{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SG37CXDV5DV7GGCK7XLHCGCQCS","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":"aad5e22534ac74d1f01ecff4b459dd96e853bf6aadafebeffe0b108b56a7a84b","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-16T20:50:42Z","title_canon_sha256":"79e7a779ef235d2ba538af2d2acf48aa1ef1954ab5626fc67a459302188729cf"},"schema_version":"1.0","source":{"id":"1210.4574","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4574","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4574v1","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4574","created_at":"2026-05-18T03:42:56Z"},{"alias_kind":"pith_short_12","alias_value":"SG37CXDV5DV7","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SG37CXDV5DV7GGCK","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SG37CXDV","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:534495ec7227da2c0ffe33564f6c3fa71052a76631f88c77435d000b770bd006","target":"graph","created_at":"2026-05-18T03:42:56Z","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 show that a topologically minimal disk in a tetrahedron with index $n$ is either a normal triangle, a normal quadrilateral, or a normal helicoid with boundary length 4(n+1). This mirrors geometric results of Colding and Minicozzi.","authors_text":"David Bachman","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-16T20:50:42Z","title":"Normalizing Topologically Minimal Surfaces II: Disks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4574","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":"sha256:0c851ce4e5e0c0a527de502d08a0d5330620139c9e616640cb27c64d43b6bb23","target":"record","created_at":"2026-05-18T03:42:56Z","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":"aad5e22534ac74d1f01ecff4b459dd96e853bf6aadafebeffe0b108b56a7a84b","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-16T20:50:42Z","title_canon_sha256":"79e7a779ef235d2ba538af2d2acf48aa1ef1954ab5626fc67a459302188729cf"},"schema_version":"1.0","source":{"id":"1210.4574","kind":"arxiv","version":1}},"canonical_sha256":"91b7f15c75e8ebf3184afdd671185014a7c5a1a9ddd80cf974e71f398f7621a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91b7f15c75e8ebf3184afdd671185014a7c5a1a9ddd80cf974e71f398f7621a0","first_computed_at":"2026-05-18T03:42:56.694597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:56.694597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b3gupeoJSunhhw71BMpdDAs2WumqFxqEHyKw2CQ2q9ErewgelCD4J2AxSQ4Oyz2I40SNS8aJpGfaCZ5CSZlhDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:56.695168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4574","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c851ce4e5e0c0a527de502d08a0d5330620139c9e616640cb27c64d43b6bb23","sha256:534495ec7227da2c0ffe33564f6c3fa71052a76631f88c77435d000b770bd006"],"state_sha256":"aabb2f28a0f0d1746bbde7ae177c3ed3b6a252ec015248649846a6555789aba2"}