{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:62RL6MM6Y4I4QBSCDBNO5T2DDD","short_pith_number":"pith:62RL6MM6","canonical_record":{"source":{"id":"1903.05548","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-13T15:41:44Z","cross_cats_sorted":[],"title_canon_sha256":"f67819494b8f43061cd688d3ab784db7b0d78bf2c2eacc40339c514a403b48d5","abstract_canon_sha256":"319390754e287437a5518076ac013d4869bad9da4046008573185499a6a1f551"},"schema_version":"1.0"},"canonical_sha256":"f6a2bf319ec711c80642185aeecf4318f1e252ec3877aa504efb405513471d0c","source":{"kind":"arxiv","id":"1903.05548","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05548","created_at":"2026-05-17T23:50:04Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05548v2","created_at":"2026-05-17T23:50:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05548","created_at":"2026-05-17T23:50:04Z"},{"alias_kind":"pith_short_12","alias_value":"62RL6MM6Y4I4","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"62RL6MM6Y4I4QBSC","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"62RL6MM6","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:62RL6MM6Y4I4QBSCDBNO5T2DDD","target":"record","payload":{"canonical_record":{"source":{"id":"1903.05548","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-13T15:41:44Z","cross_cats_sorted":[],"title_canon_sha256":"f67819494b8f43061cd688d3ab784db7b0d78bf2c2eacc40339c514a403b48d5","abstract_canon_sha256":"319390754e287437a5518076ac013d4869bad9da4046008573185499a6a1f551"},"schema_version":"1.0"},"canonical_sha256":"f6a2bf319ec711c80642185aeecf4318f1e252ec3877aa504efb405513471d0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:04.423353Z","signature_b64":"yHsX+TnNMuDjTEhHfNDE4JsL30id6DF/0BVMOUhtBFrptLD8qk+IBo5QaT3183oUH+9qia2OcCq0OIPc0RvdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6a2bf319ec711c80642185aeecf4318f1e252ec3877aa504efb405513471d0c","last_reissued_at":"2026-05-17T23:50:04.422806Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:04.422806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.05548","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":"2026-05-17T23:50:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p9RvKB6FKVi7+rqEOD5BNgCycIWRDQYptt7eFn5kFLs12Iw7xs2dPBGB9sdQpE7oVRY4GyymFMWCagE38Ce2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:38:11.016041Z"},"content_sha256":"fe3b6ce054f5535d740b4a10463939fbd1820b056d059e29bbf3b8c5767c3808","schema_version":"1.0","event_id":"sha256:fe3b6ce054f5535d740b4a10463939fbd1820b056d059e29bbf3b8c5767c3808"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:62RL6MM6Y4I4QBSCDBNO5T2DDD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schubert polynomials as projections of Minkowski sums of Gelfand-Tsetlin polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Avery St. Dizier, Karola M\\'esz\\'aros, Ricky Ini Liu","submitted_at":"2019-03-13T15:41:44Z","abstract_excerpt":"Gelfand-Tsetlin polytopes are classical objects in algebraic combinatorics arising in the representation theory of $\\mathfrak{gl}_n(\\mathbb{C})$. The integer point transform of the Gelfand-Tsetlin polytope $\\mathrm{GT}(\\lambda)$ projects to the Schur function $s_{\\lambda}$. Schur functions form a distinguished basis of the ring of symmetric functions; they are also special cases of Schubert polynomials $\\mathfrak{S}_{w}$ corresponding to Grassmannian permutations.\n  For any permutation $w \\in S_n$ with column-convex Rothe diagram, we construct a polytope $\\mathcal{P}_{w}$ whose integer point t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05548","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":"2026-05-17T23:50:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N+kRxL+HGitk/t+YBCK/rkshz3DfTuej7GyU5If1RgsI50kywVLTyOBgvWrxLbJZw9zgpCOWj1+1fJfJTe3ZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:38:11.016779Z"},"content_sha256":"ef02eaca00fe2d22392cf0a1c5a47c598d93aa6ba363e98be6a2a99453819154","schema_version":"1.0","event_id":"sha256:ef02eaca00fe2d22392cf0a1c5a47c598d93aa6ba363e98be6a2a99453819154"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/62RL6MM6Y4I4QBSCDBNO5T2DDD/bundle.json","state_url":"https://pith.science