{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JD62ZLJN4KNVQKHNI24WJA5MRE","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":"969a6611dd0d818a58e2ae8ff56376b18ed8feb0920af46a6ef27021c88a86ec","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.HO","submitted_at":"2012-04-23T00:20:30Z","title_canon_sha256":"181330e56385a70d7d12bf2318d17fe0f4bfbae1144292ab73a97c7f45f0aded"},"schema_version":"1.0","source":{"id":"1204.4952","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4952","created_at":"2026-05-18T03:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4952v2","created_at":"2026-05-18T03:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4952","created_at":"2026-05-18T03:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"JD62ZLJN4KNV","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JD62ZLJN4KNVQKHN","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JD62ZLJN","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:1216b921ba405f40182309dc400c1ea6dfb3e320f7f252df2c78f204aafac111","target":"graph","created_at":"2026-05-18T03:55:24Z","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":"We construct a number of sculptures, each based on a geometric design native to the three-dimensional sphere. Using stereographic projection we transfer the design from the three-sphere to ordinary Euclidean space. All of the sculptures are then fabricated by the 3D printing service Shapeways.","authors_text":"Henry Segerman, Saul Schleimer","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.HO","submitted_at":"2012-04-23T00:20:30Z","title":"Sculptures in S^3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4952","kind":"arxiv","version":2},"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:ed7279f6f08daf1e27088075c827fa99896889ce2732a5b7f533ffa058cdb185","target":"record","created_at":"2026-05-18T03:55:24Z","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":"969a6611dd0d818a58e2ae8ff56376b18ed8feb0920af46a6ef27021c88a86ec","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.HO","submitted_at":"2012-04-23T00:20:30Z","title_canon_sha256":"181330e56385a70d7d12bf2318d17fe0f4bfbae1144292ab73a97c7f45f0aded"},"schema_version":"1.0","source":{"id":"1204.4952","kind":"arxiv","version":2}},"canonical_sha256":"48fdacad2de29b5828ed46b96483ac8939c3f285881b6bde2ebd07273d8a7856","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48fdacad2de29b5828ed46b96483ac8939c3f285881b6bde2ebd07273d8a7856","first_computed_at":"2026-05-18T03:55:24.535888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:24.535888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RmKWvg1xSCg1tbUED4JMfRHP3/iVfJ79LumHSlp60m51sfo3qC5u+lfIUgKXSVJAHA2DAnvSRcAyQCG/iHAbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:24.536479Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4952","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed7279f6f08daf1e27088075c827fa99896889ce2732a5b7f533ffa058cdb185","sha256:1216b921ba405f40182309dc400c1ea6dfb3e320f7f252df2c78f204aafac111"],"state_sha256":"f1dc66445fc6efa21e018b3a23ccf5d7afec845609ad058358ee064a3b5c8d10"}