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The union of the curves in a filling forms a graph on the surface which is a so-called decorated fat graph. It is a fact that two fillings of $F_g$ are in the same $\\text{Mod}(F_g)$-orbit if and only if the corresponding fat graphs are isomorphic. We prove that any filling of $F_2$ whose complement is a single disc (i.e., a so-called minimal"},"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":"1503.04559","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-16T08:14:33Z","cross_cats_sorted":[],"title_canon_sha256":"1a430cc8cd7f11cb1c90cc622b4d2134fe6c4b4618aa988934da6170814af6f0","abstract_canon_sha256":"69f0395e19e4d66d253066530e445687ab401b2661371b866ac39afc880f3227"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:39.588925Z","signature_b64":"WUeKMkSSd/EjUSC1U8elqaUY/WVe5S+VChDSNQ6xz0GK7unhUQlzZ5iMCgylaMtV7Jjpakgt0sXFB/KwprUNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4369a637a817363a585583b9ab5a33b664ca994f1cc0c501f5cfce028ffe452d","last_reissued_at":"2026-05-18T00:34:39.588447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:39.588447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Filling of closed Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bidyut Sanki","submitted_at":"2015-03-16T08:14:33Z","abstract_excerpt":"Let $F_g$ denote a closed oriented surface of genus $g$. 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