{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HXTNBLWVFRNG46IJX73NHEYMRS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9a4ef39d16cc379fe94111c051faa955d7a4e6e044ab639a0a3d6b67d1a84a49","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-27T19:18:19Z","title_canon_sha256":"05ec24bbf248a1f7e042c8fee75adae60be8ca515827df01170d63a6f6d28154"},"schema_version":"1.0","source":{"id":"1203.6053","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6053","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6053v6","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6053","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"HXTNBLWVFRNG","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HXTNBLWVFRNG46IJ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HXTNBLWV","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:2a1a523c7b719928eed135cc523fbbff5534c9ff809edf9e95b058d6767b90e6","target":"graph","created_at":"2026-05-18T02:32:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We define the Weierstrass filtration for Teichmuller curves and construct the Harder-Narasimhan filtration of the Hodge bundle of a Teichmuller curve in hyperelliptic loci and low-genus nonvarying strata. As a result we obtain the sum of Lyapunov exponents of Teichmuller curves in these strata.","authors_text":"Fei Yu, Kang Zuo","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-27T19:18:19Z","title":"Weierstrass filtration on Teichmuller curves and Lyapunov exponents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6053","kind":"arxiv","version":6},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fa576587c55d752bd503629aa87bc5bbdd20dcac3b85a5b9bd51a8a25740d464","target":"record","created_at":"2026-05-18T02:32:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9a4ef39d16cc379fe94111c051faa955d7a4e6e044ab639a0a3d6b67d1a84a49","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-27T19:18:19Z","title_canon_sha256":"05ec24bbf248a1f7e042c8fee75adae60be8ca515827df01170d63a6f6d28154"},"schema_version":"1.0","source":{"id":"1203.6053","kind":"arxiv","version":6}},"canonical_sha256":"3de6d0aed52c5a6e7909bff6d3930c8ca5b2da43654aee6c7519e84a44a902cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3de6d0aed52c5a6e7909bff6d3930c8ca5b2da43654aee6c7519e84a44a902cf","first_computed_at":"2026-05-18T02:32:14.688081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:14.688081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9iNQupVRUIJkJCQIUgHn1gz+ZLKHylOfySqbaSsw7AV0vhGKa1Nz1W2ZceUe/84Ox9FnBfn8fQXeY9or5CJ5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:14.688781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6053","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa576587c55d752bd503629aa87bc5bbdd20dcac3b85a5b9bd51a8a25740d464","sha256:2a1a523c7b719928eed135cc523fbbff5534c9ff809edf9e95b058d6767b90e6"],"state_sha256":"ae32956f257db95d500cce01439235e4d64c30148d7f20db5ba1db89c5685540"}