{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DOLCXT5EEGFPKHPMKQS4GUKMWC","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":"5e0aa818c958cdc673c228497b87a17acc55adf37494368683836d6edd9d9398","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-03T12:57:12Z","title_canon_sha256":"063656934bde100491c9039ed2edcdfd3d7386f1b03fc6369e87d9078ad41b53"},"schema_version":"1.0","source":{"id":"1705.01394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01394","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01394v1","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01394","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"DOLCXT5EEGFP","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DOLCXT5EEGFPKHPM","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DOLCXT5E","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:3f421349f146a231c06b61018aed5a410d7542ddf94b82bc3dd071e406f85c08","target":"graph","created_at":"2026-05-18T00:45:05Z","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 ordering of communication channels was first introduced by Shannon. In this paper, we aim to find a characterization of the Shannon ordering. We show that $W'$ contains $W$ if and only if $W$ is the skew-composition of $W'$ with a convex-product channel. This fact is used to derive a characterization of the Shannon ordering that is similar to the Blackwell-Sherman-Stein theorem. Two channels are said to be Shannon-equivalent if each one is contained in the other. We investigate the topologies that can be constructed on the space of Shannon-equivalent channels. We introduce the strong topol","authors_text":"Rajai Nasser","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-03T12:57:12Z","title":"A Characterization of the Shannon Ordering of Communication Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01394","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:edc4418a45bfd8b286277e81cf27e442457e46a2da1bde66d471ef7f1605e8cb","target":"record","created_at":"2026-05-18T00:45:05Z","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":"5e0aa818c958cdc673c228497b87a17acc55adf37494368683836d6edd9d9398","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-03T12:57:12Z","title_canon_sha256":"063656934bde100491c9039ed2edcdfd3d7386f1b03fc6369e87d9078ad41b53"},"schema_version":"1.0","source":{"id":"1705.01394","kind":"arxiv","version":1}},"canonical_sha256":"1b962bcfa4218af51dec5425c3514cb0b7d91413d6032e353457daad6afea88f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b962bcfa4218af51dec5425c3514cb0b7d91413d6032e353457daad6afea88f","first_computed_at":"2026-05-18T00:45:05.267741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:05.267741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qyZ6GvsSjx31Eyd1Npu5x3/Abp6aCRG89/F6wk8zYTaP7zOInuMoycTIQpFi6Ql/YH4PDPrBvXbf4exjqu3gAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:05.268246Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edc4418a45bfd8b286277e81cf27e442457e46a2da1bde66d471ef7f1605e8cb","sha256:3f421349f146a231c06b61018aed5a410d7542ddf94b82bc3dd071e406f85c08"],"state_sha256":"fa06e77a3eb693722f52d4575b835d6a8c8a6cc09f72eba044109861713ac237"}