{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ZSDCNIEPH4IL3KKLUZ2H4NB77M","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":"b55d547082800adfba3ea8ff01880f1fd6fc4086aea2d3ca013778e3de636ab8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2023-05-16T17:38:00Z","title_canon_sha256":"5163a303e08477379e0e708a0636d74f770068e71e010ab3f91b374eab08de22"},"schema_version":"1.0","source":{"id":"2305.09632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.09632","created_at":"2026-07-05T06:10:50Z"},{"alias_kind":"arxiv_version","alias_value":"2305.09632v1","created_at":"2026-07-05T06:10:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.09632","created_at":"2026-07-05T06:10:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZSDCNIEPH4IL","created_at":"2026-07-05T06:10:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZSDCNIEPH4IL3KKL","created_at":"2026-07-05T06:10:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZSDCNIEP","created_at":"2026-07-05T06:10:50Z"}],"graph_snapshots":[{"event_id":"sha256:6a3c670cdada129a5ab67e6e18da50eaa8c9269e5e20419026ff945799db6834","target":"graph","created_at":"2026-07-05T06:10:50Z","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/2305.09632/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a reductive group $G$, Harder-Narasimhan theory gives a structure theorem for principal $G$ bundles on a smooth projective curve $C$. A bundle is either semistable, or it admits a canonical parabolic reduction whose associated Levi bundle is semistable. We extend this structure theorem by constructing a $\\Theta$-stratification of the moduli stack of gauged maps from $C$ to a projective-over-affine $G$-variety $X$. The open stratum coincides with the previously studied moduli of Mundet semistable maps, and in special cases coincides with the moduli of stable quasi-maps. As an application of","authors_text":"Andres Fernandez Herrero, Daniel Halpern-Leistner","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2023-05-16T17:38:00Z","title":"The structure of the moduli of gauged maps from a smooth curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.09632","kind":"arxiv","version":1},"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":"sha256:098efb5ff55da1c636d63ed46354d1b8fdc300415945d62f5301a3899449f532","target":"record","created_at":"2026-07-05T06:10:50Z","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":"b55d547082800adfba3ea8ff01880f1fd6fc4086aea2d3ca013778e3de636ab8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2023-05-16T17:38:00Z","title_canon_sha256":"5163a303e08477379e0e708a0636d74f770068e71e010ab3f91b374eab08de22"},"schema_version":"1.0","source":{"id":"2305.09632","kind":"arxiv","version":1}},"canonical_sha256":"cc8626a08f3f10bda94ba6747e343ffb0807147b2138d971aafc811e596ccf0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc8626a08f3f10bda94ba6747e343ffb0807147b2138d971aafc811e596ccf0f","first_computed_at":"2026-07-05T06:10:50.198116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:10:50.198116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qglkWjUDZJrPMtHWMwGuGWhQqwsnwgcg/f1IBVl2M6HKbGnDSdkB7Y0wFNlYB1LOBFXMol0OVqPaHUzn8evXDg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:10:50.198466Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.09632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:098efb5ff55da1c636d63ed46354d1b8fdc300415945d62f5301a3899449f532","sha256:6a3c670cdada129a5ab67e6e18da50eaa8c9269e5e20419026ff945799db6834"],"state_sha256":"ed33a2cd17679cc482d7012c5e92e25fcbcb53da162db06914636ce7312bf35a"}