{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RXQCAMQE5SGUECHZX63UM2JY4Q","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":"ea950431c812d4600eea31933fdc136ab39cda14aacedda3fe8860b9aaf906b2","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-23T07:02:05Z","title_canon_sha256":"2c7f09c0c16e0c5489277e96e21f5ab22b97f863381d3fe4cda6dc9c39db2f77"},"schema_version":"1.0","source":{"id":"1206.5365","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5365","created_at":"2026-05-18T02:40:45Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5365v2","created_at":"2026-05-18T02:40:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5365","created_at":"2026-05-18T02:40:45Z"},{"alias_kind":"pith_short_12","alias_value":"RXQCAMQE5SGU","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RXQCAMQE5SGUECHZ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RXQCAMQE","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:520dfade769499be3aa3c28847c2796e2d8a6b047b84df240c084b31ebf67af1","target":"graph","created_at":"2026-05-18T02:40:45Z","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":"Network coding can significantly improve the transmission rate of communication networks with packet loss compared with routing. However, using network coding usually incurs high computational and storage costs in the network devices and terminals. For example, some network coding schemes require the computational and/or storage capacities of an intermediate network node to increase linearly with the number of packets for transmission, making such schemes difficult to be implemented in a router-like device that has only constant computational and storage capacities. In this paper, we introduce","authors_text":"Raymond W. Yeung, Shenghao Yang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-23T07:02:05Z","title":"Batched Sparse Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5365","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:ba772d7f8e55df10b125b386ac938cba2300ef08c44acc67c397782793a5d4eb","target":"record","created_at":"2026-05-18T02:40:45Z","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":"ea950431c812d4600eea31933fdc136ab39cda14aacedda3fe8860b9aaf906b2","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-06-23T07:02:05Z","title_canon_sha256":"2c7f09c0c16e0c5489277e96e21f5ab22b97f863381d3fe4cda6dc9c39db2f77"},"schema_version":"1.0","source":{"id":"1206.5365","kind":"arxiv","version":2}},"canonical_sha256":"8de0203204ec8d4208f9bfb7466938e40fb9fd07def34e7686b76a446075b35f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8de0203204ec8d4208f9bfb7466938e40fb9fd07def34e7686b76a446075b35f","first_computed_at":"2026-05-18T02:40:45.931687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:45.931687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ae83IxUntVIVIUW2jNq7KaZcIY68CECOmT32SyU5Q5eSTe5g7N1K2/xo/DoLaa2HhbKlSswOBwb3Qd1YWDxkBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:45.932107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5365","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba772d7f8e55df10b125b386ac938cba2300ef08c44acc67c397782793a5d4eb","sha256:520dfade769499be3aa3c28847c2796e2d8a6b047b84df240c084b31ebf67af1"],"state_sha256":"8b6b4752a4b0f93de7a504e7e5525792c743e2e7b1a64843c6c801c791fa0c8a"}