{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IO35IGLODUL7A2ZAD6EAMGXJJS","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":"27a329ea79412af719cdc4a36ecc4806fef5712b13f0fd5d18d0385284dc7741","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-09-16T16:37:25Z","title_canon_sha256":"add0a33efc0a6a780d10ec7e4da15b2b50b29ad9881fc2e25234c6ef45761366"},"schema_version":"1.0","source":{"id":"1309.4026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4026","created_at":"2026-05-18T00:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4026v1","created_at":"2026-05-18T00:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4026","created_at":"2026-05-18T00:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"IO35IGLODUL7","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IO35IGLODUL7A2ZA","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IO35IGLO","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:772b564198ca47ebb527fb1e77e4705ff56035282a57ef98c1d3019f9ed0d7c7","target":"graph","created_at":"2026-05-18T00:57:52Z","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":"We investigate the problem of secure transmission over a two-user multi-input multi-output (MIMO) X-channel in which channel state information is provided with one-unit delay to both transmitters (CSIT), and each receiver feeds back its channel output to a different transmitter. We refer to this model as MIMO X-channel with asymmetric output feedback and delayed CSIT. The transmitters are equipped with M-antennas each, and the receivers are equipped with N-antennas each. For this model, accounting for both messages at each receiver, we characterize the optimal sum secure degrees of freedom (SD","authors_text":"Abdellatif Zaidi, Luc Vandendorpe, Shlomo Shamai (Shitz), Zohaib Hassan Awan","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-09-16T16:37:25Z","title":"Secure Degrees of Freedom of MIMO X-Channels with Output Feedback and Delayed CSIT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4026","kind":"arxiv","version":1},"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":"sha256:58669976d31aeedcd5e108bfc87693a59b51e2b617384dde6ee947273077bcd5","target":"record","created_at":"2026-05-18T00:57:52Z","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":"27a329ea79412af719cdc4a36ecc4806fef5712b13f0fd5d18d0385284dc7741","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-09-16T16:37:25Z","title_canon_sha256":"add0a33efc0a6a780d10ec7e4da15b2b50b29ad9881fc2e25234c6ef45761366"},"schema_version":"1.0","source":{"id":"1309.4026","kind":"arxiv","version":1}},"canonical_sha256":"43b7d4196e1d17f06b201f88061ae94ca593208b8f4a9b6bc6ebf2e816303e4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43b7d4196e1d17f06b201f88061ae94ca593208b8f4a9b6bc6ebf2e816303e4c","first_computed_at":"2026-05-18T00:57:52.676812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:52.676812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hjlR2OmVyYH1aKc/0YEAkctDYGLgLGTnYnnN1DFFCxz0/lSCqpU1erFGwlqXnK0TPdbx4qceTCRhv07o0tTMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:52.677537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58669976d31aeedcd5e108bfc87693a59b51e2b617384dde6ee947273077bcd5","sha256:772b564198ca47ebb527fb1e77e4705ff56035282a57ef98c1d3019f9ed0d7c7"],"state_sha256":"7216d62aa943e90f01075a4a4c2d55bfb5a0c0d7590c926382a571743cb0e4e2"}