{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ELCSSVSJJDVJET7V7IOKUOQ6T7","short_pith_number":"pith:ELCSSVSJ","canonical_record":{"source":{"id":"1804.05836","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-16T09:46:26Z","cross_cats_sorted":["cond-mat.other","math-ph","math.MP"],"title_canon_sha256":"9e27c9d5a2eddb98e64edc1d1c918b5722a3b56aacb1e8602093db63ac954aad","abstract_canon_sha256":"6387e402f4dd3bd2c46f118e562ecd7c892ee2b7793fe44b27a41743c33269e6"},"schema_version":"1.0"},"canonical_sha256":"22c529564948ea924ff5fa1caa3a1e9fff7d2ae480014ba0d7fd6dab7b357e89","source":{"kind":"arxiv","id":"1804.05836","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05836","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05836v3","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05836","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"ELCSSVSJJDVJ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ELCSSVSJJDVJET7V","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ELCSSVSJ","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ELCSSVSJJDVJET7V7IOKUOQ6T7","target":"record","payload":{"canonical_record":{"source":{"id":"1804.05836","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-16T09:46:26Z","cross_cats_sorted":["cond-mat.other","math-ph","math.MP"],"title_canon_sha256":"9e27c9d5a2eddb98e64edc1d1c918b5722a3b56aacb1e8602093db63ac954aad","abstract_canon_sha256":"6387e402f4dd3bd2c46f118e562ecd7c892ee2b7793fe44b27a41743c33269e6"},"schema_version":"1.0"},"canonical_sha256":"22c529564948ea924ff5fa1caa3a1e9fff7d2ae480014ba0d7fd6dab7b357e89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:28.782668Z","signature_b64":"kpyxJEawxxgGEslL8BcIhwEj1NRTtHEIexDvVwvAHd2PzdDNuDC5jVRdGQliqLCETPCyoBuuCOLiFWm5TEjUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22c529564948ea924ff5fa1caa3a1e9fff7d2ae480014ba0d7fd6dab7b357e89","last_reissued_at":"2026-05-18T00:06:28.782123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:28.782123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.05836","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j2MKBaUrK2eg2TwK6GXv89TX9gemVYuRXQtV8AMDKMwIqOZaTM184CLPcJ+6SqxORhbKkDEaJ0i3wa+9fY6JAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:10:50.404701Z"},"content_sha256":"5e6a3a91557226b2d0a9cc00f05ff5b0ecdbf90638e1c26b964ac06c3c674952","schema_version":"1.0","event_id":"sha256:5e6a3a91557226b2d0a9cc00f05ff5b0ecdbf90638e1c26b964ac06c3c674952"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ELCSSVSJJDVJET7V7IOKUOQ6T7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit Construction of the Voronoi and Delaunay Cells of W(An) and W(Dn) Lattices and Their Facets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","math-ph","math.MP"],"primary_cat":"math.MG","authors_text":"Abeer Al-Siyabi, Mehmet Koca, Nazife Ozdes Koca, Ramazan Koc","submitted_at":"2018-04-16T09:46:26Z","abstract_excerpt":"Voronoi and Delaunay (Delone) cells of the root and weight lattices of the Coxeter-Weyl groups W(an) and W(dn) are constructed. The face centered cubic (fcc) and body centered cubic (bcc)lattices are obtained in this context. Basic definitions are introduced such as parallelotope, fundamental simplex, contact polytope, root polytope, Voronoi cell, Delone cell, n-simplex, n-octahedron (cross polytope), n-cube and n-hemicube and their volumes are calculated. Voronoi cell of the root lattice is constructed as the dual of the root polytope which turns out to be the union of Delone cells. It is sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05836","kind":"arxiv","version":3},"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":"2026-05-18T00:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Becynd20/ffLDNxtNm1uEWtrhlf2wbuWLDMach51LoBQR9x1ClriuhQmL5QIr1/eQ8MjBqFUJ+RN+eP/xd5/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:10:50.405439Z"},"content_sha256":"762706586b4c8aacb877fc7145fa9db51fa8a56e541fc27d7da54dddfedc4aeb","schema_version":"1.0","event_id":"sha256:762706586b4c8aacb877fc7145fa9db51fa8a56e541fc27d7da54dddfedc4aeb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELCSSVSJJDVJET7V7IOKUOQ6T7/bundle.json","state_url":"https://pith.science/pith/ELCSSVSJJDVJET7V7IOKUOQ6T