{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IWTOPXEYCLR3N4HCYSOMVJPG3V","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":"8f9f89fcd4a9a9f9389373e427da9db91dd0fd6aa0a0d87ecf7cc0c97ed390c5","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-16T01:21:50Z","title_canon_sha256":"b73c90899cf24df1cb882de90405d61e58a7cf45babb5d66b18274dc5f28c593"},"schema_version":"1.0","source":{"id":"1305.3666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3666","created_at":"2026-05-18T03:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3666v1","created_at":"2026-05-18T03:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3666","created_at":"2026-05-18T03:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"IWTOPXEYCLR3","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IWTOPXEYCLR3N4HC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IWTOPXEY","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:b31cba111403120205cb823f355b02fdf5c9d70725d9dac69e27a47ffeb88e84","target":"graph","created_at":"2026-05-18T03:25:34Z","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":"In the present paper we prove Besocovich weighted ergodic theorem for positive contractions acting on Orlich-Kantorovich space. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices.","authors_text":"Farrukh Mukhamedov, Inomjon Ganiev","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-16T01:21:50Z","title":"Weighted ergodic theorem for contractions of Orlicz-Kantorovich lattice $L_{M}(\\hat{\\nabla},\\hat{\\mu}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3666","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":"sha256:7d92918c9251ab2157bb62ca3809683cdb70fe8c4def2cc48d76277571eba767","target":"record","created_at":"2026-05-18T03:25:34Z","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":"8f9f89fcd4a9a9f9389373e427da9db91dd0fd6aa0a0d87ecf7cc0c97ed390c5","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-16T01:21:50Z","title_canon_sha256":"b73c90899cf24df1cb882de90405d61e58a7cf45babb5d66b18274dc5f28c593"},"schema_version":"1.0","source":{"id":"1305.3666","kind":"arxiv","version":1}},"canonical_sha256":"45a6e7dc9812e3b6f0e2c49ccaa5e6dd7cd2aecf22f513dcdbacdf6da4a9b085","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45a6e7dc9812e3b6f0e2c49ccaa5e6dd7cd2aecf22f513dcdbacdf6da4a9b085","first_computed_at":"2026-05-18T03:25:34.237538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:34.237538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"svsvkTaPv96p2DW1LGG6+MeAjKZU+j4caVuml7WsrljZcQaP0XBXlxi+k1Hyh0AY+rYbQt3BuOV+wc6KjkWMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:34.238083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d92918c9251ab2157bb62ca3809683cdb70fe8c4def2cc48d76277571eba767","sha256:b31cba111403120205cb823f355b02fdf5c9d70725d9dac69e27a47ffeb88e84"],"state_sha256":"79f43f60f390cf8f77e2de0bacadd46d519e3c90b16547bfe801a52d06981f9c"}