{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:3Y5NWASFU6CCDQWHPL52CDU5ML","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":"360876de40df1e6902b6b95720740c96b7ab485627e097f854ccd67df74bd415","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-20T20:38:22Z","title_canon_sha256":"b08d828b56ab3223695efe125ce53b3ddd681bdb972b0a636304e3e161fedef5"},"schema_version":"1.0","source":{"id":"2412.16330","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.16330","created_at":"2026-07-05T10:52:57Z"},{"alias_kind":"arxiv_version","alias_value":"2412.16330v2","created_at":"2026-07-05T10:52:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16330","created_at":"2026-07-05T10:52:57Z"},{"alias_kind":"pith_short_12","alias_value":"3Y5NWASFU6CC","created_at":"2026-07-05T10:52:57Z"},{"alias_kind":"pith_short_16","alias_value":"3Y5NWASFU6CCDQWH","created_at":"2026-07-05T10:52:57Z"},{"alias_kind":"pith_short_8","alias_value":"3Y5NWASF","created_at":"2026-07-05T10:52:57Z"}],"graph_snapshots":[{"event_id":"sha256:fd6b4ae477245de045a72828d82b8a6517a8fc00ecad8bd3b08c722e44d27d05","target":"graph","created_at":"2026-07-05T10:52:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.16330/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a semisimplicity result for the boundary, in the corresponding Deligne-Mumford compactification, of a totally geodesic subvariety of a moduli space of Riemann surfaces. At the level of Teichm\\\"uller space, this semisimplicity theorem gives that each component of the boundary is a product of simple factors, each of which behaves metrically like a diagonal embedding. Building on this result, we also show that the associated totally geodesic submanifolds of Teichm\\\"uller space and orbifold fundamental groups are hierarchically hyperbolic.\n  The proof intertwines in a novel way results an","authors_text":"Alex Wright, Francisco Arana-Herrera","cross_cats":["math.DS","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-20T20:38:22Z","title":"The geometry of totally geodesic subvarieties of moduli spaces of Riemann surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16330","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":"sha256:646a73b26497d00afd8167611b87902c40e0a4dee1186b1733f0e752694cc019","target":"record","created_at":"2026-07-05T10:52:57Z","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":"360876de40df1e6902b6b95720740c96b7ab485627e097f854ccd67df74bd415","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-20T20:38:22Z","title_canon_sha256":"b08d828b56ab3223695efe125ce53b3ddd681bdb972b0a636304e3e161fedef5"},"schema_version":"1.0","source":{"id":"2412.16330","kind":"arxiv","version":2}},"canonical_sha256":"de3adb0245a78421c2c77afba10e9d62ece9f6972cb1c857300d8a82e25281e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de3adb0245a78421c2c77afba10e9d62ece9f6972cb1c857300d8a82e25281e6","first_computed_at":"2026-07-05T10:52:57.424594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:52:57.424594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0dU4DcmTwkCbQfJCIxyzBn3tkyRy5ijPRv0SMcPrdubqLF2rtWKPHJ/Qmg3nmkH+24o2YDWfFTWzvv3Iy5G2CA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:52:57.425118Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.16330","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:646a73b26497d00afd8167611b87902c40e0a4dee1186b1733f0e752694cc019","sha256:fd6b4ae477245de045a72828d82b8a6517a8fc00ecad8bd3b08c722e44d27d05"],"state_sha256":"ef75022af6fc9af056519e0a9443387012dc55e6500f4ece91ed8e8319eec99f"}