{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HKV7C4OIHNOXHYW5I2EQZ6EITR","short_pith_number":"pith:HKV7C4OI","canonical_record":{"source":{"id":"1101.1687","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-09T23:50:53Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"55e3eaa2d2677f400be08f861bf4765c88acb65a9a1d5d88905aa772e0a662e1","abstract_canon_sha256":"a5cffd3d5fb47f40feb2c714126216374011ec2475eac84cdd1e5695b14e1ad9"},"schema_version":"1.0"},"canonical_sha256":"3aabf171c83b5d73e2dd46890cf8889c7d59bbc728cda3513432d37057263c77","source":{"kind":"arxiv","id":"1101.1687","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1687","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1687v4","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1687","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"HKV7C4OIHNOX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HKV7C4OIHNOXHYW5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HKV7C4OI","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HKV7C4OIHNOXHYW5I2EQZ6EITR","target":"record","payload":{"canonical_record":{"source":{"id":"1101.1687","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-09T23:50:53Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"55e3eaa2d2677f400be08f861bf4765c88acb65a9a1d5d88905aa772e0a662e1","abstract_canon_sha256":"a5cffd3d5fb47f40feb2c714126216374011ec2475eac84cdd1e5695b14e1ad9"},"schema_version":"1.0"},"canonical_sha256":"3aabf171c83b5d73e2dd46890cf8889c7d59bbc728cda3513432d37057263c77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:06.423216Z","signature_b64":"7AffhZylRmC96/l/OWLQk+rY5AaPTzmHsRS+NhM/F7GJDumS4TP3pIzgDlP+p827b21TeSiFP6kdKrSGYPetBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3aabf171c83b5d73e2dd46890cf8889c7d59bbc728cda3513432d37057263c77","last_reissued_at":"2026-05-18T01:28:06.422614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:06.422614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.1687","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MUUnvdH62/EPUXI9IiCAL7St7Hf9k8WPtnvuTPaek7AU0aUx0SrXhpzEZ+YiMk8j9mX2BB+IIZhAmMzyE+0LCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:27:09.301655Z"},"content_sha256":"c3a44d76cc9584cc876f43e368109d3a70e622a419e4a474d27ad3a112b0541b","schema_version":"1.0","event_id":"sha256:c3a44d76cc9584cc876f43e368109d3a70e622a419e4a474d27ad3a112b0541b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HKV7C4OIHNOXHYW5I2EQZ6EITR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Crystal bases and Newton-Okounkov bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Kiumars Kaveh","submitted_at":"2011-01-09T23:50:53Z","abstract_excerpt":"Let G be a connected reductive algebraic group. We prove that the string parametrization of a crystal basis for a finite dimensional irreducible representation of G extends to a natural valuation on the field of rational functions on the flag variety G/B, which is a highest term valuation corresponding to a coordinate system on a Bott-Samelson variety. This shows that the string polytopes associated to irreducible representations, can be realized as Newton-Okounkov bodies for the flag variety. This is closely related to an earlier result of A. Okounkov for the Gelfand-Cetlin polytopes of the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1687","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6dneAg0J9xXH+dFnwZgP+gOS+DYQM9oTpMYeReUuimA8C+dbdC/dhScst9+MEKJOcIk4O212gPbX48J4UCblDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:27:09.302002Z"},"content_sha256":"9d62625405c0c1ddf0300f73abfbd5008e1b0dab4b1d0733ca990a3ff177b472","schema_version":"1.0","event_id":"sha256:9d62625405c0c1ddf0300f73abfbd5008e1b0dab4b1d0733ca990a3ff177b472"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKV7C4OIHNOXHYW5I2EQZ6EITR/bundle.json","state_url":"https://pith.science/pith/HKV7C4OIHNOXHYW5I2EQZ6EITR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKV7C4OIHNOXHYW5I2EQZ6EITR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T18:27:09Z","links":{"resolver":"https://pith.science/pith/HKV7C4OIHNOXHYW5I2EQZ6EITR","bundle":"https://pith.science/pith/HKV7C4OIHNOXHYW5I2EQZ6EITR/bundle.json","state":"https://pith.science/pith/HKV7C4OIHNOXHYW5I2EQZ6EITR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKV7C4OIHNOXHYW5I2EQZ6EITR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HKV7C4OIHNOXHYW5I2EQZ6EITR","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":"a5cffd3d5fb47f40feb2c714126216374011ec2475eac84cdd1e5695b14e1ad9","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-09T23:50:53Z","title_canon_sha256":"55e3eaa2d2677f400be08f861bf4765c88acb65a9a1d5d88905aa772e0a662e1"},"schema_version":"1.0","source":{"id":"1101.1687","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1687","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1687v4","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1687","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"HKV7C4OIHNOX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HKV7C4OIHNOXHYW5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HKV7C4OI","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:9d62625405c0c1ddf0300f73abfbd5008e1b0dab4b1d0733ca990a3ff177b472","target":"graph","created_at":"2026-05-18T01:28:06Z","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"},"paper":{"abstract_excerpt":"Let G be a connected reductive algebraic group. We prove that the string parametrization of a crystal basis for a finite dimensional irreducible representation of G extends to a natural valuation on the field of rational functions on the flag variety G/B, which is a highest term valuation corresponding to a coordinate system on a Bott-Samelson variety. This shows that the string polytopes associated to irreducible representations, can be realized as Newton-Okounkov bodies for the flag variety. This is closely related to an earlier result of A. Okounkov for the Gelfand-Cetlin polytopes of the s","authors_text":"Kiumars Kaveh","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-09T23:50:53Z","title":"Crystal bases and Newton-Okounkov bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1687","kind":"arxiv","version":4},"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:c3a44d76cc9584cc876f43e368109d3a70e622a419e4a474d27ad3a112b0541b","target":"record","created_at":"2026-05-18T01:28:06Z","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":"a5cffd3d5fb47f40feb2c714126216374011ec2475eac84cdd1e5695b14e1ad9","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-09T23:50:53Z","title_canon_sha256":"55e3eaa2d2677f400be08f861bf4765c88acb65a9a1d5d88905aa772e0a662e1"},"schema_version":"1.0","source":{"id":"1101.1687","kind":"arxiv","version":4}},"canonical_sha256":"3aabf171c83b5d73e2dd46890cf8889c7d59bbc728cda3513432d37057263c77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3aabf171c83b5d73e2dd46890cf8889c7d59bbc728cda3513432d37057263c77","first_computed_at":"2026-05-18T01:28:06.422614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:06.422614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7AffhZylRmC96/l/OWLQk+rY5AaPTzmHsRS+NhM/F7GJDumS4TP3pIzgDlP+p827b21TeSiFP6kdKrSGYPetBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:06.423216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1687","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3a44d76cc9584cc876f43e368109d3a70e622a419e4a474d27ad3a112b0541b","sha256:9d62625405c0c1ddf0300f73abfbd5008e1b0dab4b1d0733ca990a3ff177b472"],"state_sha256":"498736290be7d58e5f1736d3ed55f46dbefc06cc9bab5be58174ffd0f21f0902"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3B8QHAIA9SjNZTdyccp2gzAE0XVFBSjs4oIePLeosY5BnIuIad7GoYzr6bhZ9WBcRufLWi5/AZRMPw0rmps+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:27:09.303912Z","bundle_sha256":"de55d54dcc883463f293ce9e307c33978d940de150882ef27bd95e1940ce7c8d"}}