{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BQSE3XOE45GUFUBDADVJFVTSHT","short_pith_number":"pith:BQSE3XOE","canonical_record":{"source":{"id":"1507.07395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-27T13:20:51Z","cross_cats_sorted":["math.IT","math.NT"],"title_canon_sha256":"15d515ed7279712a66b392ecf08995c54ac37c42d4a3d3913f32697f384f0be2","abstract_canon_sha256":"e42457e39869a430204d2947cbc7f9f99344f8c831d06493fb5e9ce56e010007"},"schema_version":"1.0"},"canonical_sha256":"0c244dddc4e74d42d02300ea92d6723cd94cd9c3c428f2ef25bd775812273ef5","source":{"kind":"arxiv","id":"1507.07395","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07395","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07395v1","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07395","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"pith_short_12","alias_value":"BQSE3XOE45GU","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BQSE3XOE45GUFUBD","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BQSE3XOE","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BQSE3XOE45GUFUBDADVJFVTSHT","target":"record","payload":{"canonical_record":{"source":{"id":"1507.07395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-27T13:20:51Z","cross_cats_sorted":["math.IT","math.NT"],"title_canon_sha256":"15d515ed7279712a66b392ecf08995c54ac37c42d4a3d3913f32697f384f0be2","abstract_canon_sha256":"e42457e39869a430204d2947cbc7f9f99344f8c831d06493fb5e9ce56e010007"},"schema_version":"1.0"},"canonical_sha256":"0c244dddc4e74d42d02300ea92d6723cd94cd9c3c428f2ef25bd775812273ef5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:16.472412Z","signature_b64":"nN71NN8YtD+X1EZzeiIgfUnjRRL7Aa4eXP70g6C7/LNIIjubFW7AKLBZOUj/8hHyRdLC3RegSrE6P6SGyEP5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c244dddc4e74d42d02300ea92d6723cd94cd9c3c428f2ef25bd775812273ef5","last_reissued_at":"2026-05-18T01:36:16.471788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:16.471788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.07395","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uf+oUmQESYTMChJLgfldQtDvAnD34Fuv15EM23keOxQ6dZLGRWqe6c02pwCwHs8q0hZuYoI4rd4cWk5Z3w3RCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:22:57.371977Z"},"content_sha256":"7c9c4e90f98dce9d7abc1ba2346c96df4946777b5026706396568f78b01a321b","schema_version":"1.0","event_id":"sha256:7c9c4e90f98dce9d7abc1ba2346c96df4946777b5026706396568f78b01a321b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BQSE3XOE45GUFUBDADVJFVTSHT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost universal codes achieving ergodic MIMO capacity within a constant gap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"Laura Luzzi, Roope Vehkalahti","submitted_at":"2015-07-27T13:20:51Z","abstract_excerpt":"This work addresses the question of achieving capacity with lattice codes in multi-antenna block fading channels when the number of fading blocks tends to infinity. A design criterion based on the normalized minimum determinant is proposed for division algebra multiblock space-time codes over fading channels; this plays a similar role to the Hermite invariant for Gaussian channels. It is shown that this criterion is sufficient to guarantee transmission rates within a constant gap from capacity both for slow fading channels and ergodic fading channels. This performance is achieved both under ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07395","kind":"arxiv","version":1},"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":"2026-05-18T01:36:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5YVjNAWR4H6gYQIGNdeSgxtMJ0fE65dL4Hcc8FqhDRDTRxr2c5uztRjTzCXJ87po7ybMSWwANmAtq1W8u8p4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:22:57.372453Z"},"content_sha256":"12fa0ee886d5731cd8e72cb2c79ed0c2bd7cb1e07a52270bf3b5b7a49231ed07","schema_version":"1.0","event_id":"sha256:12fa0ee886d5731cd8e72cb2c79ed0c2bd7cb1e07a52270bf3b5b7a49231ed07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BQSE3XOE45GUFUBDADVJFVTSHT/bundle.json","state_url":"https://pith.science/pith/BQSE3XOE45GUFUBDADVJFVTSHT