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For each $k\\geq 2$, We construct a $k$-system on $S_{g}$ with on the order of $g^{\\lfloor (k+1)/2 \\rfloor +1}$ elements. The $k$-systems we construct behave well with respect to subsurface inclusion, analogously to how a pants decomposition contains pants decompo"},"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":"1403.5123","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-20T12:58:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8899deba20ca404468e292871cb1aad6aaa63935172527517347c9c085cc0896","abstract_canon_sha256":"7ce73fd3c1f9a2e5b7a12983551856a123ef9e918a734682bbdf881ad843939f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:06.645880Z","signature_b64":"RuIqSH2HfDn5m1SMd6y3UMl0ke8W38cv99dHh9aPD9F+suismebn3074JIvDXF3ErcytiHjp+yhemZf2IoFAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d67116b6755f5813bc4442e58bd805808163aed3a428316e0fcb8dcc2de721e3","last_reissued_at":"2026-05-18T01:20:06.645270Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:06.645270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructing large k-systems on Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Tarik Aougab","submitted_at":"2014-03-20T12:58:31Z","abstract_excerpt":"Let $S_{g}$ denote the genus $g$ closed orientable surface. 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