{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BULGALDOB2P7MTYQWO2WJBVCTG","short_pith_number":"pith:BULGALDO","canonical_record":{"source":{"id":"1803.01611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-05T11:32:03Z","cross_cats_sorted":[],"title_canon_sha256":"a4acf6ddda617fa9fe64b559db11a7dbc2d2e95d39480c8dd06ee0cfa804e0b8","abstract_canon_sha256":"e11ad53bdd5f4c994919e4fd638150cabfdb8be9d3408f6bcf2c5a16452a4d9e"},"schema_version":"1.0"},"canonical_sha256":"0d16602c6e0e9ff64f10b3b56486a299ae7c5cb39612ff00c8137cf99aad325b","source":{"kind":"arxiv","id":"1803.01611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01611","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01611v1","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01611","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"BULGALDOB2P7","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BULGALDOB2P7MTYQ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BULGALDO","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BULGALDOB2P7MTYQWO2WJBVCTG","target":"record","payload":{"canonical_record":{"source":{"id":"1803.01611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-05T11:32:03Z","cross_cats_sorted":[],"title_canon_sha256":"a4acf6ddda617fa9fe64b559db11a7dbc2d2e95d39480c8dd06ee0cfa804e0b8","abstract_canon_sha256":"e11ad53bdd5f4c994919e4fd638150cabfdb8be9d3408f6bcf2c5a16452a4d9e"},"schema_version":"1.0"},"canonical_sha256":"0d16602c6e0e9ff64f10b3b56486a299ae7c5cb39612ff00c8137cf99aad325b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:00.093084Z","signature_b64":"T/yanbHlY1mctcoaUiv6ud2+k69it0OXaT0l4JU2OTGhkzI09eAovlJuqcFSr4cPCTD79v3u054z1TSqqRvaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d16602c6e0e9ff64f10b3b56486a299ae7c5cb39612ff00c8137cf99aad325b","last_reissued_at":"2026-05-18T00:22:00.092506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:00.092506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.01611","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FiPuqv4MqvjcNa73IE3osF0+q8Dzb9MonFtHIWoT0bR6iYAu5mM02dqBL469IgCOQnqHBFF0A2pi7uFcoo4RBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:32:44.161996Z"},"content_sha256":"7350c844673f3f914d58ee7b0f1fefae05e94a65451500b3b80bdae29408b5ac","schema_version":"1.0","event_id":"sha256:7350c844673f3f914d58ee7b0f1fefae05e94a65451500b3b80bdae29408b5ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BULGALDOB2P7MTYQWO2WJBVCTG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higgs bundles, Lagrangians and mirror symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lucas C. Branco","submitted_at":"2018-03-05T11:32:03Z","abstract_excerpt":"This thesis is dedicated to the study of certain loci of the Higgs bundle moduli space on a compact Riemann surface. Motivated by mirror symmetry, we give a detailed description of the fibres of the $G$-Hitchin fibration containing $G_0$-Higgs bundles for the real forms $G_0 = SU^*(2m)$, $SO^*(4m)$ and $Sp(m,m)$ of $G = SL(2m,\\mathbb{C})$, $SO(4m,\\mathbb{C})$ and $Sp(4m,\\mathbb{C})$, respectively. The spectral curves associated to these fibres are examples of ribbons and our description is done in two different ways, one in term of objects on the reduced scheme associated to the spectral curve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01611","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ept656iz1AKownCUkF3wa2CcAWAmcGNdIxzeXLPO7Q3pZBjW7OiAQOV9GQWdXhWk9PpAUgE65VCrEvafvDYACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:32:44.162451Z"},"content_sha256":"bc95a248e999c631de3973669d121ab3e7b684ee518a526223a3a3b1234c695b","schema_version":"1.0","event_id":"sha256:bc95a248e999c631de3973669d121ab3e7b684ee518a526223a3a3b1234c695b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BULGALDOB2P7MTYQWO2WJBVCTG/bundle.json","state_url":"https://pith.science/pith/BULGALDOB2P7MTYQWO2WJBVCTG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