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When the complex dimension of $\\mathcal{P}(\\mu)^{\\circ}$ is at least two, Dozier--Grushevsky--Lee, through explicit degeneration techniques, showed that the boundary of $\\mathcal{P}(\\mu)^{\\circ}$ is connected in the multi-scale compactification constructed by Bainbridge--Chen--Gendron--Grushevsky--M\\\"oller.\n  A natural question is whether the connectedness of the boundary of $\\mathcal{P}(\\mu)^"},"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":"2505.07190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-12T02:40:16Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"dbe7dbd8396150e84883afd5b96dc71f05a1d925f4f423e56ca2db3fb6cb585b","abstract_canon_sha256":"691c2ae56ff0d8b345df579e917fbb28a955bc738c0bbc873024e9ecd78bc45e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:01:43.978203Z","signature_b64":"8QbeQBATa0E56nNJtlM8lT+mYRjMuFQZ8iI/iErZdRumWRi94IrINZf5sO/KHNhzNQbe26bvRLdyA5ETZdZ5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9c183763937bb1f36f5bae2d8cced92ed8ae4d8ef83585913d176b6cf1f8cde","last_reissued_at":"2026-07-05T11:01:43.977805Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:01:43.977805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connectedness of the boundaries of the strata of differentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Dawei Chen","submitted_at":"2025-05-12T02:40:16Z","abstract_excerpt":"Let $\\mathcal{P}(\\mu)^{\\circ}$ be a connected component of the projectivized stratum of differentials on smooth complex curves, where the zero and pole orders of the differentials are specified by $\\mu$. 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