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In this paper, the objects we consider are long cycles and long thetas, both as induced minors. Let $C_t$ denote the cycle with $t$ vertices and let $\\Theta_t$ be the graph consisting of three internally disjoint and anti-adjacent paths, each with $t$ internal vertices, connecting the same pair of distinct vertices.\n  We show that for every fixed $t$, both $C_t$ and $\\Theta_t$ have the induced Erd\\H{o}s--P"},"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":"2607.07697","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-08T17:55:18Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"c5684de0ccfe737703f8ccf1e743ca856bbe3a2bc0c303223fb7867777485db2","abstract_canon_sha256":"6e512d69c9a4e9b45ae8afd52e146fe8132b947e274f835692a1f8bcff55400a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:39.462764Z","signature_b64":"Sx1yvrKI1wGx1sWYyexC+hwGoCJQmp5RRVm9a8M0DpogqoEg8Pg8oUZ6LRmdehAqYNSrHszyLSL62qR4XtN9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9625d1016b80161a1e30428b3ee068953124aff7762d4af4730341c72afdb328","last_reissued_at":"2026-07-09T01:20:39.462223Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:39.462223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Induced Erd\\H{o}s--P\\'osa property for long holes, long thetas, and beyond","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Amadeus Reinald, Jadwiga Czy\\.zewska, Marcin Pilipczuk, Pawe{\\l} Rz\\k{a}\\.zewski, Tom\\'a\\v{s} Masa\\v{r}\\'ik","submitted_at":"2026-07-08T17:55:18Z","abstract_excerpt":"The induced Erd\\H{o}s--P\\'osa property in graphs relates the maximum number of pairwise anti-adjacent copies of an object with the minimum number of neighborhoods required to hit all copies. 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