{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4LQ25YAE5SB2P54S6XAD32RNVG","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":"ed8d0923b64b993380d4274816cfc907bb0a58e48cd509f85ea7e8aa6062ee1a","cross_cats_sorted":["math.AG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-13T11:23:16Z","title_canon_sha256":"974bf5758c1065c11a0568fc4dd3e93b8069cf86006d3c6075d7ab009b7f5947"},"schema_version":"1.0","source":{"id":"1209.2854","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2854","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2854v2","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2854","created_at":"2026-05-18T02:32:12Z"},{"alias_kind":"pith_short_12","alias_value":"4LQ25YAE5SB2","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4LQ25YAE5SB2P54S","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4LQ25YAE","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:ef841b59e1416a7347e7ee0bcecd4e6f58f8b85a942ee82bc8051e2013f035e3","target":"graph","created_at":"2026-05-18T02:32:12Z","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":"Suppose N is an affine SL(2,R)-invariant submanfold of the moduli space of pairs (M,w) where M is a curve, and w is a holomorphic 1-form on M. We show that the Forni bundle of N (i.e. the maximal SL(2,R)-invariant isometric subbundle of the Hodge bundle of N) is always flat and is always orthogonal to the tangent space of N. As a corollary, it follows that the Hodge bundle of N is semisimple.","authors_text":"Alex Eskin, Artur Avila, Martin Moeller","cross_cats":["math.AG","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-13T11:23:16Z","title":"Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2854","kind":"arxiv","version":2},"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":"sha256:3db3a588911dcf3dccc65577ea1cac452f5cfebceea0f7e38ae4f405140734cd","target":"record","created_at":"2026-05-18T02:32:12Z","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":"ed8d0923b64b993380d4274816cfc907bb0a58e48cd509f85ea7e8aa6062ee1a","cross_cats_sorted":["math.AG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-13T11:23:16Z","title_canon_sha256":"974bf5758c1065c11a0568fc4dd3e93b8069cf86006d3c6075d7ab009b7f5947"},"schema_version":"1.0","source":{"id":"1209.2854","kind":"arxiv","version":2}},"canonical_sha256":"e2e1aee004ec83a7f792f5c03dea2da989c2b0dbf6c350227c03568d8393b6c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2e1aee004ec83a7f792f5c03dea2da989c2b0dbf6c350227c03568d8393b6c1","first_computed_at":"2026-05-18T02:32:12.357215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:12.357215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cfVzesxd7K0gMdr9sQN+080opzGURt1kIIbGDnuKTz2qNwmuT/9V55jn9Zhop44Xl6JZJXQ32dUZVAOYZniPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:12.357611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2854","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3db3a588911dcf3dccc65577ea1cac452f5cfebceea0f7e38ae4f405140734cd","sha256:ef841b59e1416a7347e7ee0bcecd4e6f58f8b85a942ee82bc8051e2013f035e3"],"state_sha256":"7b9aa1e9e04b5acdba3b03dcf70a1c1d6c08653044ef0978bf8212e4d15dc22f"}