{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GXYJDVFYV6SW7JADRBEBBIVUI4","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":"5617de7701df0863085895f833a974cef13c6027daffd730c40769820708db45","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-28T06:36:54Z","title_canon_sha256":"2d9c6eff1e23c9b2037e7d2edfc980d2bf059fc6b2b85a5cb2dffd9f4b7ec42d"},"schema_version":"1.0","source":{"id":"1006.5271","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5271","created_at":"2026-05-18T03:35:36Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5271v3","created_at":"2026-05-18T03:35:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5271","created_at":"2026-05-18T03:35:36Z"},{"alias_kind":"pith_short_12","alias_value":"GXYJDVFYV6SW","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GXYJDVFYV6SW7JAD","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GXYJDVFY","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:a0d9168fb6652ef5a4a2650fd68259f2ffe8528acff5d1bba85234696adcc0c5","target":"graph","created_at":"2026-05-18T03:35:36Z","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 aim of this paper is to prove theorems for the Slepian-Wolf source coding and the broadcast channel coding (independent messages and no common message) based on the the notion of a stronger version of the hash property for an ensemble of functions. Since an ensemble of sparse matrices has a strong hash property, codes using sparse matrices can realize the achievable rate region. Furthermore, extensions to the multiple source coding and multiple output broadcast channel coding are investigated.","authors_text":"Jun Muramatsu, Shigeki Miyake","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-28T06:36:54Z","title":"Construction of Slepian-Wolf Source Code and Broadcast Channel Code Based on Hash Property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5271","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:b76d5d674c5c5aad3be6a192c0468255e2166bca6b4b887b8103b5ae5da1cf2d","target":"record","created_at":"2026-05-18T03:35:36Z","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":"5617de7701df0863085895f833a974cef13c6027daffd730c40769820708db45","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-28T06:36:54Z","title_canon_sha256":"2d9c6eff1e23c9b2037e7d2edfc980d2bf059fc6b2b85a5cb2dffd9f4b7ec42d"},"schema_version":"1.0","source":{"id":"1006.5271","kind":"arxiv","version":3}},"canonical_sha256":"35f091d4b8afa56fa403884810a2b44728c28c2bab58a07425998f3ba6d307a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35f091d4b8afa56fa403884810a2b44728c28c2bab58a07425998f3ba6d307a4","first_computed_at":"2026-05-18T03:35:36.867540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:36.867540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5YRzbWrl00tt0SG6fKBpckmwbxN5sYgHb78zNlITOfbz9Oxo/eBN2KmGJpEV9g3jPO3VyAUQqwNnOVUZ/X0iCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:36.868389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5271","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b76d5d674c5c5aad3be6a192c0468255e2166bca6b4b887b8103b5ae5da1cf2d","sha256:a0d9168fb6652ef5a4a2650fd68259f2ffe8528acff5d1bba85234696adcc0c5"],"state_sha256":"3d4b5382f9a8014376e12f5d3d8ace0a354875e876c1610755c45f2ef000d788"}