{"paper":{"title":"Spherical Geometrical Bases of Spherical Origami","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Spherical origami is defined by extending the seven Huzita-Justin axioms to explicit spherical equations on the unit sphere and by using equidistant curves for three-dimensional folds.","cross_cats":["cs.GR"],"primary_cat":"cs.CG","authors_text":"Takashi Yoshino","submitted_at":"2026-05-02T01:24:22Z","abstract_excerpt":"This paper establishes a rigorous geometrical framework for spherical origami, origami using spherical sheets based on spherical geometry. Two settings are treated: origami restricted to the unit sphere ($\\mathbb{S}^2$), and three-dimensional folding of spherical sheets in space. For origami on $\\mathbb{S}^2$, the definitions of Euclidean origami are systematically extended to the spherical setting, and all seven Huzita--Justin axioms are shown to admit explicit equations in spherical geometry. For three-dimensional folding, equidistant curves are introduced as fold curves, replacing geodesics"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For origami on S^2, the definitions of Euclidean origami are systematically extended to the spherical setting, and all seven Huzita--Justin axioms are shown to admit explicit equations in spherical geometry.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the standard definitions and axioms of flat Euclidean origami can be directly and consistently extended to the spherical setting without introducing new inconsistencies or requiring additional constraints not present in the Euclidean case.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A rigorous framework extends the seven Huzita-Justin origami axioms to spherical geometry on the unit sphere and introduces equidistant curves for three-dimensional spherical sheet folding.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Spherical origami is defined by extending the seven Huzita-Justin axioms to explicit spherical equations on the unit sphere and by using equidistant curves for three-dimensional folds.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0ebd96b695f770c09a074eaca072d2f6a3362c911595cd7f47a8c213feacd821"},"source":{"id":"2605.01184","kind":"arxiv","version":2},"verdict":{"id":"dd830ef0-9831-450c-9443-f2b8f6227c8d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T15:42:05.265352Z","strongest_claim":"For origami on S^2, the definitions of Euclidean origami are systematically extended to the spherical setting, and all seven Huzita--Justin axioms are shown to admit explicit equations in spherical geometry.","one_line_summary":"A rigorous framework extends the seven Huzita-Justin origami axioms to spherical geometry on the unit sphere and introduces equidistant curves for three-dimensional spherical sheet folding.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the standard definitions and axioms of flat Euclidean origami can be directly and consistently extended to the spherical setting without introducing new inconsistencies or requiring additional constraints not present in the Euclidean case.","pith_extraction_headline":"Spherical origami is defined by extending the seven Huzita-Justin axioms to explicit spherical equations on the unit sphere and by using equidistant curves for three-dimensional folds."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.01184/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T17:30:52.056023Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c2eab02e1f55859aba123085b5bcf741caf7d9a28c1758dd2a4950c071c7ed6d"},"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"}