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Rail arcs are considered up to rail isotopies, ambient isotopies of $\\mathbb{R}^3$ with each self-homeomorphism mapping $\\ell_1$ and $\\ell_2$ onto themselves. When the manifolds and maps are taken in the piecewise linear category, these rail arcs are called stick rail arcs.\n  The stick number of a rail arc class is the minimum number of sticks, line segme"},"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":"2206.11379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-06-22T20:58:46Z","cross_cats_sorted":[],"title_canon_sha256":"da957b76f0ae250ba47ba52429f537bca166716dd11f95f48a102e7f0eabdc4b","abstract_canon_sha256":"083323742a73dff639f4a3d0bb7723f8c8a1ade4000a8f3445f395c5b6c8a469"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:57:11.821086Z","signature_b64":"at4QZv/XERoxMh21ItOHTd3xX0Prkxwc8hikQH0n84hNEs6xmyn9UwV5z/xUrK/zjWE/DjdcQ3TIhlMqVZBHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d454a44d720e546c0e627c66fafa139e9b0dd363736ab8a0043b2e1f72464bb0","last_reissued_at":"2026-07-05T05:57:11.820534Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:57:11.820534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The stick number of rail arcs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Nicholas Cazet","submitted_at":"2022-06-22T20:58:46Z","abstract_excerpt":"Consider two parallel lines $\\ell_1$ and $\\ell_2$ in $\\mathbb{R}^3$. 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