{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IZGIA6XWVNVVFPS4WUNSW4G4QL","short_pith_number":"pith:IZGIA6XW","canonical_record":{"source":{"id":"1501.01773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-08T09:18:52Z","cross_cats_sorted":["math.IT","math.NT"],"title_canon_sha256":"208ee09e582a147466f4983b886e5566f45867b83b107aa743f387a5defb009f","abstract_canon_sha256":"62fe0779cf5221b69891ff3a87494f5d3b87516414216ff7128609d81681e1b1"},"schema_version":"1.0"},"canonical_sha256":"464c807af6ab6b52be5cb51b2b70dc82f5fc1191011fde1340b00b309a2515f3","source":{"kind":"arxiv","id":"1501.01773","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01773","created_at":"2026-05-18T02:29:46Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01773v1","created_at":"2026-05-18T02:29:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01773","created_at":"2026-05-18T02:29:46Z"},{"alias_kind":"pith_short_12","alias_value":"IZGIA6XWVNVV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"IZGIA6XWVNVVFPS4","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"IZGIA6XW","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IZGIA6XWVNVVFPS4WUNSW4G4QL","target":"record","payload":{"canonical_record":{"source":{"id":"1501.01773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-08T09:18:52Z","cross_cats_sorted":["math.IT","math.NT"],"title_canon_sha256":"208ee09e582a147466f4983b886e5566f45867b83b107aa743f387a5defb009f","abstract_canon_sha256":"62fe0779cf5221b69891ff3a87494f5d3b87516414216ff7128609d81681e1b1"},"schema_version":"1.0"},"canonical_sha256":"464c807af6ab6b52be5cb51b2b70dc82f5fc1191011fde1340b00b309a2515f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:46.406825Z","signature_b64":"tr8wyTI8H44Ic2eicLpTcY0SF2w8ssGpuztQCJCACtFj138+7hl9DToVIak1prosPzdrwXNVDaMEtjmFDlUZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"464c807af6ab6b52be5cb51b2b70dc82f5fc1191011fde1340b00b309a2515f3","last_reissued_at":"2026-05-18T02:29:46.406436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:46.406436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.01773","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":"2026-05-18T02:29:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gUpw0hvcei/Vv0rbWltNmKIVz2pRz193II4N58epMxXaJt6yJgXR65JYFstmibs0PUrYHO3dBomJGv03kJp3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:26:31.925433Z"},"content_sha256":"befc5d5fe1cd7c8815332bb9f5907542ea45cbc02afcd1fd55fa1e20e450897d","schema_version":"1.0","event_id":"sha256:befc5d5fe1cd7c8815332bb9f5907542ea45cbc02afcd1fd55fa1e20e450897d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IZGIA6XWVNVVFPS4WUNSW4G4QL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimates for the growth of inverse determinant sums of quasi-orthogonal and number field lattices","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":"2015-01-08T09:18:52Z","abstract_excerpt":"Inverse determinant sums appear naturally as a tool for analyzing performance of space-time codes in Rayleigh fading channels. This work will analyze the growth of inverse determinant sums of a family of quasi-orthogonal codes and will show that the growths are in logarithmic class. This is considerably lower than that of comparable number field codes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01773","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":"2026-05-18T02:29:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"39NMlgdrV9MXliZ9eI+dAEGMT94okNEXYDRLLYKADmdx2g/SHhhTKK0KeRTuOFXdmRUSPnHRTbJ9XXqiq3VgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:26:31.925838Z"},"content_sha256":"3dd31bea034f663f4f64b50121ffe98348c86a31b11ac773c8eadbfa680c6374","schema_version":"1.0","event_id":"sha256:3dd31bea034f663f4f64b50121ffe98348c86a31b11ac773c8eadbfa680c6374"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IZGIA6XWVNVVFPS4WUNSW4G4QL/bundle.json","state_url":"https://pith.science/pith/IZGIA6XWVNVVFPS4WUNSW4G4QL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IZGIA6XWVNVVFPS4WUNSW4G4QL/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":"2026-05-27T01:26:31Z","links":{"resolver":"https://pith.science/pith/IZGIA6XWVNVVFPS4WUNSW4G4QL","bundle":"https://pith.science/pith/IZGIA6XWVNVVFPS4WUNSW4G4QL/bundle.json","state":"https://pith.science/pith/IZGIA6XWVNVVFPS4WUNSW4G4QL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IZGIA6XWVNVVFPS4WUNSW4G4QL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IZGIA6XWVNVVFPS4WUNSW4G4QL","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":"62fe0779cf5221b69891ff3a87494f5d3b87516414216ff7128609d81681e1b1","cross_cats_sorted":["math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-08T09:18:52Z","title_canon_sha256":"208ee09e582a147466f4983b886e5566f45867b83b107aa743f387a5defb009f"},"schema_version":"1.0","source":{"id":"1501.01773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01773","created_at":"2026-05-18T02:29:46Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01773v1","created_at":"2026-05-18T02:29:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01773","created_at":"2026-05-18T02:29:46Z"},{"alias_kind":"pith_short_12","alias_value":"IZGIA6XWVNVV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"IZGIA6XWVNVVFPS4","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"IZGIA6XW","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:3dd31bea034f663f4f64b50121ffe98348c86a31b11ac773c8eadbfa680c6374","target":"graph","created_at":"2026-05-18T02:29:46Z","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":"Inverse determinant sums appear naturally as a tool for analyzing performance of space-time codes in Rayleigh fading channels. This work will analyze the growth of inverse determinant sums of a family of quasi-orthogonal codes and will show that the growths are in logarithmic class. This is considerably lower than that of comparable number field codes.","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":"2015-01-08T09:18:52Z","title":"Estimates for the growth of inverse determinant sums of quasi-orthogonal and number field lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01773","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:befc5d5fe1cd7c8815332bb9f5907542ea45cbc02afcd1fd55fa1e20e450897d","target":"record","created_at":"2026-05-18T02:29:46Z","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":"62fe0779cf5221b69891ff3a87494f5d3b87516414216ff7128609d81681e1b1","cross_cats_sorted":["math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-08T09:18:52Z","title_canon_sha256":"208ee09e582a147466f4983b886e5566f45867b83b107aa743f387a5defb009f"},"schema_version":"1.0","source":{"id":"1501.01773","kind":"arxiv","version":1}},"canonical_sha256":"464c807af6ab6b52be5cb51b2b70dc82f5fc1191011fde1340b00b309a2515f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"464c807af6ab6b52be5cb51b2b70dc82f5fc1191011fde1340b00b309a2515f3","first_computed_at":"2026-05-18T02:29:46.406436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:46.406436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tr8wyTI8H44Ic2eicLpTcY0SF2w8ssGpuztQCJCACtFj138+7hl9DToVIak1prosPzdrwXNVDaMEtjmFDlUZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:46.406825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:befc5d5fe1cd7c8815332bb9f5907542ea45cbc02afcd1fd55fa1e20e450897d","sha256:3dd31bea034f663f4f64b50121ffe98348c86a31b11ac773c8eadbfa680c6374"],"state_sha256":"a6efa81441fd4d803cc45620b5f716a926bb5a49fd8cbd6c753ac5bf9a5f5857"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UkCRPDo0sGdQvRMqccqWmlei5Rg8iB5whrXzE49NS9WFmygy6TuSNuyBlEPRa2sng2Nd0IBv9hV3WBlImL1aCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:26:31.928429Z","bundle_sha256":"8dbb3afd9ee7fc69e04e29721aeafe5eadcbf08bbb35198c1039583ad583bf96"}}