{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JTYWNZXZULPEUZINIYSOHU73SW","short_pith_number":"pith:JTYWNZXZ","canonical_record":{"source":{"id":"1609.06877","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-22T09:17:05Z","cross_cats_sorted":["math.IT","math.PR","math.ST","stat.TH"],"title_canon_sha256":"5495a802d9387716311dd69e6f3bcb9e8e1728eb8abf5142d025c578614c281a","abstract_canon_sha256":"0182ce2e46de6f912def5153c2395bee8b3c310fa76fef94be0f0f6686a9574f"},"schema_version":"1.0"},"canonical_sha256":"4cf166e6f9a2de4a650d4624e3d3fb95a0da9c6e7e7c24f9b6e57f0e70700466","source":{"kind":"arxiv","id":"1609.06877","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06877","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06877v3","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06877","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"JTYWNZXZULPE","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JTYWNZXZULPEUZIN","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JTYWNZXZ","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JTYWNZXZULPEUZINIYSOHU73SW","target":"record","payload":{"canonical_record":{"source":{"id":"1609.06877","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-22T09:17:05Z","cross_cats_sorted":["math.IT","math.PR","math.ST","stat.TH"],"title_canon_sha256":"5495a802d9387716311dd69e6f3bcb9e8e1728eb8abf5142d025c578614c281a","abstract_canon_sha256":"0182ce2e46de6f912def5153c2395bee8b3c310fa76fef94be0f0f6686a9574f"},"schema_version":"1.0"},"canonical_sha256":"4cf166e6f9a2de4a650d4624e3d3fb95a0da9c6e7e7c24f9b6e57f0e70700466","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:26.696545Z","signature_b64":"tPXh5g5mrHs2RouP6vKo0t9O5Jnq+M9RTmlvIdCbqO8schohStXevUDzD7KFLczYknOWIHH9j/zRQDPCVut5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cf166e6f9a2de4a650d4624e3d3fb95a0da9c6e7e7c24f9b6e57f0e70700466","last_reissued_at":"2026-05-17T23:59:26.696054Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:26.696054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.06877","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0msH81i1OwSLg9CB7dY42qgMogfMNJ9y4BkWxbhJGi/UIXhB7GuVODYCk51LQskfBXALOl5jENWu9zDWQ9LFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:48:44.226555Z"},"content_sha256":"c4e29fa090934d032abb61cca0e56aa7bc8548fc11d97f716f391bb5d4c3f29d","schema_version":"1.0","event_id":"sha256:c4e29fa090934d032abb61cca0e56aa7bc8548fc11d97f716f391bb5d4c3f29d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JTYWNZXZULPEUZINIYSOHU73SW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comparison of Channels: Criteria for Domination by a Symmetric Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Anuran Makur, Yury Polyanskiy","submitted_at":"2016-09-22T09:17:05Z","abstract_excerpt":"This paper studies the basic question of whether a given channel $V$ can be dominated (in the precise sense of being more noisy) by a $q$-ary symmetric channel. The concept of \"less noisy\" relation between channels originated in network information theory (broadcast channels) and is defined in terms of mutual information or Kullback-Leibler divergence. We provide an equivalent characterization in terms of $\\chi^2$-divergence. Furthermore, we develop a simple criterion for domination by a $q$-ary symmetric channel in terms of the minimum entry of the stochastic matrix defining the channel $V$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06877","kind":"arxiv","version":3},"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":"2026-05-17T23:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wmh/fDWlBq2FKX6xW7K5QmX5V9Sw8skQvGcv7AIXESlDGEpG0qE2fVAnAWYrlfY0cRKVeV60u9IolsrZ8gGdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:48:44.226912Z"},"content_sha256":"1f96061da4d2ee42035050f64be114e80723ea38b60d1de4d1928f6940dc91f2","schema_version":"1.0","event_id":"sha256:1f96061da4d2ee42035050f64be114e80723ea38b60d1de4d1928f6940dc91f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JTYWNZXZULPEUZINIYSOHU73SW/bundle.json","state_url":"https://pith.science/pith/JTYWNZXZULPEUZINIYSOHU73SW