{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:RRBBENZV57VT6WP4AQTLI37FHL","short_pith_number":"pith:RRBBENZV","schema_version":"1.0","canonical_sha256":"8c42123735efeb3f59fc0426b46fe53ae8b8c3ebd542e29b3e3c60f9a73a0ed9","source":{"kind":"arxiv","id":"1202.1897","version":3},"attestation_state":"computed","paper":{"title":"Criteria for existence of stable parahoric $\\SO_n$, $\\Sp_n$ and $\\Spin$ bundles on $\\PP^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yashonidhi Pandey","submitted_at":"2012-02-09T07:03:27Z","abstract_excerpt":"Let $p: Y \\ra X$ be a Galois cover of smooth projective curves over $\\CC$ with Galois group $\\Gamma$. This paper is devoted to the study of principal orthogonal and symplectic bundles $E$ on $Y$ to which the action of $\\Gamma$ on $Y$ lifts. We notably describe them intrinsically in terms of objects defined on $X$ and call these objects parahoric bundles. We give necessary and sufficient conditions for the non-emptiness of the moduli of stable (and semi-stable) parahoric special orthogonal, symplectic and spin bundles on the projective line $\\PP^1$."},"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":"1202.1897","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-09T07:03:27Z","cross_cats_sorted":[],"title_canon_sha256":"4ec5e160a471aa823246604817f981a2ef9a0b9c9179ab206501b82c4caacfae","abstract_canon_sha256":"9d39f00148aa353a98db1ffc700e3c0bc2fcd76466cf46f7e7a6cfc68210d632"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:17.632394Z","signature_b64":"SfRtH+aER65meprdv/DWBzD8QiX0GeRgECVYxj5E8r+2vNCGHGGve1GI/BVtFx1EmofEjpgYVmF08U+H+gELAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c42123735efeb3f59fc0426b46fe53ae8b8c3ebd542e29b3e3c60f9a73a0ed9","last_reissued_at":"2026-05-18T03:28:17.631777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:17.631777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Criteria for existence of stable parahoric $\\SO_n$, $\\Sp_n$ and $\\Spin$ bundles on $\\PP^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yashonidhi Pandey","submitted_at":"2012-02-09T07:03:27Z","abstract_excerpt":"Let $p: Y \\ra X$ be a Galois cover of smooth projective curves over $\\CC$ with Galois group $\\Gamma$. This paper is devoted to the study of principal orthogonal and symplectic bundles $E$ on $Y$ to which the action of $\\Gamma$ on $Y$ lifts. We notably describe them intrinsically in terms of objects defined on $X$ and call these objects parahoric bundles. We give necessary and sufficient conditions for the non-emptiness of the moduli of stable (and semi-stable) parahoric special orthogonal, symplectic and spin bundles on the projective line $\\PP^1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1897","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1202.1897","created_at":"2026-05-18T03:28:17.631875+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.1897v3","created_at":"2026-05-18T03:28:17.631875+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1897","created_at":"2026-05-18T03:28:17.631875+00:00"},{"alias_kind":"pith_short_12","alias_value":"RRBBENZV57VT","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"RRBBENZV57VT6WP4","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"RRBBENZV","created_at":"2026-05-18T12:27:20.899486+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/RRBBENZV57VT6WP4AQTLI37FHL","json":"https://pith.science/pith/RRBBENZV57VT6WP4AQTLI37FHL.json","graph_json":"https://pith.science/api/pith-number/RRBBENZV57VT6WP4AQTLI37FHL/graph.json","events_json":"https://pith.science/api/pith-number/RRBBENZV57VT6WP4AQTLI37FHL/events.json","paper":"https://pith.science/paper/RRBBENZV"},"agent_actions":{"view_html":"https://pith.science/pith/RRBBENZV57VT6WP4AQTLI37FHL","download_json":"https://pith.science/pith/RRBBENZV57VT6WP4AQTLI37FHL.json","view_paper":"https://pith.science/paper/RRBBENZV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.1897&json=true","fetch_graph":"https://pith.science/api/pith-number/RRBBENZV57VT6WP4AQTLI37FHL/graph.json","fetch_events":"https://pith.science/api/pith-number/RRBBENZV57VT6WP4AQTLI37FHL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RRBBENZV57VT6WP4AQTLI37FHL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RRBBENZV57VT6WP4AQTLI37FHL/action/storage_attestation","attest_author":"https://pith.science/pith/RRBBENZV57VT6WP4AQTLI37FHL/action/author_attestation","sign_citation":"https://pith.science/pith/RRBBENZV57VT6WP4AQTLI37FHL/action/citation_signature","submit_replication":"https://pith.science/pith/RRBBENZV57VT6WP4AQTLI37FHL/action/replication_record"}},"created_at":"2026-05-18T03:28:17.631875+00:00","updated_at":"2026-05-18T03:28:17.631875+00:00"}