{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:STV7GPDM6EPPD64EXBIYS6XDWZ","short_pith_number":"pith:STV7GPDM","canonical_record":{"source":{"id":"1702.00510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-02T00:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"9990816ac6b65270b2e5c7c56c2b3fdc2f8ca86d33d56390c69cb3b89a435131","abstract_canon_sha256":"b1a31e6aef1eca767e83a7ae707c95be7551fc8ba5e8daab85b160862b20b756"},"schema_version":"1.0"},"canonical_sha256":"94ebf33c6cf11ef1fb84b851897ae3b64e2489ff21a0b2991c8e0c3f9a6f10be","source":{"kind":"arxiv","id":"1702.00510","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00510","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00510v1","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00510","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"pith_short_12","alias_value":"STV7GPDM6EPP","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"STV7GPDM6EPPD64E","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"STV7GPDM","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:STV7GPDM6EPPD64EXBIYS6XDWZ","target":"record","payload":{"canonical_record":{"source":{"id":"1702.00510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-02T00:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"9990816ac6b65270b2e5c7c56c2b3fdc2f8ca86d33d56390c69cb3b89a435131","abstract_canon_sha256":"b1a31e6aef1eca767e83a7ae707c95be7551fc8ba5e8daab85b160862b20b756"},"schema_version":"1.0"},"canonical_sha256":"94ebf33c6cf11ef1fb84b851897ae3b64e2489ff21a0b2991c8e0c3f9a6f10be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:33.398122Z","signature_b64":"F963Ts4OJkZLllilv/TDCKsGGjVR/G0rx0Cd1IB0QRfffp12zlKO7ibbHZTHLI/rdtw6l2wf7P44XuyGmEOGDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94ebf33c6cf11ef1fb84b851897ae3b64e2489ff21a0b2991c8e0c3f9a6f10be","last_reissued_at":"2026-05-18T00:51:33.397671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:33.397671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.00510","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":"2026-05-18T00:51:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ltsk2MwGGqvCaDvmWb9nwDOrVb73qnccXvYGg/GHfXL4ZelCq2XDgGYicbb1qeNkFTacTSnxjQS94uwtm/rDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:33:18.002631Z"},"content_sha256":"c03fba4a856977b89b5d5f6599f2c5709fcbef3001ecef12d6a9a071d3e590e1","schema_version":"1.0","event_id":"sha256:c03fba4a856977b89b5d5f6599f2c5709fcbef3001ecef12d6a9a071d3e590e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:STV7GPDM6EPPD64EXBIYS6XDWZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proof of the Voronoi conjecture for 3-irreducible parallelotopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Andrei Ordine","submitted_at":"2017-02-02T00:39:22Z","abstract_excerpt":"This article proves the Voronoi conjecture on parallelotopes in the special case of 3-irreducible tilings.\n  Parallelotopes are convex polytopes which tile the Euclidean space by their translated copies, like in the honeycomb arrangement of hexagons in the plane. An important example of parallelotope is the Dirichlet-Voronoi domain for a translation lattice. For each point $x$ in a translation lattice, we define its Dirichlet-Voronoi (DV) domain to be the set of points in the space which are at least as close to $x$ as to any other lattice point. The Voronoi conjecture, formulated by the great"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00510","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":"2026-05-18T00:51:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rzqWVoJESmrqDVApaS1jxKzM6tUMLI1m0TpjMYwSrZpWBZuhBcNviHviJffosAcWxth2m3g6UR2ijwsxR5SHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:33:18.002954Z"},"content_sha256":"99bb34b2e9a2738c980961d17567d7f3f60627dce2df8289778c22fcc2ed2766","schema_version":"1.0","event_id":"sha256:99bb34b2e9a2738c980961d17567d7f3f60627dce2df8289778c22fcc2ed2766"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/STV7GPDM6EPPD64EXBIYS6XDWZ/bundle.json","state_url":"https://pith.science