7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELCSSVSJJDVJET7V7IOKUOQ6T7/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":"2026-05-25T16:10:50Z","links":{"resolver":"https://pith.science/pith/ELCSSVSJJDVJET7V7IOKUOQ6T7","bundle":"https://pith.science/pith/ELCSSVSJJDVJET7V7IOKUOQ6T7/bundle.json","state":"https://pith.science/pith/ELCSSVSJJDVJET7V7IOKUOQ6T7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELCSSVSJJDVJET7V7IOKUOQ6T7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ELCSSVSJJDVJET7V7IOKUOQ6T7","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":"6387e402f4dd3bd2c46f118e562ecd7c892ee2b7793fe44b27a41743c33269e6","cross_cats_sorted":["cond-mat.other","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-16T09:46:26Z","title_canon_sha256":"9e27c9d5a2eddb98e64edc1d1c918b5722a3b56aacb1e8602093db63ac954aad"},"schema_version":"1.0","source":{"id":"1804.05836","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05836","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05836v3","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05836","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"ELCSSVSJJDVJ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ELCSSVSJJDVJET7V","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ELCSSVSJ","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:762706586b4c8aacb877fc7145fa9db51fa8a56e541fc27d7da54dddfedc4aeb","target":"graph","created_at":"2026-05-18T00:06:28Z","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":"Voronoi and Delaunay (Delone) cells of the root and weight lattices of the Coxeter-Weyl groups W(an) and W(dn) are constructed. The face centered cubic (fcc) and body centered cubic (bcc)lattices are obtained in this context. Basic definitions are introduced such as parallelotope, fundamental simplex, contact polytope, root polytope, Voronoi cell, Delone cell, n-simplex, n-octahedron (cross polytope), n-cube and n-hemicube and their volumes are calculated. Voronoi cell of the root lattice is constructed as the dual of the root polytope which turns out to be the union of Delone cells. It is sho","authors_text":"Abeer Al-Siyabi, Mehmet Koca, Nazife Ozdes Koca, Ramazan Koc","cross_cats":["cond-mat.other","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-16T09:46:26Z","title":"Explicit Construction of the Voronoi and Delaunay Cells of W(An) and W(Dn) Lattices and Their Facets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05836","kind":"arxiv","version":3},"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":"sha256:5e6a3a91557226b2d0a9cc00f05ff5b0ecdbf90638e1c26b964ac06c3c674952","target":"record","created_at":"2026-05-18T00:06:28Z","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":"6387e402f4dd3bd2c46f118e562ecd7c892ee2b7793fe44b27a41743c33269e6","cross_cats_sorted":["cond-mat.other","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-16T09:46:26Z","title_canon_sha256":"9e27c9d5a2eddb98e64edc1d1c918b5722a3b56aacb1e8602093db63ac954aad"},"schema_version":"1.0","source":{"id":"1804.05836","kind":"arxiv","version":3}},"canonical_sha256":"22c529564948ea924ff5fa1caa3a1e9fff7d2ae480014ba0d7fd6dab7b357e89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22c529564948ea924ff5fa1caa3a1e9fff7d2ae480014ba0d7fd6dab7b357e89","first_computed_at":"2026-05-18T00:06:28.782123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:28.782123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kpyxJEawxxgGEslL8BcIhwEj1NRTtHEIexDvVwvAHd2PzdDNuDC5jVRdGQliqLCETPCyoBuuCOLiFWm5TEjUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:28.782668Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05836","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e6a3a91557226b2d0a9cc00f05ff5b0ecdbf90638e1c26b964ac06c3c674952","sha256:762706586b4c8aacb877fc7145fa9db51fa8a56e541fc27d7da54dddfedc4aeb"],"state_sha256":"d27998ad498abc17801a6ed21fc9c70bc40041d585e0ebb1139615caeae26301"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"54cys5bvwNli4El9IG6FDQbgXuxC3S5W0mTyTCQRQfFJ0ohGNzTnUkBt6Y8rzvN79uh8gc1FlmlaQDiyzVsRAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:10:50.409494Z","bundle_sha256":"d8f1fde84be70c742af573864ba070061e7ac187166cb01d59dd98a277ec6da5"}}