{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XGFOD57FZ2OVT4YSRQGLNVCH77","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":"ec6e68162c3fb6ee6616c657d2834722190e3e8ec8f8201b7696d3538ddf4f75","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-27T20:52:11Z","title_canon_sha256":"286b8b384447e1097ee81e9a643e311499af0bf1028310ecf14c723292fc69e0"},"schema_version":"1.0","source":{"id":"2605.29094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29094","created_at":"2026-05-29T01:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29094v1","created_at":"2026-05-29T01:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29094","created_at":"2026-05-29T01:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"XGFOD57FZ2OV","created_at":"2026-05-29T01:05:17Z"},{"alias_kind":"pith_short_16","alias_value":"XGFOD57FZ2OVT4YS","created_at":"2026-05-29T01:05:17Z"},{"alias_kind":"pith_short_8","alias_value":"XGFOD57F","created_at":"2026-05-29T01:05:17Z"}],"graph_snapshots":[{"event_id":"sha256:7343f94fadbccbe701f511f103ef4778c190bbeb5f858a80e002e2d35781b37d","target":"graph","created_at":"2026-05-29T01:05:17Z","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/2605.29094/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In our previous papers we repeatedly emphasized the special role in Quaternionic Analysis of the conformal group SU(2,2) and other real forms of its complexification SL(4,C). In particular, the natural product map of the left and right regular functions into a larger representation that contains the doubly regular functions as a subquotient is an intertwining operator. In this paper we show, however, that the spaces of regular and doubly regular functions do not \"interact\" - there is no invariant trilinear form on the tensor product of these representations.\n  To construct a natural invariant ","authors_text":"Igor Frenkel, Matvei Libine","cross_cats":["math-ph","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-27T20:52:11Z","title":"Reduction of Symmetry in Quaternionic Analysis and Invariant Trilinear Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29094","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":"sha256:2bb2d4eeece56166e11fc749c314ecec276cae34e25e5286d81b7d52a9cd9d34","target":"record","created_at":"2026-05-29T01:05:17Z","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":"ec6e68162c3fb6ee6616c657d2834722190e3e8ec8f8201b7696d3538ddf4f75","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-27T20:52:11Z","title_canon_sha256":"286b8b384447e1097ee81e9a643e311499af0bf1028310ecf14c723292fc69e0"},"schema_version":"1.0","source":{"id":"2605.29094","kind":"arxiv","version":1}},"canonical_sha256":"b98ae1f7e5ce9d59f3128c0cb6d447ffd28cec9623ab1794b8c507be47ca95e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b98ae1f7e5ce9d59f3128c0cb6d447ffd28cec9623ab1794b8c507be47ca95e2","first_computed_at":"2026-05-29T01:05:17.924864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:05:17.924864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kifrwH28AelBZ1u7SMIPKsTxb5MHoxOK1gwmfQQwAQI1EsXI0n35x2YQJv2m/AqkJCdoEgK6FHWShicYq7M/Ag==","signature_status":"signed_v1","signed_at":"2026-05-29T01:05:17.925702Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.29094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bb2d4eeece56166e11fc749c314ecec276cae34e25e5286d81b7d52a9cd9d34","sha256:7343f94fadbccbe701f511f103ef4778c190bbeb5f858a80e002e2d35781b37d"],"state_sha256":"2a5b2b300fe19ffff3b3b58a0fdad71f5b8a7d2cebe13df228a943e7966fe937"}