BULGALDOB2P7MTYQWO2WJBVCTG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T00:32:44Z","links":{"resolver":"https://pith.science/pith/BULGALDOB2P7MTYQWO2WJBVCTG","bundle":"https://pith.science/pith/BULGALDOB2P7MTYQWO2WJBVCTG/bundle.json","state":"https://pith.science/pith/BULGALDOB2P7MTYQWO2WJBVCTG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BULGALDOB2P7MTYQWO2WJBVCTG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BULGALDOB2P7MTYQWO2WJBVCTG","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":"e11ad53bdd5f4c994919e4fd638150cabfdb8be9d3408f6bcf2c5a16452a4d9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-05T11:32:03Z","title_canon_sha256":"a4acf6ddda617fa9fe64b559db11a7dbc2d2e95d39480c8dd06ee0cfa804e0b8"},"schema_version":"1.0","source":{"id":"1803.01611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01611","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01611v1","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01611","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"BULGALDOB2P7","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BULGALDOB2P7MTYQ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BULGALDO","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:bc95a248e999c631de3973669d121ab3e7b684ee518a526223a3a3b1234c695b","target":"graph","created_at":"2026-05-18T00:22:00Z","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":"This thesis is dedicated to the study of certain loci of the Higgs bundle moduli space on a compact Riemann surface. Motivated by mirror symmetry, we give a detailed description of the fibres of the $G$-Hitchin fibration containing $G_0$-Higgs bundles for the real forms $G_0 = SU^*(2m)$, $SO^*(4m)$ and $Sp(m,m)$ of $G = SL(2m,\\mathbb{C})$, $SO(4m,\\mathbb{C})$ and $Sp(4m,\\mathbb{C})$, respectively. The spectral curves associated to these fibres are examples of ribbons and our description is done in two different ways, one in term of objects on the reduced scheme associated to the spectral curve","authors_text":"Lucas C. Branco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-05T11:32:03Z","title":"Higgs bundles, Lagrangians and mirror symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01611","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":"sha256:7350c844673f3f914d58ee7b0f1fefae05e94a65451500b3b80bdae29408b5ac","target":"record","created_at":"2026-05-18T00:22:00Z","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":"e11ad53bdd5f4c994919e4fd638150cabfdb8be9d3408f6bcf2c5a16452a4d9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-05T11:32:03Z","title_canon_sha256":"a4acf6ddda617fa9fe64b559db11a7dbc2d2e95d39480c8dd06ee0cfa804e0b8"},"schema_version":"1.0","source":{"id":"1803.01611","kind":"arxiv","version":1}},"canonical_sha256":"0d16602c6e0e9ff64f10b3b56486a299ae7c5cb39612ff00c8137cf99aad325b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d16602c6e0e9ff64f10b3b56486a299ae7c5cb39612ff00c8137cf99aad325b","first_computed_at":"2026-05-18T00:22:00.092506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:00.092506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T/yanbHlY1mctcoaUiv6ud2+k69it0OXaT0l4JU2OTGhkzI09eAovlJuqcFSr4cPCTD79v3u054z1TSqqRvaDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:00.093084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.01611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7350c844673f3f914d58ee7b0f1fefae05e94a65451500b3b80bdae29408b5ac","sha256:bc95a248e999c631de3973669d121ab3e7b684ee518a526223a3a3b1234c695b"],"state_sha256":"68e9ef493a93a504badcb5a7f37dd9e326d4fde2d2da81c2fd10bbabb78a4cff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ZIfZC1cD2qNoScQMx3ilvRBOG57Dsm+hspx7PljfQERZMaCWTCTQj1/8yth6JTG7iqBex6DhygUiffNe0w9Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T00:32:44.166615Z","bundle_sha256":"85849bc751d599deaaaa721fe1ddc92e7e2f783cdd4deefed53b7a5d56bbb22f"}}