{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QGRCO56CCDST6E4IDVVEEHA5US","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":"f436566c258c8c4adeccb7061149d3b5aa96b98e013380a4bb9e619b192c8e84","cross_cats_sorted":["math.IT","math.NT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-11-27T19:22:13Z","title_canon_sha256":"8825d0b3dfb8e7bd766388588e6b854d70acf3610af9153e372750f6edd55ac7"},"schema_version":"1.0","source":{"id":"1111.6289","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6289","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6289v4","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6289","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"QGRCO56CCDST","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QGRCO56CCDST6E4I","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QGRCO56C","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:739764183586b8cf164119a33e2462c7622932327b69bd232c4531a7c78daa5b","target":"graph","created_at":"2026-05-18T03:11:58Z","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 work concentrates on the study of inverse determinant sums, which arise from the union bound on the error probability, as a tool for designing and analyzing algebraic space-time block codes.\n  A general framework to study these sums is established, and the connection between asymptotic growth of inverse determinant sums and the diversity-multiplexing gain trade-off is investigated. It is proven that the growth of the inverse determinant sum of a division algebra-based space-time code is completely determined by the growth of the unit group. This reduces the inverse determinant sum analysi","authors_text":"Hsiao-feng Lu, Laura Luzzi, Roope Vehkalahti","cross_cats":["math.IT","math.NT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-11-27T19:22:13Z","title":"Inverse Determinant Sums and Connections Between Fading Channel Information Theory and Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6289","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":"sha256:0b23b326e6f87733e7404ebe56ecc1900f6581984d9b70114bb3376c10f848cd","target":"record","created_at":"2026-05-18T03:11:58Z","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":"f436566c258c8c4adeccb7061149d3b5aa96b98e013380a4bb9e619b192c8e84","cross_cats_sorted":["math.IT","math.NT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-11-27T19:22:13Z","title_canon_sha256":"8825d0b3dfb8e7bd766388588e6b854d70acf3610af9153e372750f6edd55ac7"},"schema_version":"1.0","source":{"id":"1111.6289","kind":"arxiv","version":4}},"canonical_sha256":"81a22777c210e53f13881d6a421c1da49290be148a2fcec6824994313c98a88f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81a22777c210e53f13881d6a421c1da49290be148a2fcec6824994313c98a88f","first_computed_at":"2026-05-18T03:11:58.350521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:58.350521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nqKzZzJfx4WFp4yGPi79/xE06NG+61K4Xj3k/CnEn2Gbqnk+kk6gaZfSDFxUVwa1YRNAi1ye0cC0W97sp19mBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:58.351233Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6289","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b23b326e6f87733e7404ebe56ecc1900f6581984d9b70114bb3376c10f848cd","sha256:739764183586b8cf164119a33e2462c7622932327b69bd232c4531a7c78daa5b"],"state_sha256":"01eb1b6089b7c84bb7f60be998e7734dd098e5361ec614903ea76ba757e3b6f7"}