{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:REEW7H6VLRAD5JZJBFOXALHE7B","short_pith_number":"pith:REEW7H6V","canonical_record":{"source":{"id":"1302.5226","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-21T09:35:06Z","cross_cats_sorted":["cs.MA","math.DG"],"title_canon_sha256":"6daf7e4e582b7bab192e9b22bfffb6203368be964434ed4dc99fa9858420209b","abstract_canon_sha256":"e7d582eca4fb98476d4cdce77603fd1670245bd91242863865f80e2c52f3f02b"},"schema_version":"1.0"},"canonical_sha256":"89096f9fd55c403ea729095d702ce4f84a0cf3b943e4f065cd8df02cf7fcde18","source":{"kind":"arxiv","id":"1302.5226","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5226","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5226v2","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5226","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"pith_short_12","alias_value":"REEW7H6VLRAD","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"REEW7H6VLRAD5JZJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"REEW7H6V","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:REEW7H6VLRAD5JZJBFOXALHE7B","target":"record","payload":{"canonical_record":{"source":{"id":"1302.5226","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-21T09:35:06Z","cross_cats_sorted":["cs.MA","math.DG"],"title_canon_sha256":"6daf7e4e582b7bab192e9b22bfffb6203368be964434ed4dc99fa9858420209b","abstract_canon_sha256":"e7d582eca4fb98476d4cdce77603fd1670245bd91242863865f80e2c52f3f02b"},"schema_version":"1.0"},"canonical_sha256":"89096f9fd55c403ea729095d702ce4f84a0cf3b943e4f065cd8df02cf7fcde18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:01.562031Z","signature_b64":"YVztmQ3AgRft4gemW0Zsr6DK82MRGleHU5OdjdsUbwGgnDOs2oOFhpVOHNJeuWb3o/r28jm77skZ8dAifyWADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89096f9fd55c403ea729095d702ce4f84a0cf3b943e4f065cd8df02cf7fcde18","last_reissued_at":"2026-05-18T02:33:01.561677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:01.561677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.5226","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":"2026-05-18T02:33:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K/X59etMl5yAcIu02jw1tKOE8zrRdlodX9/8uGt+1FuWHcxHearBPRnqLKgjw8yMXMde3l+goholIyp9DCCmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:29:02.799669Z"},"content_sha256":"0db6ea89a86b0db03a69cda69ea1112199e70225bc4befba37441e21ed6df491","schema_version":"1.0","event_id":"sha256:0db6ea89a86b0db03a69cda69ea1112199e70225bc4befba37441e21ed6df491"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:REEW7H6VLRAD5JZJBFOXALHE7B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dobrushin ergodicity coefficient for Markov operators on cones, and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA","math.DG"],"primary_cat":"math.OA","authors_text":"St\\'ephane Gaubert, Zheng Qu","submitted_at":"2013-02-21T09:35:06Z","abstract_excerpt":"The analysis of classical consensus algorithms relies on contraction properties of adjoints of Markov operators, with respect to Hilbert's projective metric or to a related family of seminorms (Hopf's oscillation or Hilbert's seminorm). We generalize these properties to abstract consensus operators over normal cones, which include the unital completely positive maps (Kraus operators) arising in quantum information theory. In particular, we show that the contraction rate of such operators, with respect to the Hopf oscillation seminorm, is given by an analogue of Dobrushin's ergodicity coefficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5226","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":"2026-05-18T02:33:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tzhw5vtiOqQrrFOEwW/b7khAaEM2UvRFvi1q4bTzMmkRPlqcKhcXy2OjflyGFvxZncZasYz+HXZv4z+o3VGjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:29:02.800016Z"},"content_sha256":"f0347e669d417df33ad0447d080c24783e0b3cb05ae83d7cb01fd9a8a4063cab","schema_version":"1.0","event_id":"sha256:f0347e669d417df33ad0447d080c24783e0b3cb05ae83d7cb01fd9a8a4063cab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/REEW7H6VLRAD5JZJBFOXALHE7B/bundle.json","