{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:IRLHIPI6YTREU7N2WINPK3MITV","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":"1612c71ca4f23bf439ac917be2304c0f14204f42a4df35e4adcbdd454d7ef81e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-01-25T05:13:11Z","title_canon_sha256":"2f468e2d22aa3a6571546d86f74a3169e772088f2513176359a821e5fd311a6e"},"schema_version":"1.0","source":{"id":"0801.3878","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.3878","created_at":"2026-05-18T03:35:36Z"},{"alias_kind":"arxiv_version","alias_value":"0801.3878v2","created_at":"2026-05-18T03:35:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.3878","created_at":"2026-05-18T03:35:36Z"},{"alias_kind":"pith_short_12","alias_value":"IRLHIPI6YTRE","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"IRLHIPI6YTREU7N2","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"IRLHIPI6","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:e6a4339da80c1653d3658d1964304d38d97e799679a18fc996b84df2f6f71ed1","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 the achievability of several coding problems by using sparse matrices (the maximum column weight grows logarithmically in the block length) and maximal-likelihood (ML) coding. These problems are the Slepian-Wolf problem, the Gel'fand-Pinsker problem, the Wyner-Ziv problem, and the One-helps-one problem (source coding with partial side information at the decoder). To this end, the notion of a hash property for an ensemble of functions is introduced and it is proved that an ensemble of $q$-ary sparse matrices satisfies the hash property. Based on this property, ","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":"2008-01-25T05:13:11Z","title":"Hash Property and Coding Theorems for Sparse Matrices and Maximum-Likelihood Coding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3878","kind":"arxiv","version":2},"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":"sha256:2aa0431dfd9d56aaae945577f0372275f4351c6470512b6ba0e329379d321ea2","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":"1612c71ca4f23bf439ac917be2304c0f14204f42a4df35e4adcbdd454d7ef81e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-01-25T05:13:11Z","title_canon_sha256":"2f468e2d22aa3a6571546d86f74a3169e772088f2513176359a821e5fd311a6e"},"schema_version":"1.0","source":{"id":"0801.3878","kind":"arxiv","version":2}},"canonical_sha256":"4456743d1ec4e24a7dbab21af56d889d58423e2e2e59248f9c4a77e76b2c6115","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4456743d1ec4e24a7dbab21af56d889d58423e2e2e59248f9c4a77e76b2c6115","first_computed_at":"2026-05-18T03:35:36.938806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:36.938806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UzLVFSoKywXMnLPsMFuJH1quU0m4alWzUxjbYz0dRd756CVctSmef5Ea8iEWs3MqELU7eqHnDKHGY/0YOpXIDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:36.939566Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.3878","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2aa0431dfd9d56aaae945577f0372275f4351c6470512b6ba0e329379d321ea2","sha256:e6a4339da80c1653d3658d1964304d38d97e799679a18fc996b84df2f6f71ed1"],"state_sha256":"ea4f47c8eb8f6d458507bafd6b21a75560736562610adfcf71a68950673a1173"}