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We call a curve $\\beta$ in $D$ an yin-yang line if\n  $\\beta$ splits $D$ into two congruent perfect sets,\n  $\\beta$ crosses each concentric circle of $D$ twice,\n  $\\beta$ crosses each radius of $D$ once.\n  We prove that Fermat's spiral is a unique yin-yang line in the class of smooth curves algebraic in polar coordinates."},"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":"0902.1556","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-02-09T22:57:49Z","cross_cats_sorted":[],"title_canon_sha256":"df15eda4b737d68fbcc6005d0f3d8458eb773efd0b0431b61c0f2d55790101dd","abstract_canon_sha256":"60ca56f495997ba78e902a27c2d73464148f66c8e29a177031cdcf77e8ce5d71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:29.183088Z","signature_b64":"+9gWeYm4UijjzMIhWQUwmw0vGGfY7udRaDbmcjhLreixCWXmU6uJVntrIjwD3T7XkcBhDiXA7HhY2CLlwwwOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24c452567a4f53eb9cbe8a0e1f0f34930fe64c01d2b5c7706b3b692dea86495d","last_reissued_at":"2026-05-18T04:11:29.182495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:29.182495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fermat's spiral and the line between Yin and Yang","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Oleg Verbitsky, Taras Banakh, Yaroslav Vorobets","submitted_at":"2009-02-09T22:57:49Z","abstract_excerpt":"Let $D$ denote a disk of unit area. 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