/pith/62RL6MM6Y4I4QBSCDBNO5T2DDD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/62RL6MM6Y4I4QBSCDBNO5T2DDD/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":"2026-05-25T16:38:11Z","links":{"resolver":"https://pith.science/pith/62RL6MM6Y4I4QBSCDBNO5T2DDD","bundle":"https://pith.science/pith/62RL6MM6Y4I4QBSCDBNO5T2DDD/bundle.json","state":"https://pith.science/pith/62RL6MM6Y4I4QBSCDBNO5T2DDD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/62RL6MM6Y4I4QBSCDBNO5T2DDD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:62RL6MM6Y4I4QBSCDBNO5T2DDD","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":"319390754e287437a5518076ac013d4869bad9da4046008573185499a6a1f551","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-13T15:41:44Z","title_canon_sha256":"f67819494b8f43061cd688d3ab784db7b0d78bf2c2eacc40339c514a403b48d5"},"schema_version":"1.0","source":{"id":"1903.05548","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05548","created_at":"2026-05-17T23:50:04Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05548v2","created_at":"2026-05-17T23:50:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05548","created_at":"2026-05-17T23:50:04Z"},{"alias_kind":"pith_short_12","alias_value":"62RL6MM6Y4I4","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"62RL6MM6Y4I4QBSC","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"62RL6MM6","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:ef02eaca00fe2d22392cf0a1c5a47c598d93aa6ba363e98be6a2a99453819154","target":"graph","created_at":"2026-05-17T23:50:04Z","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":"Gelfand-Tsetlin polytopes are classical objects in algebraic combinatorics arising in the representation theory of $\\mathfrak{gl}_n(\\mathbb{C})$. The integer point transform of the Gelfand-Tsetlin polytope $\\mathrm{GT}(\\lambda)$ projects to the Schur function $s_{\\lambda}$. Schur functions form a distinguished basis of the ring of symmetric functions; they are also special cases of Schubert polynomials $\\mathfrak{S}_{w}$ corresponding to Grassmannian permutations.\n  For any permutation $w \\in S_n$ with column-convex Rothe diagram, we construct a polytope $\\mathcal{P}_{w}$ whose integer point t","authors_text":"Avery St. Dizier, Karola M\\'esz\\'aros, Ricky Ini Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-13T15:41:44Z","title":"Schubert polynomials as projections of Minkowski sums of Gelfand-Tsetlin polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05548","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:fe3b6ce054f5535d740b4a10463939fbd1820b056d059e29bbf3b8c5767c3808","target":"record","created_at":"2026-05-17T23:50:04Z","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":"319390754e287437a5518076ac013d4869bad9da4046008573185499a6a1f551","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-13T15:41:44Z","title_canon_sha256":"f67819494b8f43061cd688d3ab784db7b0d78bf2c2eacc40339c514a403b48d5"},"schema_version":"1.0","source":{"id":"1903.05548","kind":"arxiv","version":2}},"canonical_sha256":"f6a2bf319ec711c80642185aeecf4318f1e252ec3877aa504efb405513471d0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6a2bf319ec711c80642185aeecf4318f1e252ec3877aa504efb405513471d0c","first_computed_at":"2026-05-17T23:50:04.422806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:04.422806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yHsX+TnNMuDjTEhHfNDE4JsL30id6DF/0BVMOUhtBFrptLD8qk+IBo5QaT3183oUH+9qia2OcCq0OIPc0RvdCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:04.423353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.05548","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe3b6ce054f5535d740b4a10463939fbd1820b056d059e29bbf3b8c5767c3808","sha256:ef02eaca00fe2d22392cf0a1c5a47c598d93aa6ba363e98be6a2a99453819154"],"state_sha256":"885be02014c06a8926374c9d1c04c2707f8ed631a162bd8ad282f7e17eb61a6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pXF8wbDIf1JVPAZYR2B0cA1ksy69ie+u9JWMJYhXXtATK/15igiCa5DMsawqCPejTlMp19pYwcY2nYZFN29oDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:38:11.020479Z","bundle_sha256":"e6f785647f45c1f4cc7421282d62172e15c10e85879869bf9723894b758a93c7"}}