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BQSE3XOE45GUFUBDADVJFVTSHT/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":"2026-05-27T00:22:57Z","links":{"resolver":"https://pith.science/pith/BQSE3XOE45GUFUBDADVJFVTSHT","bundle":"https://pith.science/pith/BQSE3XOE45GUFUBDADVJFVTSHT/bundle.json","state":"https://pith.science/pith/BQSE3XOE45GUFUBDADVJFVTSHT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BQSE3XOE45GUFUBDADVJFVTSHT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BQSE3XOE45GUFUBDADVJFVTSHT","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":"e42457e39869a430204d2947cbc7f9f99344f8c831d06493fb5e9ce56e010007","cross_cats_sorted":["math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-27T13:20:51Z","title_canon_sha256":"15d515ed7279712a66b392ecf08995c54ac37c42d4a3d3913f32697f384f0be2"},"schema_version":"1.0","source":{"id":"1507.07395","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07395","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07395v1","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07395","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"pith_short_12","alias_value":"BQSE3XOE45GU","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BQSE3XOE45GUFUBD","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BQSE3XOE","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:12fa0ee886d5731cd8e72cb2c79ed0c2bd7cb1e07a52270bf3b5b7a49231ed07","target":"graph","created_at":"2026-05-18T01:36:16Z","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 addresses the question of achieving capacity with lattice codes in multi-antenna block fading channels when the number of fading blocks tends to infinity. A design criterion based on the normalized minimum determinant is proposed for division algebra multiblock space-time codes over fading channels; this plays a similar role to the Hermite invariant for Gaussian channels. It is shown that this criterion is sufficient to guarantee transmission rates within a constant gap from capacity both for slow fading channels and ergodic fading channels. This performance is achieved both under ma","authors_text":"Laura Luzzi, Roope Vehkalahti","cross_cats":["math.IT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-27T13:20:51Z","title":"Almost universal codes achieving ergodic MIMO capacity within a constant gap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07395","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":"sha256:7c9c4e90f98dce9d7abc1ba2346c96df4946777b5026706396568f78b01a321b","target":"record","created_at":"2026-05-18T01:36:16Z","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":"e42457e39869a430204d2947cbc7f9f99344f8c831d06493fb5e9ce56e010007","cross_cats_sorted":["math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-27T13:20:51Z","title_canon_sha256":"15d515ed7279712a66b392ecf08995c54ac37c42d4a3d3913f32697f384f0be2"},"schema_version":"1.0","source":{"id":"1507.07395","kind":"arxiv","version":1}},"canonical_sha256":"0c244dddc4e74d42d02300ea92d6723cd94cd9c3c428f2ef25bd775812273ef5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c244dddc4e74d42d02300ea92d6723cd94cd9c3c428f2ef25bd775812273ef5","first_computed_at":"2026-05-18T01:36:16.471788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:16.471788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nN71NN8YtD+X1EZzeiIgfUnjRRL7Aa4eXP70g6C7/LNIIjubFW7AKLBZOUj/8hHyRdLC3RegSrE6P6SGyEP5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:16.472412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07395","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c9c4e90f98dce9d7abc1ba2346c96df4946777b5026706396568f78b01a321b","sha256:12fa0ee886d5731cd8e72cb2c79ed0c2bd7cb1e07a52270bf3b5b7a49231ed07"],"state_sha256":"cc2953cd171610f3d18266dcb8e59ca3b4bc0982ea440c5e0fecd16da01ba97b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H5GxfElwgFRnGyasTRzQb6Cpe52VzhgSpomMOrHHHET16eAL0JCP2+/0QxVZ+BLBbwjF6UtYl48sHMkSzIeeDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:22:57.375160Z","bundle_sha256":"299a0a7a9509eae2cdca39e2ebafdc00318212fe1386d9df98863d260553a608"}}