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JTYWNZXZULPEUZINIYSOHU73SW/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":"2026-05-31T01:48:44Z","links":{"resolver":"https://pith.science/pith/JTYWNZXZULPEUZINIYSOHU73SW","bundle":"https://pith.science/pith/JTYWNZXZULPEUZINIYSOHU73SW/bundle.json","state":"https://pith.science/pith/JTYWNZXZULPEUZINIYSOHU73SW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JTYWNZXZULPEUZINIYSOHU73SW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JTYWNZXZULPEUZINIYSOHU73SW","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":"0182ce2e46de6f912def5153c2395bee8b3c310fa76fef94be0f0f6686a9574f","cross_cats_sorted":["math.IT","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-22T09:17:05Z","title_canon_sha256":"5495a802d9387716311dd69e6f3bcb9e8e1728eb8abf5142d025c578614c281a"},"schema_version":"1.0","source":{"id":"1609.06877","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06877","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06877v3","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06877","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"JTYWNZXZULPE","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JTYWNZXZULPEUZIN","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JTYWNZXZ","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:1f96061da4d2ee42035050f64be114e80723ea38b60d1de4d1928f6940dc91f2","target":"graph","created_at":"2026-05-17T23:59:26Z","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":"This paper studies the basic question of whether a given channel $V$ can be dominated (in the precise sense of being more noisy) by a $q$-ary symmetric channel. The concept of \"less noisy\" relation between channels originated in network information theory (broadcast channels) and is defined in terms of mutual information or Kullback-Leibler divergence. We provide an equivalent characterization in terms of $\\chi^2$-divergence. Furthermore, we develop a simple criterion for domination by a $q$-ary symmetric channel in terms of the minimum entry of the stochastic matrix defining the channel $V$. ","authors_text":"Anuran Makur, Yury Polyanskiy","cross_cats":["math.IT","math.PR","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-22T09:17:05Z","title":"Comparison of Channels: Criteria for Domination by a Symmetric Channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06877","kind":"arxiv","version":3},"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:c4e29fa090934d032abb61cca0e56aa7bc8548fc11d97f716f391bb5d4c3f29d","target":"record","created_at":"2026-05-17T23:59:26Z","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":"0182ce2e46de6f912def5153c2395bee8b3c310fa76fef94be0f0f6686a9574f","cross_cats_sorted":["math.IT","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-22T09:17:05Z","title_canon_sha256":"5495a802d9387716311dd69e6f3bcb9e8e1728eb8abf5142d025c578614c281a"},"schema_version":"1.0","source":{"id":"1609.06877","kind":"arxiv","version":3}},"canonical_sha256":"4cf166e6f9a2de4a650d4624e3d3fb95a0da9c6e7e7c24f9b6e57f0e70700466","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cf166e6f9a2de4a650d4624e3d3fb95a0da9c6e7e7c24f9b6e57f0e70700466","first_computed_at":"2026-05-17T23:59:26.696054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:26.696054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tPXh5g5mrHs2RouP6vKo0t9O5Jnq+M9RTmlvIdCbqO8schohStXevUDzD7KFLczYknOWIHH9j/zRQDPCVut5Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:26.696545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06877","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4e29fa090934d032abb61cca0e56aa7bc8548fc11d97f716f391bb5d4c3f29d","sha256:1f96061da4d2ee42035050f64be114e80723ea38b60d1de4d1928f6940dc91f2"],"state_sha256":"6ff0484b0a8c1ee452b4df16001e086d31b8bae6eb3251ad84ddc8cff6ce2ce2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tvxAjTElSac26AJGjtwW+wZrfrSfwm71DAQT6Ptr6qyKA7Pxue0jyimX8Pxl/Ug3LoTTxiZ93J3dYBLOT357Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:48:44.229137Z","bundle_sha256":"f49f701b6060a057bf2c1ccf84118c330341ccff6f5672ae946aa5473b69c0e9"}}