{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VF6ZMPEWNLARYLNZ33CTSXVRGJ","short_pith_number":"pith:VF6ZMPEW","canonical_record":{"source":{"id":"1208.3161","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-15T17:20:12Z","cross_cats_sorted":[],"title_canon_sha256":"3fce604f349244a19be9314bbdf7858efdcbdf0f1cc2587907cc0c4342ebd0ac","abstract_canon_sha256":"4c101618fb1dc7582bd6e564b78fbc35358b9e81e409ed31fafe38fbf80d1fdc"},"schema_version":"1.0"},"canonical_sha256":"a97d963c966ac11c2db9dec5395eb13248640cd8c5295f8762af6e4414dd6298","source":{"kind":"arxiv","id":"1208.3161","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3161","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3161v2","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3161","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"pith_short_12","alias_value":"VF6ZMPEWNLAR","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VF6ZMPEWNLARYLNZ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VF6ZMPEW","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VF6ZMPEWNLARYLNZ33CTSXVRGJ","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3161","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-15T17:20:12Z","cross_cats_sorted":[],"title_canon_sha256":"3fce604f349244a19be9314bbdf7858efdcbdf0f1cc2587907cc0c4342ebd0ac","abstract_canon_sha256":"4c101618fb1dc7582bd6e564b78fbc35358b9e81e409ed31fafe38fbf80d1fdc"},"schema_version":"1.0"},"canonical_sha256":"a97d963c966ac11c2db9dec5395eb13248640cd8c5295f8762af6e4414dd6298","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:11.686696Z","signature_b64":"XdIrUSjgX5QKwmOejnhTAGl0c+aTWdirzatn2dJ6/pxubzndUVTyIpB/Eo8T0/HohNvqwzyDIiXsSlWVzrSFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a97d963c966ac11c2db9dec5395eb13248640cd8c5295f8762af6e4414dd6298","last_reissued_at":"2026-05-18T02:04:11.685920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:11.685920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3161","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":"2026-05-18T02:04:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XPVcusxYQYLp7Yp3FYY5naGWZpBNe9QdddPkl+e3EOtOFq5CoPf7ZWetZCKntmUKS9Y56a6ZuKb4RdOaDBVJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:37:26.969626Z"},"content_sha256":"94ccf1c68397e4dd1f4882db42a09ccb7595f53d85906a80da30ac7c88be6589","schema_version":"1.0","event_id":"sha256:94ccf1c68397e4dd1f4882db42a09ccb7595f53d85906a80da30ac7c88be6589"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VF6ZMPEWNLARYLNZ33CTSXVRGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Rationally Ergodic and Rationally Weakly Mixing Rank-One Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Cesar E. Silva, Irving Dai, Tudor P\\u{a}durariu, Xavier Garcia","submitted_at":"2012-08-15T17:20:12Z","abstract_excerpt":"We study the notions of weak rational ergodicity and rational weak mixing as defined by Jon Aaronson. We prove that various families of infinite measure-preserving rank-one transformations possess (or do not posses) these properties, and consider their relation to other notions of mixing in infinite measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3161","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":"2026-05-18T02:04:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lt7UOquDLblSY8p2Jg9BvW4S1IslJbWJUupQhdUcMZS5RterZWpFhkkQSC5DS43gZiCvDJpBmMs2tr1p3lNrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:37:26.970269Z"},"content_sha256":"bf26377dea4e28b52ae124fec4cb0e0798138285be8245634488b37f86350444","schema_version":"1.0","event_id":"sha256:bf26377dea4e28b52ae124fec4cb0e0798138285be8245634488b37f86350444"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VF6ZMPEWNLARYLNZ33CTSXVRGJ/bundle.json","state_url":"https://pith.science/pith/VF6ZMPEWNLARYLNZ33CTSXVRGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VF6ZMPEWNLARYLNZ33CTSXVRGJ/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":"2026-05-30T02:37:26Z","links":{"resolver":"https://pith.science/pith/VF6ZMPEWNLARYLNZ33CTSXVRGJ","bundle":"https://pith.science/pith/VF6ZMPEWNLARYLNZ33CTSXVRGJ/bundle.json","state":"https://pith.science/pith/VF6ZMPEWNLARYLNZ33CTSXVRGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VF6ZMPEWNLARYLNZ33CTSXVRGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VF6ZMPEWNLARYLNZ33CTSXVRGJ","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":"4c101618fb1dc7582bd6e564b78fbc35358b9e81e409ed31fafe38fbf80d1fdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-15T17:20:12Z","title_canon_sha256":"3fce604f349244a19be9314bbdf7858efdcbdf0f1cc2587907cc0c4342ebd0ac"},"schema_version":"1.0","source":{"id":"1208.3161","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3161","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3161v2","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3161","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"pith_short_12","alias_value":"VF6ZMPEWNLAR","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VF6ZMPEWNLARYLNZ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VF6ZMPEW","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:bf26377dea4e28b52ae124fec4cb0e0798138285be8245634488b37f86350444","target":"graph","created_at":"2026-05-18T02:04:11Z","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":"We study the notions of weak rational ergodicity and rational weak mixing as defined by Jon Aaronson. We prove that various families of infinite measure-preserving rank-one transformations possess (or do not posses) these properties, and consider their relation to other notions of mixing in infinite measure.","authors_text":"Cesar E. Silva, Irving Dai, Tudor P\\u{a}durariu, Xavier Garcia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-15T17:20:12Z","title":"On Rationally Ergodic and Rationally Weakly Mixing Rank-One Transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3161","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":"sha256:94ccf1c68397e4dd1f4882db42a09ccb7595f53d85906a80da30ac7c88be6589","target":"record","created_at":"2026-05-18T02:04:11Z","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":"4c101618fb1dc7582bd6e564b78fbc35358b9e81e409ed31fafe38fbf80d1fdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-15T17:20:12Z","title_canon_sha256":"3fce604f349244a19be9314bbdf7858efdcbdf0f1cc2587907cc0c4342ebd0ac"},"schema_version":"1.0","source":{"id":"1208.3161","kind":"arxiv","version":2}},"canonical_sha256":"a97d963c966ac11c2db9dec5395eb13248640cd8c5295f8762af6e4414dd6298","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a97d963c966ac11c2db9dec5395eb13248640cd8c5295f8762af6e4414dd6298","first_computed_at":"2026-05-18T02:04:11.685920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:11.685920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XdIrUSjgX5QKwmOejnhTAGl0c+aTWdirzatn2dJ6/pxubzndUVTyIpB/Eo8T0/HohNvqwzyDIiXsSlWVzrSFAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:11.686696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3161","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94ccf1c68397e4dd1f4882db42a09ccb7595f53d85906a80da30ac7c88be6589","sha256:bf26377dea4e28b52ae124fec4cb0e0798138285be8245634488b37f86350444"],"state_sha256":"77a9b341562f5fc136951d8dad13b56a22dbb5841aad40cbbedbd300c2252a9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JFXgxmwsHHXyB/mVw4TV92reQxzQZ5M3tiqC5TF55pY5rVuNTY+ZqeYKvk+lbp4KhonV1DWQGYs+JDHRy+S2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:37:26.973547Z","bundle_sha256":"513a005f617b4a3518b7f7c392bc9d760bbede28625d35f20e78a6e1bb33f81f"}}