3aafb46554b8c9f5df0b9eb9bb3da4e1d812b060f136f8f23e","target":"graph","created_at":"2026-05-17T23:57:55Z","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 construct two staircase rank one transformations whose Cartesian product is not loosely Bernoulli.","authors_text":"Adam Kanigowski, Thierry de la Rue (LMRS)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-19T15:37:46Z","title":"Product of two staircase rank one transformations that is not loosely Bernoulli"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08027","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":"sha256:2a510ac88c4339d9b0dd627eec1597bb766fc2fab89c86eb7959c70c042e4c40","target":"record","created_at":"2026-05-17T23:57:55Z","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":"4f90dbeb5ece016c13154ea5162eec59383138f528d03948a2d2658547ef64b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-19T15:37:46Z","title_canon_sha256":"05dba94999046f175f6fb873e1c54323d2d7c718e4bc7dd34ef156b4345a928d"},"schema_version":"1.0","source":{"id":"1812.08027","kind":"arxiv","version":1}},"canonical_sha256":"d7f44d08aa774dbcec9a5bcb1c601c63a243aec53ac9dfdb6b53eee718d3d6c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7f44d08aa774dbcec9a5bcb1c601c63a243aec53ac9dfdb6b53eee718d3d6c6","first_computed_at":"2026-05-17T23:57:55.124808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:55.124808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/NibLUrN7reQVcj9pR2zFuo5t9yB1DwwRVZVWJv+jfexWnHmVh61Luh7cIYeh8LnLE2J624HeXce9vLXTd1rDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:55.125375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.08027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a510ac88c4339d9b0dd627eec1597bb766fc2fab89c86eb7959c70c042e4c40","sha256:be211b691af98a3aafb46554b8c9f5df0b9eb9bb3da4e1d812b060f136f8f23e"],"state_sha256":"a7d3ccf06b3e75c935099043a3d3d7703daadabf05fa3aed6fa551ad4b02387b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RhRC8oSnMmFoWnrYtpR/yDz976qoNKf70dil7fTNvbIixjaI6dCOx3ueHjg8+Rj6xT2jG7ePMuq7rWBADp/QCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T12:24:20.653207Z","bundle_sha256":"058e6fc427d95704a1203ceb0e708bdeeedaae361e6be96e6f650e78d7c93a3a"}}