{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LBIYJ7QFK6353NBLTCJ7HPVESY","short_pith_number":"pith:LBIYJ7QF","canonical_record":{"source":{"id":"1306.1432","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-06-06T15:14:41Z","cross_cats_sorted":[],"title_canon_sha256":"2852cadba63a3de4bb5741444cd3ebfc1d5930f5115e2603ecd5d607a8582e65","abstract_canon_sha256":"6974d423f80c12720ac47b8d6b7f7da42132cdcdf11a251b3375d5eeb70487e8"},"schema_version":"1.0"},"canonical_sha256":"585184fe0557b7ddb42b9893f3bea49609da44396a6b44f99dbecafbecd04af8","source":{"kind":"arxiv","id":"1306.1432","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1432","created_at":"2026-05-18T02:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1432v8","created_at":"2026-05-18T02:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1432","created_at":"2026-05-18T02:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"LBIYJ7QFK635","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LBIYJ7QFK6353NBL","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LBIYJ7QF","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LBIYJ7QFK6353NBLTCJ7HPVESY","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1432","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-06-06T15:14:41Z","cross_cats_sorted":[],"title_canon_sha256":"2852cadba63a3de4bb5741444cd3ebfc1d5930f5115e2603ecd5d607a8582e65","abstract_canon_sha256":"6974d423f80c12720ac47b8d6b7f7da42132cdcdf11a251b3375d5eeb70487e8"},"schema_version":"1.0"},"canonical_sha256":"585184fe0557b7ddb42b9893f3bea49609da44396a6b44f99dbecafbecd04af8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:52.053993Z","signature_b64":"FitNSm8vvXt4iLNz4sN8fH1YV3KXbhUirIpO5q32cPSVQF4RbRjjMshS29ha1ii2FwjSyrW5JlkrqurcR+PmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"585184fe0557b7ddb42b9893f3bea49609da44396a6b44f99dbecafbecd04af8","last_reissued_at":"2026-05-18T02:18:52.053325Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:52.053325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1432","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GjrZLHZdAlbN+uJNMebAz5kpt5extalUorVLi/pk87Aj4a9bVsnspOxF/02VGNYwPpmrkpemh92PjYm37ogHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:29:57.661603Z"},"content_sha256":"a7e7c5f3ba8a3fc55c083ce7b3e16a8efbdbb7688149b223bc26b8366eab0136","schema_version":"1.0","event_id":"sha256:a7e7c5f3ba8a3fc55c083ce7b3e16a8efbdbb7688149b223bc26b8366eab0136"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LBIYJ7QFK6353NBLTCJ7HPVESY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A ternary construction of lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hao Chen","submitted_at":"2013-06-06T15:14:41Z","abstract_excerpt":"In this paper we propose a general ternary construction of lattices from three rows and ternary codes. Most laminated lattices and Kappa lattices in ${\\bf R}^n$, $n\\leq 24$ can be recovered from our tenary construction naturally. This ternary construction of lattices can be used to generate many new \"sub-optimal\" lattices of low dimensions.Based on this ternary construction new extremal even lattices of dimensions $32, 40$ and $48$ are also constructed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1432","kind":"arxiv","version":8},"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":"2026-05-18T02:18:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DB6asyZHg/hFCsNNhK7EUsTfI81Gy9HIkTlWghhYl9Jlr8NNZRm2Lnz0SzjFIb8POOxNtgrgcwG0qJRDSsbNBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:29:57.661937Z"},"content_sha256":"425180a50b6bdcf2e5ad505585b4ca91fb88d8d4ae20ba59d94109fbd0fd4ddd","schema_version":"1.0","event_id":"sha256:425180a50b6bdcf2e5ad505585b4ca91fb88d8d4ae20ba59d94109fbd0fd4ddd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBIYJ7QFK6353NBLTCJ7HPVESY/bundle.json","state_url":"https://pith.science/pith/LBIYJ7QFK6353NBLTCJ7HPVESY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBIYJ7QFK6353NBLTCJ7HPVESY/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":"2026-06-06T16:29:57Z","links":{"resolver":"https://pith.science/pith/LBIYJ7QFK6353NBLTCJ7HPVESY","bundle":"https://pith.science/pith/LBIYJ7QFK6353NBLTCJ7HPVESY/bundle.json","state":"https://pith.science/pith/LBIYJ7QFK6353NBLTCJ7HPVESY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBIYJ7QFK6353NBLTCJ7HPVESY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LBIYJ7QFK6353NBLTCJ7HPVESY","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":"6974d423f80c12720ac47b8d6b7f7da42132cdcdf11a251b3375d5eeb70487e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-06-06T15:14:41Z","title_canon_sha256":"2852cadba63a3de4bb5741444cd3ebfc1d5930f5115e2603ecd5d607a8582e65"},"schema_version":"1.0","source":{"id":"1306.1432","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1432","created_at":"2026-05-18T02:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1432v8","created_at":"2026-05-18T02:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1432","created_at":"2026-05-18T02:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"LBIYJ7QFK635","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LBIYJ7QFK6353NBL","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LBIYJ7QF","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:425180a50b6bdcf2e5ad505585b4ca91fb88d8d4ae20ba59d94109fbd0fd4ddd","target":"graph","created_at":"2026-05-18T02:18:52Z","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":"In this paper we propose a general ternary construction of lattices from three rows and ternary codes. Most laminated lattices and Kappa lattices in ${\\bf R}^n$, $n\\leq 24$ can be recovered from our tenary construction naturally. This ternary construction of lattices can be used to generate many new \"sub-optimal\" lattices of low dimensions.Based on this ternary construction new extremal even lattices of dimensions $32, 40$ and $48$ are also constructed.","authors_text":"Hao Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-06-06T15:14:41Z","title":"A ternary construction of lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1432","kind":"arxiv","version":8},"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:a7e7c5f3ba8a3fc55c083ce7b3e16a8efbdbb7688149b223bc26b8366eab0136","target":"record","created_at":"2026-05-18T02:18:52Z","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":"6974d423f80c12720ac47b8d6b7f7da42132cdcdf11a251b3375d5eeb70487e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-06-06T15:14:41Z","title_canon_sha256":"2852cadba63a3de4bb5741444cd3ebfc1d5930f5115e2603ecd5d607a8582e65"},"schema_version":"1.0","source":{"id":"1306.1432","kind":"arxiv","version":8}},"canonical_sha256":"585184fe0557b7ddb42b9893f3bea49609da44396a6b44f99dbecafbecd04af8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"585184fe0557b7ddb42b9893f3bea49609da44396a6b44f99dbecafbecd04af8","first_computed_at":"2026-05-18T02:18:52.053325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:52.053325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FitNSm8vvXt4iLNz4sN8fH1YV3KXbhUirIpO5q32cPSVQF4RbRjjMshS29ha1ii2FwjSyrW5JlkrqurcR+PmAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:52.053993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1432","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7e7c5f3ba8a3fc55c083ce7b3e16a8efbdbb7688149b223bc26b8366eab0136","sha256:425180a50b6bdcf2e5ad505585b4ca91fb88d8d4ae20ba59d94109fbd0fd4ddd"],"state_sha256":"087998988ad888105a137d4fb76b0f3d3595a648a8cfac75d642a2ece8b98c10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hgf+fyNtbZp24zB6s0jxW0TLQ5dGmBtNEYlKXe9eZyhmWmqTtOoKiIVs3rb8TDUtTH0iVwpA/Y+lI/wyOo7fAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:29:57.663824Z","bundle_sha256":"b9d281399a584063bf16a9d64b2a896cae1e0ea991b995ccf36e4bcdd92a9274"}}