{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YNDQW2NVKEC72UD72M6S3OWICD","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":"9dbbe90202933de70542607a9f386adcc98eb72e70caf931221512f95fa2437a","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-07-04T14:17:24Z","title_canon_sha256":"9abea06849db34620b64387200a57dd21e1c2954cc3b5e66dfc3203b02fc7a94"},"schema_version":"1.0","source":{"id":"1707.01006","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01006","created_at":"2026-07-05T02:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01006v4","created_at":"2026-07-05T02:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01006","created_at":"2026-07-05T02:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"YNDQW2NVKEC7","created_at":"2026-07-05T02:04:53Z"},{"alias_kind":"pith_short_16","alias_value":"YNDQW2NVKEC72UD7","created_at":"2026-07-05T02:04:53Z"},{"alias_kind":"pith_short_8","alias_value":"YNDQW2NV","created_at":"2026-07-05T02:04:53Z"}],"graph_snapshots":[{"event_id":"sha256:71dbccf2e35e69b372daf9178f6fcc0f8e0b79a8758c8104008cc96b7686e0d6","target":"graph","created_at":"2026-07-05T02:04:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1707.01006/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The main result of this paper is a proof that a nearly flat, acutely triangulated convex cap C in R^3 has an edge-unfolding to a non-overlapping polygon in the plane. A convex cap is the intersection of the surface of a convex polyhedron and a halfspace. \"Nearly flat\" means that every outer face normal forms a sufficiently small angle phi < Phi with the z-axis orthogonal to the halfspace bounding plane. The size of Phi depends on the acuteness gap alpha: if every triangle angle is at most pi/2-alpha, then Phi ~= 0.36 sqrt(alpha) suffices; e.g., for alpha ~= 3deg, Phi = 5deg. Even if C is close","authors_text":"Joseph O'Rourke","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-07-04T14:17:24Z","title":"Edge-Unfolding Nearly Flat Convex Caps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01006","kind":"arxiv","version":4},"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":"sha256:3b59bae13d71d99adeb1bbb9528827d3fb9577e1fa1e0e0d5fa2bf3da29bf776","target":"record","created_at":"2026-07-05T02:04:53Z","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":"9dbbe90202933de70542607a9f386adcc98eb72e70caf931221512f95fa2437a","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-07-04T14:17:24Z","title_canon_sha256":"9abea06849db34620b64387200a57dd21e1c2954cc3b5e66dfc3203b02fc7a94"},"schema_version":"1.0","source":{"id":"1707.01006","kind":"arxiv","version":4}},"canonical_sha256":"c3470b69b55105fd507fd33d2dbac810f88f6a4a58e19dfa381c0290b9a327cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3470b69b55105fd507fd33d2dbac810f88f6a4a58e19dfa381c0290b9a327cc","first_computed_at":"2026-07-05T02:04:53.130859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:04:53.130859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"53HRGerEVnUsIvrlKdA8fwjzNWIP2UqhbJHffL7bc9Ibx/YsAnriKAGNXYL3bJ7AP5az9Jb0eLS59mqjrQCJDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:04:53.131330Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01006","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b59bae13d71d99adeb1bbb9528827d3fb9577e1fa1e0e0d5fa2bf3da29bf776","sha256:71dbccf2e35e69b372daf9178f6fcc0f8e0b79a8758c8104008cc96b7686e0d6"],"state_sha256":"119a252a2a740cc4d0149f2fed51aa9bb30ce4ac823bf20ce11bd902fea408f3"}