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Let $\\mathcal{D}_g (1)$ be the subset of the moduli space of Abelian differentials $\\mathcal{M}_g$ whose elements have period matrix derivative of rank one. There is an $\\text{SL}_2(\\mathbb{R})$-invariant ergodic probability measure $\\nu$ with completely degenerate Kontsevich-Zorich spectrum, i.e. $\\lambda_1 = 1 > \\lambda_2 = \\cdots ="},"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":"1205.2359","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-10T19:31:40Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"1b6914713718e9d01686e3cf7353d51861a940eef171e101697bb077d4b85c41","abstract_canon_sha256":"05b8cd2f86d1593a0c8395f91fdb8424ba6ba2b20b3e004e4309aa5563f63d28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:31.859410Z","signature_b64":"gmKvpgF7ApdftP+8kdQBhLwUw+1IfzIavRSgGlPkGSjwJ1xYxW2NeNSJVa6hdKHZd4TEPX3FXs8rdxikGHHpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43b75df0bfec3cdcb3fd983ad550ef4df8bf2b980a686cb2c9ae75640f53695a","last_reissued_at":"2026-05-18T01:36:31.858834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:31.858834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Teichm\\\"uller Discs with Completely Degenerate Kontsevich-Zorich Spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"David Aulicino","submitted_at":"2012-05-10T19:31:40Z","abstract_excerpt":"We reduce a question of Eskin-Kontsevich-Zorich and Forni-Matheus-Zorich, which asks for a classification of all $\\text{SL}_2(\\mathbb{R})$-invariant ergodic probability measures with completely degenerate Kontsevich-Zorich spectrum, to a conjecture of M\\\"oller's. Let $\\mathcal{D}_g (1)$ be the subset of the moduli space of Abelian differentials $\\mathcal{M}_g$ whose elements have period matrix derivative of rank one. 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