{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:SMYKMUSKDOE2YZTSEWIBR236G5","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":"6e71360c2d276f9707d3327f1de5fd178f55ac2c7268754504f137aae53e9425","cross_cats_sorted":["math-ph","math.AG","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2007-12-07T16:44:13Z","title_canon_sha256":"cc1cb7d3f0e6da2eab7f1c563da70cc6e1207192cf6902e7adbf83a2b63b54ab"},"schema_version":"1.0","source":{"id":"0712.1183","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1183","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1183v2","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1183","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"pith_short_12","alias_value":"SMYKMUSKDOE2","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"SMYKMUSKDOE2YZTS","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"SMYKMUSK","created_at":"2026-07-05T00:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:9ff14bf5dee0c0ce8f02514e108d20b4f185a20bf8ae00fc07a42bd7907f9426","target":"graph","created_at":"2026-07-05T00:26:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0712.1183/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras math.RT/0606380, math.QA/0612798. We prove that generically their action on finite-dimensional modules is diagonalizable and their joint spectra are in bijection with the set of monodromy-free opers for the Langlands dual group of G on the projective line with regular singularity at one point and irregular singularity of order two at another point. We also prove a multi-point generalization of this result, describing the spectra of commutin","authors_text":"Boris Feigin, Edward Frenkel, Leonid Rybnikov","cross_cats":["math-ph","math.AG","math.MP"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2007-12-07T16:44:13Z","title":"Opers with irregular singularity and spectra of the shift of argument subalgebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1183","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:cd524c1e5c4b236a3bf187bac811d12c321e0cd5d6b8ee47dda101dc49a002aa","target":"record","created_at":"2026-07-05T00:26:50Z","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":"6e71360c2d276f9707d3327f1de5fd178f55ac2c7268754504f137aae53e9425","cross_cats_sorted":["math-ph","math.AG","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2007-12-07T16:44:13Z","title_canon_sha256":"cc1cb7d3f0e6da2eab7f1c563da70cc6e1207192cf6902e7adbf83a2b63b54ab"},"schema_version":"1.0","source":{"id":"0712.1183","kind":"arxiv","version":2}},"canonical_sha256":"9330a6524a1b89ac6672259018eb7e37512e6f11b85fac293d9a4785b01189b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9330a6524a1b89ac6672259018eb7e37512e6f11b85fac293d9a4785b01189b3","first_computed_at":"2026-07-05T00:26:50.234888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:26:50.234888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ROEWeuLtX0qQrfIb3THWilVRKFviQ/j5M4d1UQika1TPzStQnDm6FoxObhUs8lFrxLp05OZMSeG9XDaWIfFdCA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:26:50.235350Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.1183","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd524c1e5c4b236a3bf187bac811d12c321e0cd5d6b8ee47dda101dc49a002aa","sha256:9ff14bf5dee0c0ce8f02514e108d20b4f185a20bf8ae00fc07a42bd7907f9426"],"state_sha256":"5ec60aad09dc8b8e41f7e463d74115b760c3acc62f6b5bcced781f2e1b9d34af"}