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The only surface corresponding to $L_1\\approx 3.057$ is the Bolza surface in genus $2$. For every genus $g\\geq 13$, we obtain either one or two local maxima in $\\mathcal{M}_g$ whose systoles have length $L_2\\approx 5.909$. For each $n\\geq 3$, there is an arithmetic sequence of genera $(g_k)_{k\\geq 1}$ such that the number of local maxima of the systole "},"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":"1807.08367","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-22T21:04:03Z","cross_cats_sorted":[],"title_canon_sha256":"1c621c05c477297af516be0d8cc5c8ea8630b138e0c0fd0ade528013ef1a45f0","abstract_canon_sha256":"b7942c60629a219dbe083ade70d868bbcd650715f76c7b785584ef2594080078"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:36.958953Z","signature_b64":"lsTMNgX5RAvxPvfcdATru6NAnpq3wAHwCiy3+7JE+48hhn8aZRGlyjB/kPyWYbUiqFWizueuN6VkBBsLZMrZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2e16cebff94aebc0f9fb6eab11d0ad06106a14439b71f5e5b4aff631db5006e","last_reissued_at":"2026-05-18T00:05:36.958521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:36.958521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local maxima of the systole function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kasra Rafi, Maxime Fortier Bourque","submitted_at":"2018-07-22T21:04:03Z","abstract_excerpt":"We construct infinite families of closed hyperbolic surfaces that are local maxima for the systole function on their respective moduli spaces. The systole takes values along a linearly divergent sequence $(L_n)_{n\\geq 1}$ at these local maxima. The only surface corresponding to $L_1\\approx 3.057$ is the Bolza surface in genus $2$. For every genus $g\\geq 13$, we obtain either one or two local maxima in $\\mathcal{M}_g$ whose systoles have length $L_2\\approx 5.909$. 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