{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:PM5IFIRCF6YJWKLHEESJHTYS6C","short_pith_number":"pith:PM5IFIRC","schema_version":"1.0","canonical_sha256":"7b3a82a2222fb09b2967212493cf12f08eb42497a366da9c4e3e5b2f659ffed5","source":{"kind":"arxiv","id":"2505.01152","version":2},"attestation_state":"computed","paper":{"title":"Polarization Decomposition and Its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jun Wang, Tianfu Qi","submitted_at":"2025-05-02T09:53:31Z","abstract_excerpt":"The polarization decomposition of arbitrary binary-input memoryless channels (BMCs) is studied in this work. By introducing the polarization factor (PF), defined in terms of the conditional entropy of the channel output under various input configurations, we demonstrate that the symmetric capacities of the polarized subchannels can be uniformly expressed as functions of the PF. The explicit formulation of the PF as a function of the block length and subchannel index is derived. Furthermore, an efficient algorithm is proposed for the computation of the PF. Notably, we establish a one-to-one cor"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.01152","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-05-02T09:53:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d2fb5552b24a380862048566121d38b3fec23bdabee4d4e54a7aaa67adb9b902","abstract_canon_sha256":"df916051cf94d2ec514f9b3765006c275804b7982170058106afdc2d25f1fbc1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:58:27.605719Z","signature_b64":"85uew0dMSki/T52RUS1WbC15gR/qz1ct3uwcNuyu2xjOLWLFgixhVzIG0o0mMzi/p9+mvuunUZbAmmmxKgtwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b3a82a2222fb09b2967212493cf12f08eb42497a366da9c4e3e5b2f659ffed5","last_reissued_at":"2026-07-05T10:58:27.605250Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:58:27.605250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polarization Decomposition and Its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jun Wang, Tianfu Qi","submitted_at":"2025-05-02T09:53:31Z","abstract_excerpt":"The polarization decomposition of arbitrary binary-input memoryless channels (BMCs) is studied in this work. By introducing the polarization factor (PF), defined in terms of the conditional entropy of the channel output under various input configurations, we demonstrate that the symmetric capacities of the polarized subchannels can be uniformly expressed as functions of the PF. The explicit formulation of the PF as a function of the block length and subchannel index is derived. Furthermore, an efficient algorithm is proposed for the computation of the PF. Notably, we establish a one-to-one cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.01152","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.01152/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2505.01152","created_at":"2026-07-05T10:58:27.605309+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.01152v2","created_at":"2026-07-05T10:58:27.605309+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.01152","created_at":"2026-07-05T10:58:27.605309+00:00"},{"alias_kind":"pith_short_12","alias_value":"PM5IFIRCF6YJ","created_at":"2026-07-05T10:58:27.605309+00:00"},{"alias_kind":"pith_short_16","alias_value":"PM5IFIRCF6YJWKLH","created_at":"2026-07-05T10:58:27.605309+00:00"},{"alias_kind":"pith_short_8","alias_value":"PM5IFIRC","created_at":"2026-07-05T10:58:27.605309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PM5IFIRCF6YJWKLHEESJHTYS6C","json":"https://pith.science/pith/PM5IFIRCF6YJWKLHEESJHTYS6C.json","graph_json":"https://pith.science/api/pith-number/PM5IFIRCF6YJWKLHEESJHTYS6C/graph.json","events_json":"https://pith.science/api/pith-number/PM5IFIRCF6YJWKLHEESJHTYS6C/events.json","paper":"https://pith.science/paper/PM5IFIRC"},"agent_actions":{"view_html":"https://pith.science/pith/PM5IFIRCF6YJWKLHEESJHTYS6C","download_json":"https://pith.science/pith/PM5IFIRCF6YJWKLHEESJHTYS6C.json","view_paper":"https://pith.science/paper/PM5IFIRC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.01152&json=true","fetch_graph":"https://pith.science/api/pith-number/PM5IFIRCF6YJWKLHEESJHTYS6C/graph.json","fetch_events":"https://pith.science/api/pith-number/PM5IFIRCF6YJWKLHEESJHTYS6C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PM5IFIRCF6YJWKLHEESJHTYS6C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PM5IFIRCF6YJWKLHEESJHTYS6C/action/storage_attestation","attest_author":"https://pith.science/pith/PM5IFIRCF6YJWKLHEESJHTYS6C/action/author_attestation","sign_citation":"https://pith.science/pith/PM5IFIRCF6YJWKLHEESJHTYS6C/action/citation_signature","submit_replication":"https://pith.science/pith/PM5IFIRCF6YJWKLHEESJHTYS6C/action/replication_record"}},"created_at":"2026-07-05T10:58:27.605309+00:00","updated_at":"2026-07-05T10:58:27.605309+00:00"}