{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DMKA2D3GRXHDULJUAQWMXF32UO","short_pith_number":"pith:DMKA2D3G","schema_version":"1.0","canonical_sha256":"1b140d0f668dce3a2d34042ccb977aa3aaaaf438082e556cac9a3d9749eedcc0","source":{"kind":"arxiv","id":"1407.2629","version":4},"attestation_state":"computed","paper":{"title":"Torification of diagonalizable group actions on toroidal schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Abramovich, Michael Temkin","submitted_at":"2014-07-09T20:30:23Z","abstract_excerpt":"We study actions of diagonalizable groups on toroidal schemes (i.e. logarithmically regular logarithmic schemes). In particular, we show that for so-called toroidal actions the quotient is again a toroidal scheme. Our main result constructs for an arbitrary action a canonical torification - making the action toridal after an equivariant blowings up. This extends earlier results of Abramovich-de Jong, Abramovich-Karu-Matsuki-W{\\l}odarczyk, and Gabber in various aspects."},"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":"1407.2629","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-09T20:30:23Z","cross_cats_sorted":[],"title_canon_sha256":"b6dafb56eb21496bff97960a8c7984df95d81d7868a9d5cdff93352368933a13","abstract_canon_sha256":"1596b15dc31526d004ffc75f7b952c12dc94488aebec418be14ad8bbbf17b591"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:55.384795Z","signature_b64":"uTI7dhg5siLccIZ3mbEOJAX9ul1Bs+EyJ4QKbnNXIOJ22HD0GF2efrbA5RYjJFJKYnKtQ9U4gyvg206uP6TSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b140d0f668dce3a2d34042ccb977aa3aaaaf438082e556cac9a3d9749eedcc0","last_reissued_at":"2026-05-18T01:11:55.384467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:55.384467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Torification of diagonalizable group actions on toroidal schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Abramovich, Michael Temkin","submitted_at":"2014-07-09T20:30:23Z","abstract_excerpt":"We study actions of diagonalizable groups on toroidal schemes (i.e. logarithmically regular logarithmic schemes). In particular, we show that for so-called toroidal actions the quotient is again a toroidal scheme. Our main result constructs for an arbitrary action a canonical torification - making the action toridal after an equivariant blowings up. This extends earlier results of Abramovich-de Jong, Abramovich-Karu-Matsuki-W{\\l}odarczyk, and Gabber in various aspects."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2629","kind":"arxiv","version":4},"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":"1407.2629","created_at":"2026-05-18T01:11:55.384522+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.2629v4","created_at":"2026-05-18T01:11:55.384522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2629","created_at":"2026-05-18T01:11:55.384522+00:00"},{"alias_kind":"pith_short_12","alias_value":"DMKA2D3GRXHD","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DMKA2D3GRXHDULJU","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DMKA2D3G","created_at":"2026-05-18T12:28:25.294606+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/DMKA2D3GRXHDULJUAQWMXF32UO","json":"https://pith.science/pith/DMKA2D3GRXHDULJUAQWMXF32UO.json","graph_json":"https://pith.science/api/pith-number/DMKA2D3GRXHDULJUAQWMXF32UO/graph.json","events_json":"https://pith.science/api/pith-number/DMKA2D3GRXHDULJUAQWMXF32UO/events.json","paper":"https://pith.science/paper/DMKA2D3G"},"agent_actions":{"view_html":"https://pith.science/pith/DMKA2D3GRXHDULJUAQWMXF32UO","download_json":"https://pith.science/pith/DMKA2D3GRXHDULJUAQWMXF32UO.json","view_paper":"https://pith.science/paper/DMKA2D3G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.2629&json=true","fetch_graph":"https://pith.science/api/pith-number/DMKA2D3GRXHDULJUAQWMXF32UO/graph.json","fetch_events":"https://pith.science/api/pith-number/DMKA2D3GRXHDULJUAQWMXF32UO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DMKA2D3GRXHDULJUAQWMXF32UO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DMKA2D3GRXHDULJUAQWMXF32UO/action/storage_attestation","attest_author":"https://pith.science/pith/DMKA2D3GRXHDULJUAQWMXF32UO/action/author_attestation","sign_citation":"https://pith.science/pith/DMKA2D3GRXHDULJUAQWMXF32UO/action/citation_signature","submit_replication":"https://pith.science/pith/DMKA2D3GRXHDULJUAQWMXF32UO/action/replication_record"}},"created_at":"2026-05-18T01:11:55.384522+00:00","updated_at":"2026-05-18T01:11:55.384522+00:00"}