{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:MHK5AEMKYZOQMMZD6T7PB6Q6KY","short_pith_number":"pith:MHK5AEMK","schema_version":"1.0","canonical_sha256":"61d5d0118ac65d063323f4fef0fa1e561f8995113ca3b832a6e926335358c999","source":{"kind":"arxiv","id":"1102.0865","version":6},"attestation_state":"computed","paper":{"title":"Equivalence of symplectic singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yoshinori Namikawa","submitted_at":"2011-02-04T09:44:22Z","abstract_excerpt":"Let X be an affine normal variety with a C^*-action having only positive weights. Assume that X_{reg} has a symplectic 2-form w of weight l. We prove that, when l is not zero, the w is a unique symplectic 2-form of weight l up to C^*-equivariant automorphism\n  When $l = 0$, we have a counter-example to this statement.\n  In the latter half of the article, we associate to X a projective variety P(X) and prove that P(X) has a contact orbifold structure. Moreover, when X has canonical singularities, the contact orbifold structure is rigid under a small deformation. By using the contact structure o"},"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":"1102.0865","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-04T09:44:22Z","cross_cats_sorted":[],"title_canon_sha256":"84f332a5ee02eff289f511745babdd1587b43ce8872672ff1fca6cc00b737b67","abstract_canon_sha256":"14d5210b876225fe5c351862dc8c3e993ffcd43e75a6b35c6d2ac51cb85d2812"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:25.620929Z","signature_b64":"GM1wd2IiAumAJPczt6Nc4Q2bVDegKiwFMmEWDVp8A4Q+KapucJMMJFYmiHUsioCUDV3WARmodtzLfsSTlwJQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61d5d0118ac65d063323f4fef0fa1e561f8995113ca3b832a6e926335358c999","last_reissued_at":"2026-05-18T02:29:25.620310Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:25.620310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivalence of symplectic singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yoshinori Namikawa","submitted_at":"2011-02-04T09:44:22Z","abstract_excerpt":"Let X be an affine normal variety with a C^*-action having only positive weights. Assume that X_{reg} has a symplectic 2-form w of weight l. We prove that, when l is not zero, the w is a unique symplectic 2-form of weight l up to C^*-equivariant automorphism\n  When $l = 0$, we have a counter-example to this statement.\n  In the latter half of the article, we associate to X a projective variety P(X) and prove that P(X) has a contact orbifold structure. Moreover, when X has canonical singularities, the contact orbifold structure is rigid under a small deformation. By using the contact structure o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0865","kind":"arxiv","version":6},"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":"1102.0865","created_at":"2026-05-18T02:29:25.620435+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.0865v6","created_at":"2026-05-18T02:29:25.620435+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0865","created_at":"2026-05-18T02:29:25.620435+00:00"},{"alias_kind":"pith_short_12","alias_value":"MHK5AEMKYZOQ","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"MHK5AEMKYZOQMMZD","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"MHK5AEMK","created_at":"2026-05-18T12:26:34.985390+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/MHK5AEMKYZOQMMZD6T7PB6Q6KY","json":"https://pith.science/pith/MHK5AEMKYZOQMMZD6T7PB6Q6KY.json","graph_json":"https://pith.science/api/pith-number/MHK5AEMKYZOQMMZD6T7PB6Q6KY/graph.json","events_json":"https://pith.science/api/pith-number/MHK5AEMKYZOQMMZD6T7PB6Q6KY/events.json","paper":"https://pith.science/paper/MHK5AEMK"},"agent_actions":{"view_html":"https://pith.science/pith/MHK5AEMKYZOQMMZD6T7PB6Q6KY","download_json":"https://pith.science/pith/MHK5AEMKYZOQMMZD6T7PB6Q6KY.json","view_paper":"https://pith.science/paper/MHK5AEMK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.0865&json=true","fetch_graph":"https://pith.science/api/pith-number/MHK5AEMKYZOQMMZD6T7PB6Q6KY/graph.json","fetch_events":"https://pith.science/api/pith-number/MHK5AEMKYZOQMMZD6T7PB6Q6KY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MHK5AEMKYZOQMMZD6T7PB6Q6KY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MHK5AEMKYZOQMMZD6T7PB6Q6KY/action/storage_attestation","attest_author":"https://pith.science/pith/MHK5AEMKYZOQMMZD6T7PB6Q6KY/action/author_attestation","sign_citation":"https://pith.science/pith/MHK5AEMKYZOQMMZD6T7PB6Q6KY/action/citation_signature","submit_replication":"https://pith.science/pith/MHK5AEMKYZOQMMZD6T7PB6Q6KY/action/replication_record"}},"created_at":"2026-05-18T02:29:25.620435+00:00","updated_at":"2026-05-18T02:29:25.620435+00:00"}