{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RZ4NB4KYR2JJRDKBV6SKXK7VLI","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":"fa9cc08f8c4c57429a95c1769d82a5fee19cd893326eecc268068ce22b3bb01f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-06-16T08:55:06Z","title_canon_sha256":"147573a55a9251d5c48182569ab4d155eb231fd15db437f9797cddb09ea6af81"},"schema_version":"1.0","source":{"id":"1206.3647","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3647","created_at":"2026-05-18T02:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3647v4","created_at":"2026-05-18T02:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3647","created_at":"2026-05-18T02:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"RZ4NB4KYR2JJ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RZ4NB4KYR2JJRDKB","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RZ4NB4KY","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:9115d64c31ae4711b2a2c75ae05412dd8fe5e9b8699316bbbea0aca6a66ba33c","target":"graph","created_at":"2026-05-18T02:43:54Z","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 $U$ be either classical or quantized universal enveloping algebra of $\\s\\l(n+1)$ extended over the field of fractions of the Cartan subalgebra. We suggest a PBW basis in $U$ over the extended Cartan subalgebra diagonalizing the contravariant Shapovalov form on generic Verma module. The matrix coefficients of the form are calculated and the inverse of the form is explicitly constructed.","authors_text":"Andrey Mudrov","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-06-16T08:55:06Z","title":"Orthogonal basis for the Shapovalov form on $A_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3647","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":"sha256:16793480fe75c750d62e3698994622dc33adc4bca4f475bb4593f600d31c1529","target":"record","created_at":"2026-05-18T02:43:54Z","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":"fa9cc08f8c4c57429a95c1769d82a5fee19cd893326eecc268068ce22b3bb01f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-06-16T08:55:06Z","title_canon_sha256":"147573a55a9251d5c48182569ab4d155eb231fd15db437f9797cddb09ea6af81"},"schema_version":"1.0","source":{"id":"1206.3647","kind":"arxiv","version":4}},"canonical_sha256":"8e78d0f1588e92988d41afa4ababf55a34882c7e46eb5ae20ce3d70af31b31d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e78d0f1588e92988d41afa4ababf55a34882c7e46eb5ae20ce3d70af31b31d1","first_computed_at":"2026-05-18T02:43:54.522565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:54.522565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GBpEx3gVfbu80aoQmreRhil3stKivHHmvvr5Z4Was+W8VfAoL3c4HASe0BgVwltctZU4JS6LJ4TzdWIykTRQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:54.523074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3647","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16793480fe75c750d62e3698994622dc33adc4bca4f475bb4593f600d31c1529","sha256:9115d64c31ae4711b2a2c75ae05412dd8fe5e9b8699316bbbea0aca6a66ba33c"],"state_sha256":"2e4470c43e4b13554df822c9884ce0631b8a305775ee295dec7b141249024818"}