{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2DERYQVOH2CL6KJUASMVUM3KY4","short_pith_number":"pith:2DERYQVO","canonical_record":{"source":{"id":"1209.4792","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-21T11:50:13Z","cross_cats_sorted":[],"title_canon_sha256":"0be10873a2feb5e0f4de2c729a210be901cf73774b46ea708562614067e7e211","abstract_canon_sha256":"f80002c08ac33fde79bf2d5ef3f04a2ef8fc650729fabbb28470c291d3581690"},"schema_version":"1.0"},"canonical_sha256":"d0c91c42ae3e84bf293404995a336ac724d7805f7ad2175ec62786bd397f03cf","source":{"kind":"arxiv","id":"1209.4792","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4792","created_at":"2026-05-18T02:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4792v2","created_at":"2026-05-18T02:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4792","created_at":"2026-05-18T02:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"2DERYQVOH2CL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2DERYQVOH2CL6KJU","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2DERYQVO","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2DERYQVOH2CL6KJUASMVUM3KY4","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4792","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-21T11:50:13Z","cross_cats_sorted":[],"title_canon_sha256":"0be10873a2feb5e0f4de2c729a210be901cf73774b46ea708562614067e7e211","abstract_canon_sha256":"f80002c08ac33fde79bf2d5ef3f04a2ef8fc650729fabbb28470c291d3581690"},"schema_version":"1.0"},"canonical_sha256":"d0c91c42ae3e84bf293404995a336ac724d7805f7ad2175ec62786bd397f03cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:18.066115Z","signature_b64":"sYnKjah+BaS19McJfOjZasWekZrhBmCSF9Ws/t/zjZzdFbArMm4IjjVjWP7hRM7+qy1mcpxs/BjEvRC2PD2vBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0c91c42ae3e84bf293404995a336ac724d7805f7ad2175ec62786bd397f03cf","last_reissued_at":"2026-05-18T02:20:18.065569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:18.065569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4792","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":"2026-05-18T02:20:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cJv1MvgH6VcdzyPBm15mCFGsiVtHre6sECyp6k2w5jPzSd1hhLr2K0DTsnjkqBH7MtL1fnbt/PTMzPxBbcW9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:28:35.332878Z"},"content_sha256":"40aed3b37cccd57f337271a7f4a8cfcb65dd7cfe06bd29d1c167eda39d2d0d5a","schema_version":"1.0","event_id":"sha256:40aed3b37cccd57f337271a7f4a8cfcb65dd7cfe06bd29d1c167eda39d2d0d5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2DERYQVOH2CL6KJUASMVUM3KY4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relative ergodic properties of C*-dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Farrukh Mukhamedov, Rocco Duvenhage","submitted_at":"2012-09-21T11:50:13Z","abstract_excerpt":"We study various ergodic properties of C*-dynamical systems inspired by unique ergodicity. In particular we work in a framework allowing for ergodic properties defined relative to various subspaces, and in terms of weighted means. Our main results are characterizations of such relative ergodic properties, ergodic theorems resulting from these properties, and examples exhibiting these properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4792","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":"2026-05-18T02:20:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+SDCwshx518dAWvgWlhBCvBZagR+itsukFzX1lsAf0nB3S0E80yEAmG/mZcmn+FWvMi/wF4faklruqhTY9r5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:28:35.333218Z"},"content_sha256":"311616106093e104ef0abcdb0e3542a52deeed34a7064267d5bd2ffc01ceda2d","schema_version":"1.0","event_id":"sha256:311616106093e104ef0abcdb0e3542a52deeed34a7064267d5bd2ffc01ceda2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2DERYQVOH2CL6KJUASMVUM3KY4/bundle.json","state_url":"https://pith.science/pith/2DERYQVOH2CL6KJUASMVUM3KY4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2DERYQVOH2CL6KJUASMVUM3KY4/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":"2026-06-01T13:28:35Z","links":{"resolver":"https://pith.science/pith/2DERYQVOH2CL6KJUASMVUM3KY4","bundle":"https://pith.science/pith/2DERYQVOH2CL6KJUASMVUM3KY4/bundle.json","state":"https://pith.science/pith/2DERYQVOH2CL6KJUASMVUM3KY4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2DERYQVOH2CL6KJUASMVUM3KY4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2DERYQVOH2CL6KJUASMVUM3KY4","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":"f80002c08ac33fde79bf2d5ef3f04a2ef8fc650729fabbb28470c291d3581690","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-21T11:50:13Z","title_canon_sha256":"0be10873a2feb5e0f4de2c729a210be901cf73774b46ea708562614067e7e211"},"schema_version":"1.0","source":{"id":"1209.4792","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4792","created_at":"2026-05-18T02:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4792v2","created_at":"2026-05-18T02:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4792","created_at":"2026-05-18T02:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"2DERYQVOH2CL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2DERYQVOH2CL6KJU","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2DERYQVO","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:311616106093e104ef0abcdb0e3542a52deeed34a7064267d5bd2ffc01ceda2d","target":"graph","created_at":"2026-05-18T02:20:18Z","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 various ergodic properties of C*-dynamical systems inspired by unique ergodicity. In particular we work in a framework allowing for ergodic properties defined relative to various subspaces, and in terms of weighted means. Our main results are characterizations of such relative ergodic properties, ergodic theorems resulting from these properties, and examples exhibiting these properties.","authors_text":"Farrukh Mukhamedov, Rocco Duvenhage","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-21T11:50:13Z","title":"Relative ergodic properties of C*-dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4792","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":"sha256:40aed3b37cccd57f337271a7f4a8cfcb65dd7cfe06bd29d1c167eda39d2d0d5a","target":"record","created_at":"2026-05-18T02:20:18Z","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":"f80002c08ac33fde79bf2d5ef3f04a2ef8fc650729fabbb28470c291d3581690","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-21T11:50:13Z","title_canon_sha256":"0be10873a2feb5e0f4de2c729a210be901cf73774b46ea708562614067e7e211"},"schema_version":"1.0","source":{"id":"1209.4792","kind":"arxiv","version":2}},"canonical_sha256":"d0c91c42ae3e84bf293404995a336ac724d7805f7ad2175ec62786bd397f03cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0c91c42ae3e84bf293404995a336ac724d7805f7ad2175ec62786bd397f03cf","first_computed_at":"2026-05-18T02:20:18.065569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:18.065569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sYnKjah+BaS19McJfOjZasWekZrhBmCSF9Ws/t/zjZzdFbArMm4IjjVjWP7hRM7+qy1mcpxs/BjEvRC2PD2vBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:18.066115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4792","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40aed3b37cccd57f337271a7f4a8cfcb65dd7cfe06bd29d1c167eda39d2d0d5a","sha256:311616106093e104ef0abcdb0e3542a52deeed34a7064267d5bd2ffc01ceda2d"],"state_sha256":"7166a7199c7c9b9cccaae68c9d041cb9e23e3a071b2940ee52c01ccd98ea06c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UVsMxEajUXjUyWoijtm1tlgIzPPMno49dTs8mtqWLQdM6LJd2oU3bn5V5PHP+Ldwf1A7q5+rCyFpZif9VQhMAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:28:35.335191Z","bundle_sha256":"3a4a0e0b8ffa3ee1a7432d92ed1b2f6d4c90223ba1d16d899ac618324c8f3347"}}