{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VSWFFRW744N3CS7AUEZFH6FCZB","short_pith_number":"pith:VSWFFRW7","canonical_record":{"source":{"id":"1002.2293","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-11T08:20:14Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ec639b4a13c972dbe9c31589f5b9648b63574254c6d23d406f41d92048fe340a","abstract_canon_sha256":"1bd91eba3e989ae5735de85bc1861e75331ed1122dc01dcd0f90e025aa4680f7"},"schema_version":"1.0"},"canonical_sha256":"acac52c6dfe71bb14be0a13253f8a2c85da56e80179ab676ab045fa99c10f910","source":{"kind":"arxiv","id":"1002.2293","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2293","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2293v2","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2293","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"VSWFFRW744N3","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VSWFFRW744N3CS7A","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VSWFFRW7","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VSWFFRW744N3CS7AUEZFH6FCZB","target":"record","payload":{"canonical_record":{"source":{"id":"1002.2293","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-11T08:20:14Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ec639b4a13c972dbe9c31589f5b9648b63574254c6d23d406f41d92048fe340a","abstract_canon_sha256":"1bd91eba3e989ae5735de85bc1861e75331ed1122dc01dcd0f90e025aa4680f7"},"schema_version":"1.0"},"canonical_sha256":"acac52c6dfe71bb14be0a13253f8a2c85da56e80179ab676ab045fa99c10f910","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:47.728696Z","signature_b64":"LKgEVB7wgbsWKnivH7tKON2sqmPgNWooFSjeGZc8YyMhGHFCM7LY1bAmQ+WvrTbmhc+HbnTt+2BMF8kMx45yDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acac52c6dfe71bb14be0a13253f8a2c85da56e80179ab676ab045fa99c10f910","last_reissued_at":"2026-05-18T00:58:47.728050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:47.728050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.2293","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9XgCgqv1H9Bxzq3dBFsWL8QzEksraTmWS9tfjQa+KP2rhXT/Mpat1DH4WTjs2bgi5pkgLL3HMABX2nbRW+ooCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:51:36.676400Z"},"content_sha256":"de32d3b49ae22de57d0476cef004b64a508032aa38d6c6a89d04bbb0368a25e5","schema_version":"1.0","event_id":"sha256:de32d3b49ae22de57d0476cef004b64a508032aa38d6c6a89d04bbb0368a25e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VSWFFRW744N3CS7AUEZFH6FCZB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Linear Operator Channels over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"En-hui Yang, Jin Meng, Raymond W. Yeung, Shenghao Yang, Siu-Wai Ho","submitted_at":"2010-02-11T08:20:14Z","abstract_excerpt":"Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The  transformation matrix is assumed to remain constant for every T input vectors and to be unknown to both the transmitter and the receiver. There are NO constraints on the distribution of the transformation matrix and the field size.\n Specifically, the optimality of subspac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2293","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tTt963Q4z1hMx9shQmqsMJ3+yT/6LEuI9q1UUuJ9/WiHAinb3w7Bv4JRWhJBhFUSC6W4cq0upBPJ94woXSS4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:51:36.676748Z"},"content_sha256":"6393506bc15957da65ea9d24d763f78bdf4c4d5453932c6850ea71644be2e7e6","schema_version":"1.0","event_id":"sha256:6393506bc15957da65ea9d24d763f78bdf4c4d5453932c6850ea71644be2e7e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSWFFRW744N3CS7AUEZFH6FCZB/bundle.json","state_url":"https://pith.science/pith/VSWFFRW744N3CS7AUEZFH6FCZB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSWFFRW744N3CS7AUEZFH6FCZB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T13:51:36Z","links":{"resolver":"https://pith.science/pith/VSWFFRW744N3CS7AUEZFH6FCZB","bundle":"https://pith.science/pith/VSWFFRW744N3CS7AUEZFH6FCZB/bundle.json","state":"https://pith.science/pith/VSWFFRW744N3CS7AUEZFH6FCZB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSWFFRW744N3CS7AUEZFH6FCZB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VSWFFRW744N3CS7AUEZFH6FCZB","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":"1bd91eba3e989ae5735de85bc1861e75331ed1122dc01dcd0f90e025aa4680f7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-11T08:20:14Z","title_canon_sha256":"ec639b4a13c972dbe9c31589f5b9648b63574254c6d23d406f41d92048fe340a"},"schema_version":"1.0","source":{"id":"1002.2293","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2293","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2293v2","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2293","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"VSWFFRW744N3","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VSWFFRW744N3CS7A","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VSWFFRW7","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:6393506bc15957da65ea9d24d763f78bdf4c4d5453932c6850ea71644be2e7e6","target":"graph","created_at":"2026-05-18T00:58:47Z","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":"Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The  transformation matrix is assumed to remain constant for every T input vectors and to be unknown to both the transmitter and the receiver. There are NO constraints on the distribution of the transformation matrix and the field size.\n Specifically, the optimality of subspac","authors_text":"En-hui Yang, Jin Meng, Raymond W. Yeung, Shenghao Yang, Siu-Wai Ho","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-11T08:20:14Z","title":"On Linear Operator Channels over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2293","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:de32d3b49ae22de57d0476cef004b64a508032aa38d6c6a89d04bbb0368a25e5","target":"record","created_at":"2026-05-18T00:58:47Z","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":"1bd91eba3e989ae5735de85bc1861e75331ed1122dc01dcd0f90e025aa4680f7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-11T08:20:14Z","title_canon_sha256":"ec639b4a13c972dbe9c31589f5b9648b63574254c6d23d406f41d92048fe340a"},"schema_version":"1.0","source":{"id":"1002.2293","kind":"arxiv","version":2}},"canonical_sha256":"acac52c6dfe71bb14be0a13253f8a2c85da56e80179ab676ab045fa99c10f910","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acac52c6dfe71bb14be0a13253f8a2c85da56e80179ab676ab045fa99c10f910","first_computed_at":"2026-05-18T00:58:47.728050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:47.728050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LKgEVB7wgbsWKnivH7tKON2sqmPgNWooFSjeGZc8YyMhGHFCM7LY1bAmQ+WvrTbmhc+HbnTt+2BMF8kMx45yDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:47.728696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.2293","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de32d3b49ae22de57d0476cef004b64a508032aa38d6c6a89d04bbb0368a25e5","sha256:6393506bc15957da65ea9d24d763f78bdf4c4d5453932c6850ea71644be2e7e6"],"state_sha256":"57dea434887c5c46569478d526cf2df0f8a8b0816b02ce2becf5614defb63117"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UqtWJnRhtWmoTq9OuooWuzrXo4fM1yJO3I7FWvaQLgxsjx4s5sj8H8HQaqdgErPgZCOsVPKjLhUfAY5DhfseDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T13:51:36.678690Z","bundle_sha256":"af9f2230bf854a9df9c1e202f48062851fe27a064ec1185f98c2e3337aa9e87f"}}