{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:BLF3SLLVY7PIBXFAFGEDZC6UFU","short_pith_number":"pith:BLF3SLLV","schema_version":"1.0","canonical_sha256":"0acbb92d75c7de80dca029883c8bd42d3605e9dbf1e2d4a05953b2f2858f23d3","source":{"kind":"arxiv","id":"2509.14812","version":5},"attestation_state":"computed","paper":{"title":"From Hitchin Systems to Rational Elliptic Surfaces with C*-actions via Orbifold Hilbert Schemes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AG","authors_text":"Yonghong Huang","submitted_at":"2025-09-18T10:13:03Z","abstract_excerpt":"Using orbifold Hilbert schemes, we compactify all two-dimensional Hitchin systems corresponding to types A0-tilde, D4-tilde, E6-tilde, E7-tilde, and E8-tilde, thereby obtaining four rational elliptic surfaces with C*-actions. Their singular fibers and relative minimal models are listed in the main table. A particularly interesting point is that we found they can all be obtained by performing a finite number of blow-ups on the second Hirzebruch surface. To this end, we prove that Hilbert schemes of orbifold surfaces are connected smooth projective schemes under suitable conditions, and we use t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2509.14812","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-09-18T10:13:03Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"37165f703789742e60867fbc8da617b6ed227b7fd6597b92cf66512e4f535fd8","abstract_canon_sha256":"cad644737779d88ecaa0f531c4b97e491a9c46277485d6d32bde78bb77f40b58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:14:22.129905Z","signature_b64":"GisOZX4Htjy8SOnSsUHT/fz52Qycwm+Z33KnJFEF5wjI5gKC6ShqhHBztS/8+hYvgTtggIOE+IKhP4P1m1qeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0acbb92d75c7de80dca029883c8bd42d3605e9dbf1e2d4a05953b2f2858f23d3","last_reissued_at":"2026-06-24T01:14:22.129260Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:14:22.129260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From Hitchin Systems to Rational Elliptic Surfaces with C*-actions via Orbifold Hilbert Schemes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AG","authors_text":"Yonghong Huang","submitted_at":"2025-09-18T10:13:03Z","abstract_excerpt":"Using orbifold Hilbert schemes, we compactify all two-dimensional Hitchin systems corresponding to types A0-tilde, D4-tilde, E6-tilde, E7-tilde, and E8-tilde, thereby obtaining four rational elliptic surfaces with C*-actions. Their singular fibers and relative minimal models are listed in the main table. A particularly interesting point is that we found they can all be obtained by performing a finite number of blow-ups on the second Hirzebruch surface. To this end, we prove that Hilbert schemes of orbifold surfaces are connected smooth projective schemes under suitable conditions, and we use t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.14812","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.14812/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2509.14812","created_at":"2026-06-24T01:14:22.129362+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.14812v5","created_at":"2026-06-24T01:14:22.129362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.14812","created_at":"2026-06-24T01:14:22.129362+00:00"},{"alias_kind":"pith_short_12","alias_value":"BLF3SLLVY7PI","created_at":"2026-06-24T01:14:22.129362+00:00"},{"alias_kind":"pith_short_16","alias_value":"BLF3SLLVY7PIBXFA","created_at":"2026-06-24T01:14:22.129362+00:00"},{"alias_kind":"pith_short_8","alias_value":"BLF3SLLV","created_at":"2026-06-24T01:14:22.129362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BLF3SLLVY7PIBXFAFGEDZC6UFU","json":"https://pith.science/pith/BLF3SLLVY7PIBXFAFGEDZC6UFU.json","graph_json":"https://pith.science/api/pith-number/BLF3SLLVY7PIBXFAFGEDZC6UFU/graph.json","events_json":"https://pith.science/api/pith-number/BLF3SLLVY7PIBXFAFGEDZC6UFU/events.json","paper":"https://pith.science/paper/BLF3SLLV"},"agent_actions":{"view_html":"https://pith.science/pith/BLF3SLLVY7PIBXFAFGEDZC6UFU","download_json":"https://pith.science/pith/BLF3SLLVY7PIBXFAFGEDZC6UFU.json","view_paper":"https://pith.science/paper/BLF3SLLV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.14812&json=true","fetch_graph":"https://pith.science/api/pith-number/BLF3SLLVY7PIBXFAFGEDZC6UFU/graph.json","fetch_events":"https://pith.science/api/pith-number/BLF3SLLVY7PIBXFAFGEDZC6UFU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BLF3SLLVY7PIBXFAFGEDZC6UFU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BLF3SLLVY7PIBXFAFGEDZC6UFU/action/storage_attestation","attest_author":"https://pith.science/pith/BLF3SLLVY7PIBXFAFGEDZC6UFU/action/author_attestation","sign_citation":"https://pith.science/pith/BLF3SLLVY7PIBXFAFGEDZC6UFU/action/citation_signature","submit_replication":"https://pith.science/pith/BLF3SLLVY7PIBXFAFGEDZC6UFU/action/replication_record"}},"created_at":"2026-06-24T01:14:22.129362+00:00","updated_at":"2026-06-24T01:14:22.129362+00:00"}