{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FO5TUFOXCHOQUH73URUXIQJGTA","short_pith_number":"pith:FO5TUFOX","canonical_record":{"source":{"id":"1609.01166","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-05T13:58:19Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"04581409adfb470c37f72ecccb84a8025dae70eabefce31198a70a58f934f7d0","abstract_canon_sha256":"8a4725733c72674eafa0926709eb4374710f0e06fc35fe31589552a97feaacde"},"schema_version":"1.0"},"canonical_sha256":"2bbb3a15d711dd0a1ffba46974412698206f11f8c53e8102dd7816714ffcf057","source":{"kind":"arxiv","id":"1609.01166","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01166","created_at":"2026-05-18T01:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01166v1","created_at":"2026-05-18T01:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01166","created_at":"2026-05-18T01:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"FO5TUFOXCHOQ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FO5TUFOXCHOQUH73","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FO5TUFOX","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FO5TUFOXCHOQUH73URUXIQJGTA","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01166","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-05T13:58:19Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"04581409adfb470c37f72ecccb84a8025dae70eabefce31198a70a58f934f7d0","abstract_canon_sha256":"8a4725733c72674eafa0926709eb4374710f0e06fc35fe31589552a97feaacde"},"schema_version":"1.0"},"canonical_sha256":"2bbb3a15d711dd0a1ffba46974412698206f11f8c53e8102dd7816714ffcf057","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:18.860981Z","signature_b64":"0vh0N/p3sAorWgCX4Mk9afFoXPncOin/RLS5E9KX5StAlxT3VfZMvgSya6rpBCnZ5A19/TgIgwYAyxOjwS67Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bbb3a15d711dd0a1ffba46974412698206f11f8c53e8102dd7816714ffcf057","last_reissued_at":"2026-05-18T01:06:18.860288Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:18.860288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01166","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zj7cGsp7LH2xY6d1RBjSbpsIGqMFzcB1oDs416kO/GNlaLbmuvvA+zziTGgyJY6MMdebynXzYO6cT6peF681Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:48:59.258780Z"},"content_sha256":"74312bb44fd44273a560a2a910feae7955aff7998ca54099b12be65201334202","schema_version":"1.0","event_id":"sha256:74312bb44fd44273a560a2a910feae7955aff7998ca54099b12be65201334202"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FO5TUFOXCHOQUH73URUXIQJGTA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On toric degenerations of flag varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.AG","authors_text":"Ghislain Fourier, Peter Littelmann, Xin Fang","submitted_at":"2016-09-05T13:58:19Z","abstract_excerpt":"Following the historical track in pursuing $T$-equivariant flat toric degenerations of flag varieties and spherical varieties, we explain how powerful tools in algebraic geometry and representation theory, such as canonical bases, Newton-Okounkov bodies, PBW-filtrations and cluster algebras come to push the subject forward."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01166","kind":"arxiv","version":1},"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":"2026-05-18T01:06:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RwT/ZVDa2br0GwRs91YYyooQ2OtNq3YYxc1cx38Ar3wdeYBfMqbcmTmzFq3MMRQdv+73TYhH09hmXTYQskyBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:48:59.259123Z"},"content_sha256":"f68971144734229cbc7250bbfc5de64e77d1cedb29dbbd3a7a91239fa1386115","schema_version":"1.0","event_id":"sha256:f68971144734229cbc7250bbfc5de64e77d1cedb29dbbd3a7a91239fa1386115"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FO5TUFOXCHOQUH73URUXIQJGTA/bundle.json","state_url":"https://pith.science/pith/FO5TUFOXCHOQUH73URUXIQJGTA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FO5TUFOXCHOQUH73URUXIQJGTA/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":"2026-06-03T20:48:59Z","links":{"resolver":"https://pith.science/pith/FO5TUFOXCHOQUH73URUXIQJGTA","bundle":"https://pith.science/pith/FO5TUFOXCHOQUH73URUXIQJGTA/bundle.json","state":"https://pith.science/pith/FO5TUFOXCHOQUH73URUXIQJGTA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FO5TUFOXCHOQUH73URUXIQJGTA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FO5TUFOXCHOQUH73URUXIQJGTA","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":"8a4725733c72674eafa0926709eb4374710f0e06fc35fe31589552a97feaacde","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-05T13:58:19Z","title_canon_sha256":"04581409adfb470c37f72ecccb84a8025dae70eabefce31198a70a58f934f7d0"},"schema_version":"1.0","source":{"id":"1609.01166","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01166","created_at":"2026-05-18T01:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01166v1","created_at":"2026-05-18T01:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01166","created_at":"2026-05-18T01:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"FO5TUFOXCHOQ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FO5TUFOXCHOQUH73","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FO5TUFOX","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:f68971144734229cbc7250bbfc5de64e77d1cedb29dbbd3a7a91239fa1386115","target":"graph","created_at":"2026-05-18T01:06:18Z","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":"Following the historical track in pursuing $T$-equivariant flat toric degenerations of flag varieties and spherical varieties, we explain how powerful tools in algebraic geometry and representation theory, such as canonical bases, Newton-Okounkov bodies, PBW-filtrations and cluster algebras come to push the subject forward.","authors_text":"Ghislain Fourier, Peter Littelmann, Xin Fang","cross_cats":["math.CO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-05T13:58:19Z","title":"On toric degenerations of flag varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01166","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":"sha256:74312bb44fd44273a560a2a910feae7955aff7998ca54099b12be65201334202","target":"record","created_at":"2026-05-18T01:06:18Z","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":"8a4725733c72674eafa0926709eb4374710f0e06fc35fe31589552a97feaacde","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-05T13:58:19Z","title_canon_sha256":"04581409adfb470c37f72ecccb84a8025dae70eabefce31198a70a58f934f7d0"},"schema_version":"1.0","source":{"id":"1609.01166","kind":"arxiv","version":1}},"canonical_sha256":"2bbb3a15d711dd0a1ffba46974412698206f11f8c53e8102dd7816714ffcf057","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bbb3a15d711dd0a1ffba46974412698206f11f8c53e8102dd7816714ffcf057","first_computed_at":"2026-05-18T01:06:18.860288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:18.860288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0vh0N/p3sAorWgCX4Mk9afFoXPncOin/RLS5E9KX5StAlxT3VfZMvgSya6rpBCnZ5A19/TgIgwYAyxOjwS67Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:18.860981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01166","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74312bb44fd44273a560a2a910feae7955aff7998ca54099b12be65201334202","sha256:f68971144734229cbc7250bbfc5de64e77d1cedb29dbbd3a7a91239fa1386115"],"state_sha256":"d931b902edae4e758d2d30863c0b107d27664d5d30f700d53cdd96ea1245c12c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VtmZ2oV4jOuVGjw+GjeqqAb2uwmlXSN095/B02LffjqEAz5oY2ltaaOURxrK/kZFqhix925klIyW0bloW5kmBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:48:59.261032Z","bundle_sha256":"0e952af3a20283c6c5873ab70f163423131c3cfad8d534ea4f2dd1e35f1c6aee"}}