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We also give polynomial estimates in |chi| for sets of arcs and curves pairwise intersecting a uniformly bounded number of times. Finally, we prove that on a punctured sphere the maximal cardinality of a set of arcs starting and ending at specified punctures and pai"},"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":"1402.1570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-02-07T08:36:34Z","cross_cats_sorted":[],"title_canon_sha256":"50da2c621fefabcb7f722e505cdb2dc1aaa7142cc0d884a5b7c30a4182ed0a93","abstract_canon_sha256":"09c488923b9a36bb0f0ef880fac8d59ba375462added306034e86f784c02afa6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:18.124162Z","signature_b64":"jctmBAJKqedPc/V1PPHBGyrKrqV7ugzTLOEwuh9ds2qlTNIq4xlkSZnvXtv4gp3Ik4dSNeHnVcdl2jFc3EFDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01bfe4ef9d12b601fbd67b48797e0064617a73839a46ef53f70b2d45f3805d60","last_reissued_at":"2026-05-18T02:44:18.123613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:18.123613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arcs intersecting at most once","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Piotr Przytycki","submitted_at":"2014-02-07T08:36:34Z","abstract_excerpt":"We prove that on a punctured oriented surface with Euler characteristic chi < 0, the maximal cardinality of a set of essential simple arcs that are pairwise non-homotopic and intersecting at most once is 2|chi|(|chi|+1). 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