{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4HFOETDKSG3L3QMVSM2HDVRZFR","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":"b9d216980d0280ded6ce8d785f7431415fc8a04cb21917609dbfc2f6128c0861","cross_cats_sorted":["math.AG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-30T19:23:28Z","title_canon_sha256":"e61d0fc1158b0d205e49bcf51c691faf2cb55c4e7ea544838d555318de3ca2f4"},"schema_version":"1.0","source":{"id":"1003.5903","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5903","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5903v3","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5903","created_at":"2026-05-18T03:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"4HFOETDKSG3L","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4HFOETDKSG3L3QMV","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4HFOETDK","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:ee701c59f0a6a218d8c30f45ff1b3964ffa9ae58c57f5ba323a067e9101c4125","target":"graph","created_at":"2026-05-18T03:22:08Z","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 consider the extension of classical 2-dimensional topological quantum field theories to Klein topological quantum field theories which allow unorientable surfaces. We approach this using the theory of modular operads by introducing a new operad governing associative algebras with involution. This operad is Koszul and we identify the dual dg operad governing A-infinity algebras with involution in terms of Mobius graphs which are a generalisation of ribbon graphs. We then generalise open topological conformal field theories to open Klein topological conformal field theories and give a generat","authors_text":"Christopher Braun","cross_cats":["math.AG","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-30T19:23:28Z","title":"Moduli spaces of Klein surfaces and related operads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5903","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:df757b9fc014bafb753b532895ec88cb754bf96c83566726a01b577bbe4bddd1","target":"record","created_at":"2026-05-18T03:22:08Z","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":"b9d216980d0280ded6ce8d785f7431415fc8a04cb21917609dbfc2f6128c0861","cross_cats_sorted":["math.AG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-30T19:23:28Z","title_canon_sha256":"e61d0fc1158b0d205e49bcf51c691faf2cb55c4e7ea544838d555318de3ca2f4"},"schema_version":"1.0","source":{"id":"1003.5903","kind":"arxiv","version":3}},"canonical_sha256":"e1cae24c6a91b6bdc195933471d6392c5c7746f12d99d50e94c139730fc2ec7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1cae24c6a91b6bdc195933471d6392c5c7746f12d99d50e94c139730fc2ec7c","first_computed_at":"2026-05-18T03:22:08.288813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:08.288813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EOvaxO5gGZaTxYulux3Q/PAIFHaroBGhrArIfuTcIx1tBFbqwz9ugGa3iSKUGqSYiEXBhsdMslJPUBmX7bzYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:08.289471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5903","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df757b9fc014bafb753b532895ec88cb754bf96c83566726a01b577bbe4bddd1","sha256:ee701c59f0a6a218d8c30f45ff1b3964ffa9ae58c57f5ba323a067e9101c4125"],"state_sha256":"b7841beb7c42f02325f7d4cdd240f75d9e9d6bad24f9c2668f5f7d4b1e0b6bc3"}