{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5X3QTZPD3CO6EUVGCAMIH3MAZJ","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":"890cf53fce22845bc294a06840188705f146bfa37a049dcd84ace2575f19a635","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-07-17T06:08:18Z","title_canon_sha256":"1d999eb6af5fa13b84f51c59c31ffa2f74860ffd90b0d2deba52c9f7fcf21691"},"schema_version":"1.0","source":{"id":"0907.2984","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2984","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2984v4","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2984","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"5X3QTZPD3CO6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5X3QTZPD3CO6EUVG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5X3QTZPD","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:96ea89bbf2fb37acaf01dd5ac16247c598c12060db040da44d3f91a91928cbde","target":"graph","created_at":"2026-05-18T04:20:14Z","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":"This paper extends linear-complexity concatenated coding schemes to fountain communication over the discrete-time memoryless channel. Achievable fountain error exponents for one-level and multi-level concatenated fountain codes are derived. It is also shown that concatenated coding schemes possess interesting properties in several multi-user fountain communication scenarios.","authors_text":"Jie Luo, Zheng Wang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-07-17T06:08:18Z","title":"Fountain Communication using Concatenated Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2984","kind":"arxiv","version":4},"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:d5b4d5d19eeced15613e4134da038bb5568a5f9c6f6dd980dbce838803650d7e","target":"record","created_at":"2026-05-18T04:20:14Z","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":"890cf53fce22845bc294a06840188705f146bfa37a049dcd84ace2575f19a635","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-07-17T06:08:18Z","title_canon_sha256":"1d999eb6af5fa13b84f51c59c31ffa2f74860ffd90b0d2deba52c9f7fcf21691"},"schema_version":"1.0","source":{"id":"0907.2984","kind":"arxiv","version":4}},"canonical_sha256":"edf709e5e3d89de252a6101883ed80ca6779156112b3d616869f6fb0a50296b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edf709e5e3d89de252a6101883ed80ca6779156112b3d616869f6fb0a50296b6","first_computed_at":"2026-05-18T04:20:14.801229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:14.801229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MHaQ4dYErBDn+m9zFFm/6M1lMObRXOORHylshH7+sttM204BtdPibfPdOEvVVhbxgt6hH/No0zRYnnc3yxkRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:14.801684Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.2984","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5b4d5d19eeced15613e4134da038bb5568a5f9c6f6dd980dbce838803650d7e","sha256:96ea89bbf2fb37acaf01dd5ac16247c598c12060db040da44d3f91a91928cbde"],"state_sha256":"9f61447d2baeb179af7baf36b8839980feba23e89e3e8836cfad92aa0ca320c3"}