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Let $\\mathcal B$ be a set of blue curves and $\\mathcal G$ a set of green curves in the plane such that $\\mathcal B\\cup\\mathcal G$ is a collection of $t$-intersecting curves in general position. We show that there exist subfamilies $\\mathcal B'\\subseteq\\mathcal B$ and $\\mathcal G'\\subseteq\\mathcal G$ such that $|\\mathcal B'|\\geq \\varepsilon|\\mathcal B|$ and $|\\mathcal G'|\\geq \\varepsilon|\\mathcal G|$, where $\\varepsilon>0$ depends only on $t$, such that either e"},"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":"2606.11649","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-10T04:27:18Z","cross_cats_sorted":[],"title_canon_sha256":"f9a2f33f3d437e8bc081bf31e6870c83e9bd62cdd8a6d7cf0db9b9e3cb46c94c","abstract_canon_sha256":"d34ef42abecba5cb8d9250fa541efeb72d1d5592cb312ab3cccccc8a1ab01a7e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:10:00.922172Z","signature_b64":"UaD0730LagUyWZn7MuOll85D1xJxan/CoP2+PycC9FgxVyCUR6kYUYdZl4+0msgBzbJmFTlRxP9QSyRYIIOqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"652f79ca17ef44ca264da9104740a13afe9037732f1abf817d39f4ab899a00c4","last_reissued_at":"2026-06-11T01:10:00.921367Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:10:00.921367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A parity Erd\\H{o}s-Hajnal theorem for $t$-intersecting curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Suk, Su Zhou","submitted_at":"2026-06-10T04:27:18Z","abstract_excerpt":"For every fixed $t\\ge 1$, we prove a parity analogue of the mighty Erd\\H{o}s-Hajnal property for $t$-intersecting curves in the plane. 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