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We also bound the least dilatation of any pseudo-Anosov in the point-pushing subgroup of a closed surface and prove that this number tends to infinity with genus. Lastly, we investigate the minimal entropy of any ps"},"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":"1004.3936","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-22T14:49:28Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"038c4da495ee5da884b027ae5d7ee820c548e225da666461273274d69428535f","abstract_canon_sha256":"d01102957c963d312944cbb4025aa7a2a1f0681b14be0513b25a523a0734f6a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:06.847869Z","signature_b64":"zcih40y0K2YpVbA0T3B7s2SGZxcvEm2Xlg8ukI7tzEVzFEmia0+Zvkamk5DlNbT3j2RSVebSX/gjOsYq/a42Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ece1367d3a1f463bd301428de9153c76f96e10fe55daef675cb483a882453f43","last_reissued_at":"2026-05-18T04:07:06.847209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:06.847209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dilatation versus self-intersection number for point-pushing pseudo-Anosov homeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Spencer Dowdall","submitted_at":"2010-04-22T14:49:28Z","abstract_excerpt":"A filling curve $\\gamma$ on a based surface $S$ determines a pseudo-Anosov homeomorphism $P(\\gamma)$ of $S$ via the process of \"point-pushing along $\\gamma$.\" We consider the relationship between the self-intersection number $i(\\gamma)$ of $\\gamma$ and the dilatation of $P(\\gamma)$; our main result is that the dilatation is bounded between $(i(\\gamma)+1)^{1/5}$ and $9^{i(\\gamma)}$. We also bound the least dilatation of any pseudo-Anosov in the point-pushing subgroup of a closed surface and prove that this number tends to infinity with genus. 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