{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X4YRIRTYC4AO5E5TZR6YJSV6YM","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":"04c723d6dfb726f6392cbe92dd054a3e04bd9334746e82dcee5fe98bd6767c10","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-22T15:11:35Z","title_canon_sha256":"38b0ec5dddecb412af88e6e73aa8cff62f282ef30ba9fa23ad8b110137d44f7b"},"schema_version":"1.0","source":{"id":"1601.06037","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06037","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06037v4","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06037","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"X4YRIRTYC4AO","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X4YRIRTYC4AO5E5T","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X4YRIRTY","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:239a6320e29b419e42cae9cb6c6a724f8c7e5bf974b164c21caa66e90d31d1fb","target":"graph","created_at":"2026-05-18T00:24:45Z","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":"In 2010, Silva, Kschischang and K\\\"otter studied certain classes of finite field matrix channels in order to model random linear network coding where exactly $t$ random errors are introduced.\n  In this paper we consider a generalisation of these matrix channels where the number of errors is not required to be constant, indeed the number of errors may follow any distribution. We show that a capacity-achieving input distribution can always be taken to have a very restricted form (the distribution should be uniform given the rank of the input matrix). This result complements, and is inspired by, ","authors_text":"Jessica Claridge, Simon R. Blackburn","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-22T15:11:35Z","title":"Finite field matrix channels for network coding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06037","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:dc34c7acd9bd3498d75fd1a60e8aea76174e08f994efb210948ca126602a4f21","target":"record","created_at":"2026-05-18T00:24:45Z","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":"04c723d6dfb726f6392cbe92dd054a3e04bd9334746e82dcee5fe98bd6767c10","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-22T15:11:35Z","title_canon_sha256":"38b0ec5dddecb412af88e6e73aa8cff62f282ef30ba9fa23ad8b110137d44f7b"},"schema_version":"1.0","source":{"id":"1601.06037","kind":"arxiv","version":4}},"canonical_sha256":"bf311446781700ee93b3cc7d84cabec3131c1e5631e99b66a4dcb335d0855d25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf311446781700ee93b3cc7d84cabec3131c1e5631e99b66a4dcb335d0855d25","first_computed_at":"2026-05-18T00:24:45.392075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:45.392075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"370e8V5Q80O7QTnJVLIAvmLzGOGRPbqZRx5yaQsJGZ6veb9EClUyUstjFv/pS1IMH8Wa6rl/siVqN8YzWjpPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:45.392651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06037","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc34c7acd9bd3498d75fd1a60e8aea76174e08f994efb210948ca126602a4f21","sha256:239a6320e29b419e42cae9cb6c6a724f8c7e5bf974b164c21caa66e90d31d1fb"],"state_sha256":"76c9be95380143e5dda2443fd9480c55b11284f1d13023c57cbb8c189ad54c23"}