{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VUFYFRAGO5BYJKSYFZKWHR4GC5","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":"c27a301437f1f93dddd2b20a929e56d6451a506fd3132769a7de650a1a6ef02a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-10T11:35:24Z","title_canon_sha256":"91ba48ee2c676db592b588a122f8a71ed5948cc1e9166cab337e8eca3b14296a"},"schema_version":"1.0","source":{"id":"1006.2006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2006","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2006v1","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2006","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"pith_short_12","alias_value":"VUFYFRAGO5BY","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VUFYFRAGO5BYJKSY","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VUFYFRAG","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:61531cae45547c15757305feec324825fc514e2178bc4092da5ed967ad30f368","target":"graph","created_at":"2026-05-18T00:57:57Z","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":"It is shown that given two copies of a q-ary input channel $W$, where q is prime, it is possible to create two channels $W^-$ and $W^+$ whose symmetric capacities satisfy $I(W^-)\\le I(W)\\le I(W^+)$, where the inequalities are strict except in trivial cases. This leads to a simple proof of channel polarization in the q-ary case.","authors_text":"Eren Sasoglu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-10T11:35:24Z","title":"An entropy inequality for q-ary random variables and its application to channel polarization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2006","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:b95f376041d30eb750af6712f12e0ef32456cc6de618c504af7e821945d60044","target":"record","created_at":"2026-05-18T00:57:57Z","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":"c27a301437f1f93dddd2b20a929e56d6451a506fd3132769a7de650a1a6ef02a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-10T11:35:24Z","title_canon_sha256":"91ba48ee2c676db592b588a122f8a71ed5948cc1e9166cab337e8eca3b14296a"},"schema_version":"1.0","source":{"id":"1006.2006","kind":"arxiv","version":1}},"canonical_sha256":"ad0b82c406774384aa582e5563c7861765a4c4986d7321a08beca29fbbc6d5a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad0b82c406774384aa582e5563c7861765a4c4986d7321a08beca29fbbc6d5a4","first_computed_at":"2026-05-18T00:57:57.755324Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:57.755324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zmm+7q/ov32T9IlB35qVLkXvYI3626o8wv5wLT7oz/bMf91v27VPLmvQyJmcKMwP7js8FYLZpMVVm3Kimd8CBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:57.755918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.2006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b95f376041d30eb750af6712f12e0ef32456cc6de618c504af7e821945d60044","sha256:61531cae45547c15757305feec324825fc514e2178bc4092da5ed967ad30f368"],"state_sha256":"a1dfccbbcda7e8c9221da10878420c117eba02da22833265f8f769951884f363"}