{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6T352L4IGLDSZO5DMMX44OAWYV","short_pith_number":"pith:6T352L4I","canonical_record":{"source":{"id":"1610.08783","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-27T14:00:44Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"6989973e7cfcd27cc405064cfd27966acecc8016e217bf4d112dfdd32592aebe","abstract_canon_sha256":"9b7269a8109b4680948a044410aa9ff61c1e899d798234becdba5f6255896d41"},"schema_version":"1.0"},"canonical_sha256":"f4f7dd2f8832c72cbba3632fce3816c54adc20304ac3ee0e0075e1264ce99b2a","source":{"kind":"arxiv","id":"1610.08783","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08783","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08783v2","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08783","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"6T352L4IGLDS","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6T352L4IGLDSZO5D","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6T352L4I","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6T352L4IGLDSZO5DMMX44OAWYV","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08783","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-27T14:00:44Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"6989973e7cfcd27cc405064cfd27966acecc8016e217bf4d112dfdd32592aebe","abstract_canon_sha256":"9b7269a8109b4680948a044410aa9ff61c1e899d798234becdba5f6255896d41"},"schema_version":"1.0"},"canonical_sha256":"f4f7dd2f8832c72cbba3632fce3816c54adc20304ac3ee0e0075e1264ce99b2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:47.240737Z","signature_b64":"aixqDJzluCEoQm5xoIcxyNP1I+LQS2qDQwtXhKA4G45/8jsxJWtQ+hVbOVnWbcpQcXJR/4FI0PVcmF9KXfgaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4f7dd2f8832c72cbba3632fce3816c54adc20304ac3ee0e0075e1264ce99b2a","last_reissued_at":"2026-05-18T00:39:47.239983Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:47.239983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08783","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6LuZl5WHObcHgd/wN+e5D/zgEaBe9d6Q27hoxN4ZnziVSuGKzX79DV/TwYLcaqnA5H3eMTm6Ocd16HGQ4AgZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:28:43.541359Z"},"content_sha256":"98994f6d2073545346b0058aaf7d7d1b74e26b5df4cc8d8dfa02dd8689e90258","schema_version":"1.0","event_id":"sha256:98994f6d2073545346b0058aaf7d7d1b74e26b5df4cc8d8dfa02dd8689e90258"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6T352L4IGLDSZO5DMMX44OAWYV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A comparison of Newton-Okounkov polytopes of Schubert varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.AG","authors_text":"Hironori Oya, Naoki Fujita","submitted_at":"2016-10-27T14:00:44Z","abstract_excerpt":"A Newton-Okounkov body is a convex body constructed from a polarized variety with a valuation on its function field. Kaveh (resp., the first author and Naito) proved that the Newton-Okounkov body of a Schubert variety associated with a specific valuation is identical to the Littelmann string polytope (resp., the Nakashima-Zelevinsky polyhedral realization) of a Demazure crystal. These specific valuations are defined algebraically to be the highest term valuations with respect to certain local coordinate systems on a Bott-Samelson variety. Another class of valuations, which is geometrically nat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08783","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bXC09DOfTui/h3HsDec+DKtsklFfy/3xqAE74AYqF2HVUQ2p4qkNY6Xgr5r3Kv+27MSPDAXu0EJMNDfzb3M2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:28:43.541748Z"},"content_sha256":"c4330564eff09625d3314d7ad673af05370ecf5b70a87acd1b93e3baf3012c05","schema_version":"1.0","event_id":"sha256:c4330564eff09625d3314d7ad673af05370ecf5b70a87acd1b93e3baf3012c05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6T352L4IGLDSZO5DMMX44OAWYV/bundle.json","state_url":"https://pith.science/pith/6T352L4IGLDSZO5DMMX44OAWYV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6T352L4IGLDSZO5DMMX44OAWYV/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":"2026-07-01T08:28:43Z","links":{"resolver":"https://pith.science/pith/6T352L4IGLDSZO5DMMX44OAWYV","bundle":"https://pith.science/pith/6T352L4IGLDSZO5DMMX44OAWYV/bundle.json","state":"https://pith.science/pith/6T352L4IGLDSZO5DMMX44OAWYV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6T352L4IGLDSZO5DMMX44OAWYV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6T352L4IGLDSZO5DMMX44OAWYV","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":"9b7269a8109b4680948a044410aa9ff61c1e899d798234becdba5f6255896d41","cross_cats_sorted":["math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-27T14:00:44Z","title_canon_sha256":"6989973e7cfcd27cc405064cfd27966acecc8016e217bf4d112dfdd32592aebe"},"schema_version":"1.0","source":{"id":"1610.08783","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08783","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08783v2","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08783","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"6T352L4IGLDS","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6T352L4IGLDSZO5D","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6T352L4I","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:c4330564eff09625d3314d7ad673af05370ecf5b70a87acd1b93e3baf3012c05","target":"graph","created_at":"2026-05-18T00:39:47Z","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":"A Newton-Okounkov body is a convex body constructed from a polarized variety with a valuation on its function field. Kaveh (resp., the first author and Naito) proved that the Newton-Okounkov body of a Schubert variety associated with a specific valuation is identical to the Littelmann string polytope (resp., the Nakashima-Zelevinsky polyhedral realization) of a Demazure crystal. These specific valuations are defined algebraically to be the highest term valuations with respect to certain local coordinate systems on a Bott-Samelson variety. Another class of valuations, which is geometrically nat","authors_text":"Hironori Oya, Naoki Fujita","cross_cats":["math.QA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-27T14:00:44Z","title":"A comparison of Newton-Okounkov polytopes of Schubert varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08783","kind":"arxiv","version":2},"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":"sha256:98994f6d2073545346b0058aaf7d7d1b74e26b5df4cc8d8dfa02dd8689e90258","target":"record","created_at":"2026-05-18T00:39:47Z","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":"9b7269a8109b4680948a044410aa9ff61c1e899d798234becdba5f6255896d41","cross_cats_sorted":["math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-27T14:00:44Z","title_canon_sha256":"6989973e7cfcd27cc405064cfd27966acecc8016e217bf4d112dfdd32592aebe"},"schema_version":"1.0","source":{"id":"1610.08783","kind":"arxiv","version":2}},"canonical_sha256":"f4f7dd2f8832c72cbba3632fce3816c54adc20304ac3ee0e0075e1264ce99b2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4f7dd2f8832c72cbba3632fce3816c54adc20304ac3ee0e0075e1264ce99b2a","first_computed_at":"2026-05-18T00:39:47.239983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:47.239983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aixqDJzluCEoQm5xoIcxyNP1I+LQS2qDQwtXhKA4G45/8jsxJWtQ+hVbOVnWbcpQcXJR/4FI0PVcmF9KXfgaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:47.240737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08783","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98994f6d2073545346b0058aaf7d7d1b74e26b5df4cc8d8dfa02dd8689e90258","sha256:c4330564eff09625d3314d7ad673af05370ecf5b70a87acd1b93e3baf3012c05"],"state_sha256":"79756e19bd2751f699c85b6fdb0a9ff9feed3358a9af6107c1cab043e17bc5e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hxJiHL0ZhRVQTdPCCor/yR9zWyIM3tN0XKDfo78cH0d+7EcWPg9DZJmzW7JRZX8CpLR11gJ66bqomzjJgQm7Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T08:28:43.544063Z","bundle_sha256":"5f4629d8438d5196f6d1a98f1239642620447b2d4f18a6c3e791d64650720548"}}