{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GPX2KCBXRTZ5E5ED6OQM2LOV7N","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":"2003149a029cb3f3ae3532a6b0b3376553eeb2edad3afb1eb58a78a9514352f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-21T05:43:26Z","title_canon_sha256":"bf781754551d9ed3c1e0b4a2d401db5de11989095741e6c5e9c7847fa20d8487"},"schema_version":"1.0","source":{"id":"1709.07163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.07163","created_at":"2026-05-18T00:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1709.07163v1","created_at":"2026-05-18T00:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07163","created_at":"2026-05-18T00:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"GPX2KCBXRTZ5","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GPX2KCBXRTZ5E5ED","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GPX2KCBX","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:7b2e1f7da567b841bd2fd4bcfaa91c0ecf1524c5a958b431b0c86878bef4fe90","target":"graph","created_at":"2026-05-18T00:34:36Z","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":"We study the algebra of invariant differential operators on a certain homogeneous vector bundle over a Riemannian symmetric space of type $A_2$. We computed radial parts of its generators explicitly to obtain matrix-valued commuting differential operators with $A_2$ symmetry. Moreover, we generalize the commuting differential operators with respect to a parameter and the potential function.","authors_text":"Nobukazu shimeno","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-21T05:43:26Z","title":"Matrix valued commuting differential operators with $A_2$ symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07163","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":"sha256:13d65754797222aa1bf55fd9ae505795631f770df492ac5535afbff78a774c6c","target":"record","created_at":"2026-05-18T00:34:36Z","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":"2003149a029cb3f3ae3532a6b0b3376553eeb2edad3afb1eb58a78a9514352f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-21T05:43:26Z","title_canon_sha256":"bf781754551d9ed3c1e0b4a2d401db5de11989095741e6c5e9c7847fa20d8487"},"schema_version":"1.0","source":{"id":"1709.07163","kind":"arxiv","version":1}},"canonical_sha256":"33efa508378cf3d27483f3a0cd2dd5fb7b75ffb8adee12d3a21cbd930ace4995","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33efa508378cf3d27483f3a0cd2dd5fb7b75ffb8adee12d3a21cbd930ace4995","first_computed_at":"2026-05-18T00:34:36.421071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:36.421071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c9gPm5qTQ2xf64jeJ3Gk7hA4swtqf0L3C6RrZWikwFoOtTov2q2Hw/gDSa7OKilvywrW4mP/mKlyjXig/cBrBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:36.421465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.07163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13d65754797222aa1bf55fd9ae505795631f770df492ac5535afbff78a774c6c","sha256:7b2e1f7da567b841bd2fd4bcfaa91c0ecf1524c5a958b431b0c86878bef4fe90"],"state_sha256":"23a452fff81c3f9ed2a7ca8487eaaf00baa43900338b58448f9d9eadaf943673"}