{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:VZRB5H5M37NZBA6MNJSVAPRWW5","short_pith_number":"pith:VZRB5H5M","canonical_record":{"source":{"id":"math/0612025","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2006-12-01T15:30:18Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"16cecc54cbc3d0debe21b9b347b9fea9dc188cf69ac7ab96aafa52c5b883dd02","abstract_canon_sha256":"7df310d0d4ce039bb5f087f62e7cb405da800ba930ba0fe5f0c1bbc1563003c7"},"schema_version":"1.0"},"canonical_sha256":"ae621e9facdfdb9083cc6a65503e36b7654f00113d50b621b831d39673007e13","source":{"kind":"arxiv","id":"math/0612025","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612025","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612025v1","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612025","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"VZRB5H5M37NZ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"VZRB5H5M37NZBA6M","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"VZRB5H5M","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:VZRB5H5M37NZBA6MNJSVAPRWW5","target":"record","payload":{"canonical_record":{"source":{"id":"math/0612025","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2006-12-01T15:30:18Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"16cecc54cbc3d0debe21b9b347b9fea9dc188cf69ac7ab96aafa52c5b883dd02","abstract_canon_sha256":"7df310d0d4ce039bb5f087f62e7cb405da800ba930ba0fe5f0c1bbc1563003c7"},"schema_version":"1.0"},"canonical_sha256":"ae621e9facdfdb9083cc6a65503e36b7654f00113d50b621b831d39673007e13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:23.498007Z","signature_b64":"6tgmeZ1+nWmEiKCoTdgbCaAzUbvcoUD6mx5kt1jkEy+B7N3HKA98LHJVx5Ya0bGOpLCBLzieSEpa05itU9gdAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae621e9facdfdb9083cc6a65503e36b7654f00113d50b621b831d39673007e13","last_reissued_at":"2026-05-18T01:38:23.497307Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:23.497307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0612025","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":"2026-05-18T01:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z1L/7i9Vq1hQ6gv10V+nuCdyc5xZ9OWcdiGj+eHIhq5ZPmTXutdR3VHN0/rGvOc8Ddsr1cDeH9qQOuAgqN84DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:23:12.738787Z"},"content_sha256":"f7f214761a9c4f2e127d3662972b2073d2c40eb831bebb601826c07cda1f8edc","schema_version":"1.0","event_id":"sha256:f7f214761a9c4f2e127d3662972b2073d2c40eb831bebb601826c07cda1f8edc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:VZRB5H5M37NZBA6MNJSVAPRWW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strict weak mixing of some C*-dynamical systems based on free shifts","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Farrukh Mukhamedov, Francesco Fidaleo","submitted_at":"2006-12-01T15:30:18Z","abstract_excerpt":"We define a stronger property than unique ergodicity with respect to the fixed-point subalgebra previously investigated by Abadie and Dykema. Such a property is denoted as F-strict weak mixing (F stands for the Markov projection onto the fixed-point operator system). Then we show that the free shifts on the reduced C*-algebras of RD-groups, including the free group on infinitely many generators, and amalgamated free product C*-algebras, considered by Abadie and Dykema, are all strictly weak mixing and not merely uniquely ergodic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612025","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":"2026-05-18T01:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8esB+rIwxblFz6BBWZ54jCmPSyNMSSJWXcyZNQw6M/TwyXTG83Bd8SNEFiQXlVXs3niwdw+HtyqhlRjdg09Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:23:12.739138Z"},"content_sha256":"d03c43cd1d3b59866bf979896c7bfbf7d049c5ea99b247d48f79014c1c46c92c","schema_version":"1.0","event_id":"sha256:d03c43cd1d3b59866bf979896c7bfbf7d049c5ea99b247d48f79014c1c46c92c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZRB5H5M37NZBA6MNJSVAPRWW5/bundle.json","state_url":"https://pith.science