{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:7D6EILYWOJNEBVWRVENPQQTUPJ","short_pith_number":"pith:7D6EILYW","schema_version":"1.0","canonical_sha256":"f8fc442f16725a40d6d1a91af842747a4f8ef2c00a8652457170c68771bdd364","source":{"kind":"arxiv","id":"2203.14173","version":1},"attestation_state":"computed","paper":{"title":"Maximal origami flip graphs of flat-foldable vertices: properties and algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Manuel Morales, Natalya Ter-Saakov, Sarah Nash, Thomas C. Hull","submitted_at":"2022-03-27T00:09:52Z","abstract_excerpt":"Flat origami studies straight line, planar graphs $C=(V,E)$ drawn on a region $R\\subset\\mathbb{R}^2$ that can act as crease patterns to map, or fold, $R$ into $\\mathbb{R}^2$ in a way that is continuous and a piecewise isometry exactly on the faces of $C$. Associated with such crease pattern graphs are valid mountain-valley (MV) assignments $\\mu:E\\to\\{-1,1\\}$, indicating which creases can be mountains (convex) or valleys (concave) to allow $R$ to physically fold flat without self-intersecting. In this paper, we initiate the first study of how valid MV assignments of single-vertex crease pattern"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2203.14173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-03-27T00:09:52Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"379618d616d23d0edf7ab6059d3ad44508bbba8b0d2a3570e76c6a0afcf888e8","abstract_canon_sha256":"e647614241337a1ac1cb8f1b90286358fad5ddfa8f0deb5550715526e31f1243"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:18:39.047445Z","signature_b64":"uxEGiXPMf8bQzo/J1yDD/4vEuRGuPLzRilEwls1taNnP/rnz1KfB30A4dTEiZlCYhDhUTmIiPhbrhTUNO6NiBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8fc442f16725a40d6d1a91af842747a4f8ef2c00a8652457170c68771bdd364","last_reissued_at":"2026-07-05T08:18:39.046887Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:18:39.046887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal origami flip graphs of flat-foldable vertices: properties and algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Manuel Morales, Natalya Ter-Saakov, Sarah Nash, Thomas C. Hull","submitted_at":"2022-03-27T00:09:52Z","abstract_excerpt":"Flat origami studies straight line, planar graphs $C=(V,E)$ drawn on a region $R\\subset\\mathbb{R}^2$ that can act as crease patterns to map, or fold, $R$ into $\\mathbb{R}^2$ in a way that is continuous and a piecewise isometry exactly on the faces of $C$. Associated with such crease pattern graphs are valid mountain-valley (MV) assignments $\\mu:E\\to\\{-1,1\\}$, indicating which creases can be mountains (convex) or valleys (concave) to allow $R$ to physically fold flat without self-intersecting. In this paper, we initiate the first study of how valid MV assignments of single-vertex crease pattern"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.14173","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.14173/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2203.14173","created_at":"2026-07-05T08:18:39.046948+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.14173v1","created_at":"2026-07-05T08:18:39.046948+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.14173","created_at":"2026-07-05T08:18:39.046948+00:00"},{"alias_kind":"pith_short_12","alias_value":"7D6EILYWOJNE","created_at":"2026-07-05T08:18:39.046948+00:00"},{"alias_kind":"pith_short_16","alias_value":"7D6EILYWOJNEBVWR","created_at":"2026-07-05T08:18:39.046948+00:00"},{"alias_kind":"pith_short_8","alias_value":"7D6EILYW","created_at":"2026-07-05T08:18:39.046948+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.22614","citing_title":"Height functions on the $m \\times n$ Miura-ori flip graph: degree sequence and diameter","ref_index":7,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7D6EILYWOJNEBVWRVENPQQTUPJ","json":"https://pith.science/pith/7D6EILYWOJNEBVWRVENPQQTUPJ.json","graph_json":"https://pith.science/api/pith-number/7D6EILYWOJNEBVWRVENPQQTUPJ/graph.json","events_json":"https://pith.science/api/pith-number/7D6EILYWOJNEBVWRVENPQQTUPJ/events.json","paper":"https://pith.science/paper/7D6EILYW"},"agent_actions":{"view_html":"https://pith.science/pith/7D6EILYWOJNEBVWRVENPQQTUPJ","download_json":"https://pith.science/pith/7D6EILYWOJNEBVWRVENPQQTUPJ.json","view_paper":"https://pith.science/paper/7D6EILYW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.14173&json=true","fetch_graph":"https://pith.science/api/pith-number/7D6EILYWOJNEBVWRVENPQQTUPJ/graph.json","fetch_events":"https://pith.science/api/pith-number/7D6EILYWOJNEBVWRVENPQQTUPJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7D6EILYWOJNEBVWRVENPQQTUPJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7D6EILYWOJNEBVWRVENPQQTUPJ/action/storage_attestation","attest_author":"https://pith.science/pith/7D6EILYWOJNEBVWRVENPQQTUPJ/action/author_attestation","sign_citation":"https://pith.science/pith/7D6EILYWOJNEBVWRVENPQQTUPJ/action/citation_signature","submit_replication":"https://pith.science/pith/7D6EILYWOJNEBVWRVENPQQTUPJ/action/replication_record"}},"created_at":"2026-07-05T08:18:39.046948+00:00","updated_at":"2026-07-05T08:18:39.046948+00:00"}