state_url":"https://pith.science/pith/REEW7H6VLRAD5JZJBFOXALHE7B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/REEW7H6VLRAD5JZJBFOXALHE7B/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":"2026-06-02T00:29:02Z","links":{"resolver":"https://pith.science/pith/REEW7H6VLRAD5JZJBFOXALHE7B","bundle":"https://pith.science/pith/REEW7H6VLRAD5JZJBFOXALHE7B/bundle.json","state":"https://pith.science/pith/REEW7H6VLRAD5JZJBFOXALHE7B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/REEW7H6VLRAD5JZJBFOXALHE7B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:REEW7H6VLRAD5JZJBFOXALHE7B","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":"e7d582eca4fb98476d4cdce77603fd1670245bd91242863865f80e2c52f3f02b","cross_cats_sorted":["cs.MA","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-21T09:35:06Z","title_canon_sha256":"6daf7e4e582b7bab192e9b22bfffb6203368be964434ed4dc99fa9858420209b"},"schema_version":"1.0","source":{"id":"1302.5226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5226","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5226v2","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5226","created_at":"2026-05-18T02:33:01Z"},{"alias_kind":"pith_short_12","alias_value":"REEW7H6VLRAD","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"REEW7H6VLRAD5JZJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"REEW7H6V","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:f0347e669d417df33ad0447d080c24783e0b3cb05ae83d7cb01fd9a8a4063cab","target":"graph","created_at":"2026-05-18T02:33:01Z","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":"The analysis of classical consensus algorithms relies on contraction properties of adjoints of Markov operators, with respect to Hilbert's projective metric or to a related family of seminorms (Hopf's oscillation or Hilbert's seminorm). We generalize these properties to abstract consensus operators over normal cones, which include the unital completely positive maps (Kraus operators) arising in quantum information theory. In particular, we show that the contraction rate of such operators, with respect to the Hopf oscillation seminorm, is given by an analogue of Dobrushin's ergodicity coefficie","authors_text":"St\\'ephane Gaubert, Zheng Qu","cross_cats":["cs.MA","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-21T09:35:06Z","title":"Dobrushin ergodicity coefficient for Markov operators on cones, and beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5226","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":"sha256:0db6ea89a86b0db03a69cda69ea1112199e70225bc4befba37441e21ed6df491","target":"record","created_at":"2026-05-18T02:33:01Z","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":"e7d582eca4fb98476d4cdce77603fd1670245bd91242863865f80e2c52f3f02b","cross_cats_sorted":["cs.MA","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-21T09:35:06Z","title_canon_sha256":"6daf7e4e582b7bab192e9b22bfffb6203368be964434ed4dc99fa9858420209b"},"schema_version":"1.0","source":{"id":"1302.5226","kind":"arxiv","version":2}},"canonical_sha256":"89096f9fd55c403ea729095d702ce4f84a0cf3b943e4f065cd8df02cf7fcde18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89096f9fd55c403ea729095d702ce4f84a0cf3b943e4f065cd8df02cf7fcde18","first_computed_at":"2026-05-18T02:33:01.561677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:01.561677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YVztmQ3AgRft4gemW0Zsr6DK82MRGleHU5OdjdsUbwGgnDOs2oOFhpVOHNJeuWb3o/r28jm77skZ8dAifyWADA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:01.562031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0db6ea89a86b0db03a69cda69ea1112199e70225bc4befba37441e21ed6df491","sha256:f0347e669d417df33ad0447d080c24783e0b3cb05ae83d7cb01fd9a8a4063cab"],"state_sha256":"fef890c3a2d4dd63557df7b3f46c9bc4c7ecb0111d3800f94b7d53f853132a3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EfQ+4b+OGBEu1h8aDX4haNeP4fclUdMFEyHczEtgQQZlrTtUU82Vxzy7A5x65hsGK8jWzshCF2pcNFnjp8t1Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:29:02.801951Z","bundle_sha256":"f482f738624130c34284aa6ff4b638e0c6062e1152d750f8b12ea7ed6c6182a0"}}