/pith/VZRB5H5M37NZBA6MNJSVAPRWW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZRB5H5M37NZBA6MNJSVAPRWW5/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":"2026-06-01T13:23:12Z","links":{"resolver":"https://pith.science/pith/VZRB5H5M37NZBA6MNJSVAPRWW5","bundle":"https://pith.science/pith/VZRB5H5M37NZBA6MNJSVAPRWW5/bundle.json","state":"https://pith.science/pith/VZRB5H5M37NZBA6MNJSVAPRWW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZRB5H5M37NZBA6MNJSVAPRWW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:VZRB5H5M37NZBA6MNJSVAPRWW5","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":"7df310d0d4ce039bb5f087f62e7cb405da800ba930ba0fe5f0c1bbc1563003c7","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"math.OA","submitted_at":"2006-12-01T15:30:18Z","title_canon_sha256":"16cecc54cbc3d0debe21b9b347b9fea9dc188cf69ac7ab96aafa52c5b883dd02"},"schema_version":"1.0","source":{"id":"math/0612025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612025","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612025v1","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612025","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"VZRB5H5M37NZ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"VZRB5H5M37NZBA6M","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"VZRB5H5M","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:d03c43cd1d3b59866bf979896c7bfbf7d049c5ea99b247d48f79014c1c46c92c","target":"graph","created_at":"2026-05-18T01:38:23Z","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 define a stronger property than unique ergodicity with respect to the fixed-point subalgebra previously investigated by Abadie and Dykema. Such a property is denoted as F-strict weak mixing (F stands for the Markov projection onto the fixed-point operator system). Then we show that the free shifts on the reduced C*-algebras of RD-groups, including the free group on infinitely many generators, and amalgamated free product C*-algebras, considered by Abadie and Dykema, are all strictly weak mixing and not merely uniquely ergodic.","authors_text":"Farrukh Mukhamedov, Francesco Fidaleo","cross_cats":["math.FA"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2006-12-01T15:30:18Z","title":"Strict weak mixing of some C*-dynamical systems based on free shifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612025","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:f7f214761a9c4f2e127d3662972b2073d2c40eb831bebb601826c07cda1f8edc","target":"record","created_at":"2026-05-18T01:38:23Z","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":"7df310d0d4ce039bb5f087f62e7cb405da800ba930ba0fe5f0c1bbc1563003c7","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"math.OA","submitted_at":"2006-12-01T15:30:18Z","title_canon_sha256":"16cecc54cbc3d0debe21b9b347b9fea9dc188cf69ac7ab96aafa52c5b883dd02"},"schema_version":"1.0","source":{"id":"math/0612025","kind":"arxiv","version":1}},"canonical_sha256":"ae621e9facdfdb9083cc6a65503e36b7654f00113d50b621b831d39673007e13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae621e9facdfdb9083cc6a65503e36b7654f00113d50b621b831d39673007e13","first_computed_at":"2026-05-18T01:38:23.497307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:23.497307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6tgmeZ1+nWmEiKCoTdgbCaAzUbvcoUD6mx5kt1jkEy+B7N3HKA98LHJVx5Ya0bGOpLCBLzieSEpa05itU9gdAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:23.498007Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7f214761a9c4f2e127d3662972b2073d2c40eb831bebb601826c07cda1f8edc","sha256:d03c43cd1d3b59866bf979896c7bfbf7d049c5ea99b247d48f79014c1c46c92c"],"state_sha256":"12883405bb9937e077b302a182cb5e8199618aaa19131c2ae6f48cc1acd45249"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zvl4lpWl7CsTMPsSqVTkoa/7XaYs05Si+qIB91GMDkl+2ghEYiSANRvY/k+833N5yzffvubq8zK7RfN+6y6fDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:23:12.741140Z","bundle_sha256":"6186d6d1da83651dc2a8bb7eccc48731cc7476282b68c432a5a2a95d25b3ed41"}}