{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:FLYASJAFGMW6ZYZJEAHXTOH3ZP","short_pith_number":"pith:FLYASJAF","schema_version":"1.0","canonical_sha256":"2af0092405332dece329200f79b8fbcbfd6eae2cd01a3bb545be0681d7180287","source":{"kind":"arxiv","id":"1409.1857","version":2},"attestation_state":"computed","paper":{"title":"Global Okounkov bodies for Bott-Samelson varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"David Schmitz, Henrik Sepp\\\"anen","submitted_at":"2014-09-05T16:13:24Z","abstract_excerpt":"We use the theory of Mori dream spaces to prove that the global Okounkov body of a Bott-Samelson variety with respect to a natural flag of subvarieties is rational polyhedral. In fact, we prove more generally that this holds for any Mori dream space which admits a flag of Mori dream spaces satisfying a certain regularity condition. As a corollary, Okounkov bodies of effective line bundles over Schubert varieties are shown to be rational polyhedral. In particular, it follows that the global Okounkov body of a flag variety $G/B$ is rational polyhedral.\n  As an application we show that the asympt"},"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":"1409.1857","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-05T16:13:24Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"cbe2b251f463f78c9164cce4175a239298ad781a98aa2c3f89e06cd9a2858eaa","abstract_canon_sha256":"898b59b875d5ee181f1c0e9afddad5379098b4f748b400537efff5991d74893b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:10.132664Z","signature_b64":"WHMrKB9dwU0NwpU3L2b98+2WpKtelRgqtYzhR13K1Lx3ANpeZskQDDUPd4mFWvqwWdW1fGnBgJgn8e+Yga7aCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2af0092405332dece329200f79b8fbcbfd6eae2cd01a3bb545be0681d7180287","last_reissued_at":"2026-05-18T02:20:10.132116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:10.132116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Okounkov bodies for Bott-Samelson varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"David Schmitz, Henrik Sepp\\\"anen","submitted_at":"2014-09-05T16:13:24Z","abstract_excerpt":"We use the theory of Mori dream spaces to prove that the global Okounkov body of a Bott-Samelson variety with respect to a natural flag of subvarieties is rational polyhedral. In fact, we prove more generally that this holds for any Mori dream space which admits a flag of Mori dream spaces satisfying a certain regularity condition. As a corollary, Okounkov bodies of effective line bundles over Schubert varieties are shown to be rational polyhedral. In particular, it follows that the global Okounkov body of a flag variety $G/B$ is rational polyhedral.\n  As an application we show that the asympt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1857","kind":"arxiv","version":2},"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":"1409.1857","created_at":"2026-05-18T02:20:10.132201+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1857v2","created_at":"2026-05-18T02:20:10.132201+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1857","created_at":"2026-05-18T02:20:10.132201+00:00"},{"alias_kind":"pith_short_12","alias_value":"FLYASJAFGMW6","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FLYASJAFGMW6ZYZJ","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FLYASJAF","created_at":"2026-05-18T12:28:28.263976+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/FLYASJAFGMW6ZYZJEAHXTOH3ZP","json":"https://pith.science/pith/FLYASJAFGMW6ZYZJEAHXTOH3ZP.json","graph_json":"https://pith.science/api/pith-number/FLYASJAFGMW6ZYZJEAHXTOH3ZP/graph.json","events_json":"https://pith.science/api/pith-number/FLYASJAFGMW6ZYZJEAHXTOH3ZP/events.json","paper":"https://pith.science/paper/FLYASJAF"},"agent_actions":{"view_html":"https://pith.science/pith/FLYASJAFGMW6ZYZJEAHXTOH3ZP","download_json":"https://pith.science/pith/FLYASJAFGMW6ZYZJEAHXTOH3ZP.json","view_paper":"https://pith.science/paper/FLYASJAF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1857&json=true","fetch_graph":"https://pith.science/api/pith-number/FLYASJAFGMW6ZYZJEAHXTOH3ZP/graph.json","fetch_events":"https://pith.science/api/pith-number/FLYASJAFGMW6ZYZJEAHXTOH3ZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FLYASJAFGMW6ZYZJEAHXTOH3ZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FLYASJAFGMW6ZYZJEAHXTOH3ZP/action/storage_attestation","attest_author":"https://pith.science/pith/FLYASJAFGMW6ZYZJEAHXTOH3ZP/action/author_attestation","sign_citation":"https://pith.science/pith/FLYASJAFGMW6ZYZJEAHXTOH3ZP/action/citation_signature","submit_replication":"https://pith.science/pith/FLYASJAFGMW6ZYZJEAHXTOH3ZP/action/replication_record"}},"created_at":"2026-05-18T02:20:10.132201+00:00","updated_at":"2026-05-18T02:20:10.132201+00:00"}