{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6U4VBGS3YEHNSZEG4K2M3I3HXY","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":"6c66a8eb28ada30c5c78d6593b7d821f0735cae15654f519f1189c41fd408b8c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-05T16:29:58Z","title_canon_sha256":"fcb4a27f1225c0fa97b353264419edd929173903728fe0c3647b0973273c5433"},"schema_version":"1.0","source":{"id":"1303.1088","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1088","created_at":"2026-05-18T03:15:20Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1088v3","created_at":"2026-05-18T03:15:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1088","created_at":"2026-05-18T03:15:20Z"},{"alias_kind":"pith_short_12","alias_value":"6U4VBGS3YEHN","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6U4VBGS3YEHNSZEG","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6U4VBGS3","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:9e45726c8f66f4a1e41ddccdfecb0224a564a109b454bbb6316459cfdae42c74","target":"graph","created_at":"2026-05-18T03:15:20Z","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":"If the monodromy representation of a VHS over a hyperbolic curve stabilizes a rank two subspace, there is a single non-negative Lyapunov exponent associated with it. We derive an explicit formula using only the representation in the case when the monodromy is discrete.","authors_text":"Andr\\'e Kappes","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-05T16:29:58Z","title":"Lyapunov Exponents of Rank 2-Variations of Hodge Structures and Modular Embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1088","kind":"arxiv","version":3},"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:ff683eff08d340a3e6869ec36c33329fba3556c6ea7403489ef1376cd388bdde","target":"record","created_at":"2026-05-18T03:15:20Z","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":"6c66a8eb28ada30c5c78d6593b7d821f0735cae15654f519f1189c41fd408b8c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-05T16:29:58Z","title_canon_sha256":"fcb4a27f1225c0fa97b353264419edd929173903728fe0c3647b0973273c5433"},"schema_version":"1.0","source":{"id":"1303.1088","kind":"arxiv","version":3}},"canonical_sha256":"f539509a5bc10ed96486e2b4cda367be2a2a358bae8c67f510672be6e1ec92aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f539509a5bc10ed96486e2b4cda367be2a2a358bae8c67f510672be6e1ec92aa","first_computed_at":"2026-05-18T03:15:20.719286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:20.719286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xrLawt1YpuGxUr3Q+zI0TRj92R2b9bHaC+xcEAw5yGBOtJnGuDcsf3dOoNJXy5ryFWBviyJ/Ol0KrtM4dHUgCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:20.719878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1088","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff683eff08d340a3e6869ec36c33329fba3556c6ea7403489ef1376cd388bdde","sha256:9e45726c8f66f4a1e41ddccdfecb0224a564a109b454bbb6316459cfdae42c74"],"state_sha256":"a5f10457c8801aaa1172e1ef7d5a398c22edfc1d8578c92833b43dc88954de7d"}