{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:TMRXAH7HO5BIHQG5DLLZ67JWHW","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":"6ac7fb25f493ec6413de35b55aa642c09fb56855330dce14c21e8948ad374f97","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2000-04-04T16:43:36Z","title_canon_sha256":"79320a28bab431d4fcbfce6484c5275b9fd7b6f76edd15aefab4203c1ca17437"},"schema_version":"1.0","source":{"id":"math/0004017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0004017","created_at":"2026-07-04T14:34:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0004017v1","created_at":"2026-07-04T14:34:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0004017","created_at":"2026-07-04T14:34:26Z"},{"alias_kind":"pith_short_12","alias_value":"TMRXAH7HO5BI","created_at":"2026-07-04T14:34:26Z"},{"alias_kind":"pith_short_16","alias_value":"TMRXAH7HO5BIHQG5","created_at":"2026-07-04T14:34:26Z"},{"alias_kind":"pith_short_8","alias_value":"TMRXAH7H","created_at":"2026-07-04T14:34:26Z"}],"graph_snapshots":[{"event_id":"sha256:40e91ec88976739fe0f9648b466a11dc1a089b366af80051cf1b463c63c5543e","target":"graph","created_at":"2026-07-04T14:34:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0004017/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The main goal of this paper is to study varieties with the best possible Mori theoretic properties (measured by the existence of a certain decomposition of the cone of effective divisors). We call such a variety a Mori Dream Space. There turn out to be many examples, including quasi-smooth projective toric (or more generally, spherical) varieties, many GIT quotients, and log Fano 3-folds. We characterize Mori dream spaces as GIT quotients of affine varieties by a torus in a manner generalizing Cox's construction of toric varieties as quotients of affine space. Via the quotient description, the","authors_text":"Sean Keel, Yi Hu","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2000-04-04T16:43:36Z","title":"Mori Dream Spaces and GIT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0004017","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":"sha256:6cbfd92be433e0f9911f1818f0ec85bb084e66c1b9223519b017ce76fd56be3e","target":"record","created_at":"2026-07-04T14:34:26Z","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":"6ac7fb25f493ec6413de35b55aa642c09fb56855330dce14c21e8948ad374f97","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2000-04-04T16:43:36Z","title_canon_sha256":"79320a28bab431d4fcbfce6484c5275b9fd7b6f76edd15aefab4203c1ca17437"},"schema_version":"1.0","source":{"id":"math/0004017","kind":"arxiv","version":1}},"canonical_sha256":"9b23701fe7774283c0dd1ad79f7d363db711ed334cb14cd6ddc095689ca322c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b23701fe7774283c0dd1ad79f7d363db711ed334cb14cd6ddc095689ca322c5","first_computed_at":"2026-07-04T14:34:26.876332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:34:26.876332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0kgmzmMI4C83D3P21SqxkvI2luFJ4GLB4HrxQcntiv+IJk0OFepoEiGwb4YB1yxP058ThE5iyq52HYGLNvTuCg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:34:26.876694Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0004017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cbfd92be433e0f9911f1818f0ec85bb084e66c1b9223519b017ce76fd56be3e","sha256:40e91ec88976739fe0f9648b466a11dc1a089b366af80051cf1b463c63c5543e"],"state_sha256":"70f997fc75f8e89a3ab77563cec6228ec8f873589033b2aecc6ffd9613738be3"}