{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4CRZHSQKEE4Y64Z23SOZJLS233","short_pith_number":"pith:4CRZHSQK","schema_version":"1.0","canonical_sha256":"e0a393ca0a21398f733adc9d94ae5adec55b0d8661401db532bb2d761d3585dc","source":{"kind":"arxiv","id":"1409.5180","version":2},"attestation_state":"computed","paper":{"title":"Affine Manifolds and Zero Lyapunov Exponents in Genus 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"David Aulicino","submitted_at":"2014-09-18T03:06:53Z","abstract_excerpt":"In previous work, the author fully classified orbit closures in genus three with maximally many (four) zero Lyapunov exponents of the Kontsevich-Zorich cocycle. In this paper, we prove that there are no higher dimensional orbit closures in genus three with any zero Lyapunov exponents. Furthermore, if a Teichm\\\"uller curve in genus three has two zero Lyapunov exponents in the Kontsevich-Zorich cocycle, then it lies in the principal stratum and has at most quadratic trace field. Moreover, there can be at most finitely many such Teichm\\\"uller curves."},"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":"1409.5180","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-18T03:06:53Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"d529dd8fad115359b3064efc3cd09f7e93e6c49e54fef95e2817e2f4fc74ab91","abstract_canon_sha256":"d4d06a9a8574d6a521f7de845992b6248f867fb7bab98f547ba5efdf05df27bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:05.235384Z","signature_b64":"SvD5XG8nTdpQIbabRX6/ie29Zrh1dRYduHN4TAvC72qp5ZkmIRK9QOGoxJl06P44DYjyCdXHHyZYKuJAl04SBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0a393ca0a21398f733adc9d94ae5adec55b0d8661401db532bb2d761d3585dc","last_reissued_at":"2026-05-18T01:24:05.234765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:05.234765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Affine Manifolds and Zero Lyapunov Exponents in Genus 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"David Aulicino","submitted_at":"2014-09-18T03:06:53Z","abstract_excerpt":"In previous work, the author fully classified orbit closures in genus three with maximally many (four) zero Lyapunov exponents of the Kontsevich-Zorich cocycle. In this paper, we prove that there are no higher dimensional orbit closures in genus three with any zero Lyapunov exponents. Furthermore, if a Teichm\\\"uller curve in genus three has two zero Lyapunov exponents in the Kontsevich-Zorich cocycle, then it lies in the principal stratum and has at most quadratic trace field. Moreover, there can be at most finitely many such Teichm\\\"uller curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5180","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.5180","created_at":"2026-05-18T01:24:05.234891+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.5180v2","created_at":"2026-05-18T01:24:05.234891+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5180","created_at":"2026-05-18T01:24:05.234891+00:00"},{"alias_kind":"pith_short_12","alias_value":"4CRZHSQKEE4Y","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4CRZHSQKEE4Y64Z2","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4CRZHSQK","created_at":"2026-05-18T12:28:14.216126+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4CRZHSQKEE4Y64Z23SOZJLS233","json":"https://pith.science/pith/4CRZHSQKEE4Y64Z23SOZJLS233.json","graph_json":"https://pith.science/api/pith-number/4CRZHSQKEE4Y64Z23SOZJLS233/graph.json","events_json":"https://pith.science/api/pith-number/4CRZHSQKEE4Y64Z23SOZJLS233/events.json","paper":"https://pith.science/paper/4CRZHSQK"},"agent_actions":{"view_html":"https://pith.science/pith/4CRZHSQKEE4Y64Z23SOZJLS233","download_json":"https://pith.science/pith/4CRZHSQKEE4Y64Z23SOZJLS233.json","view_paper":"https://pith.science/paper/4CRZHSQK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.5180&json=true","fetch_graph":"https://pith.science/api/pith-number/4CRZHSQKEE4Y64Z23SOZJLS233/graph.json","fetch_events":"https://pith.science/api/pith-number/4CRZHSQKEE4Y64Z23SOZJLS233/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4CRZHSQKEE4Y64Z23SOZJLS233/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4CRZHSQKEE4Y64Z23SOZJLS233/action/storage_attestation","attest_author":"https://pith.science/pith/4CRZHSQKEE4Y64Z23SOZJLS233/action/author_attestation","sign_citation":"https://pith.science/pith/4CRZHSQKEE4Y64Z23SOZJLS233/action/citation_signature","submit_replication":"https://pith.science/pith/4CRZHSQKEE4Y64Z23SOZJLS233/action/replication_record"}},"created_at":"2026-05-18T01:24:05.234891+00:00","updated_at":"2026-05-18T01:24:05.234891+00:00"}