/pith/STV7GPDM6EPPD64EXBIYS6XDWZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/STV7GPDM6EPPD64EXBIYS6XDWZ/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":"2026-06-22T20:33:18Z","links":{"resolver":"https://pith.science/pith/STV7GPDM6EPPD64EXBIYS6XDWZ","bundle":"https://pith.science/pith/STV7GPDM6EPPD64EXBIYS6XDWZ/bundle.json","state":"https://pith.science/pith/STV7GPDM6EPPD64EXBIYS6XDWZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/STV7GPDM6EPPD64EXBIYS6XDWZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:STV7GPDM6EPPD64EXBIYS6XDWZ","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":"b1a31e6aef1eca767e83a7ae707c95be7551fc8ba5e8daab85b160862b20b756","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-02T00:39:22Z","title_canon_sha256":"9990816ac6b65270b2e5c7c56c2b3fdc2f8ca86d33d56390c69cb3b89a435131"},"schema_version":"1.0","source":{"id":"1702.00510","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00510","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00510v1","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00510","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"pith_short_12","alias_value":"STV7GPDM6EPP","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"STV7GPDM6EPPD64E","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"STV7GPDM","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:99bb34b2e9a2738c980961d17567d7f3f60627dce2df8289778c22fcc2ed2766","target":"graph","created_at":"2026-05-18T00:51:33Z","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 article proves the Voronoi conjecture on parallelotopes in the special case of 3-irreducible tilings.\n  Parallelotopes are convex polytopes which tile the Euclidean space by their translated copies, like in the honeycomb arrangement of hexagons in the plane. An important example of parallelotope is the Dirichlet-Voronoi domain for a translation lattice. For each point $x$ in a translation lattice, we define its Dirichlet-Voronoi (DV) domain to be the set of points in the space which are at least as close to $x$ as to any other lattice point. The Voronoi conjecture, formulated by the great","authors_text":"Andrei Ordine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-02T00:39:22Z","title":"Proof of the Voronoi conjecture for 3-irreducible parallelotopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00510","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:c03fba4a856977b89b5d5f6599f2c5709fcbef3001ecef12d6a9a071d3e590e1","target":"record","created_at":"2026-05-18T00:51:33Z","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":"b1a31e6aef1eca767e83a7ae707c95be7551fc8ba5e8daab85b160862b20b756","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-02T00:39:22Z","title_canon_sha256":"9990816ac6b65270b2e5c7c56c2b3fdc2f8ca86d33d56390c69cb3b89a435131"},"schema_version":"1.0","source":{"id":"1702.00510","kind":"arxiv","version":1}},"canonical_sha256":"94ebf33c6cf11ef1fb84b851897ae3b64e2489ff21a0b2991c8e0c3f9a6f10be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94ebf33c6cf11ef1fb84b851897ae3b64e2489ff21a0b2991c8e0c3f9a6f10be","first_computed_at":"2026-05-18T00:51:33.397671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:33.397671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F963Ts4OJkZLllilv/TDCKsGGjVR/G0rx0Cd1IB0QRfffp12zlKO7ibbHZTHLI/rdtw6l2wf7P44XuyGmEOGDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:33.398122Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.00510","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c03fba4a856977b89b5d5f6599f2c5709fcbef3001ecef12d6a9a071d3e590e1","sha256:99bb34b2e9a2738c980961d17567d7f3f60627dce2df8289778c22fcc2ed2766"],"state_sha256":"0dfb7099a50f0b5954b81765da1b8eb93dc463d580a70ba903b8b70feb23bba9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLffAIaS0duHGevrfWrGzGJYfTEOfeo/b0jWopXwa2l783etEnZuU767hdHTNRIKilLOILA+AI2g9THt1b+zCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:33:18.004787Z","bundle_sha256":"a453f95cd57d0e87daf1a1e842a4ba8848489c7c01410c29da837e4fe3f7b873"}}