{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:D64KBDT2C73MVDPWWKL7377OJP","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":"440d1065002fa2c690fc86ed29693bc64ddd11fdf785ea4b19643f0136b5a501","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-30T09:27:37Z","title_canon_sha256":"be5eacaacfc900ddbd6996f76b25eb6e8df6d80b8e1044c1ac5bbbab2f9e5fc4"},"schema_version":"1.0","source":{"id":"2606.31398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.31398","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.31398v1","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31398","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"pith_short_12","alias_value":"D64KBDT2C73M","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"pith_short_16","alias_value":"D64KBDT2C73MVDPW","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"pith_short_8","alias_value":"D64KBDT2","created_at":"2026-07-01T01:18:01Z"}],"graph_snapshots":[{"event_id":"sha256:e940800d96741ad6e7efa7fad2e55f703c32d9d34c1672f22282d791b086947d","target":"graph","created_at":"2026-07-01T01:18:01Z","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/2606.31398/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the image of a regular unipotent element under any finite-dimensional irreducible polynomial representations of $\\mathrm{GL}_3(\\mathbb{C})$. This problem is equivalent to decomposing certain compositions of irreducible representations as $\\mathrm{SL}_2(\\mathbb{C})$-modules. We give an explicit decomposition of this finding, its Jordan decomposition.","authors_text":"Dibyendu Biswas","cross_cats":["math.CO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-30T09:27:37Z","title":"Image of Regular Unipotent under a Representation of $\\mathrm{GL}_3(\\mathbb{C})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31398","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:fa489266ca16c8af1ae3dc0bc8cdcdef0dde9c8d11455365b97f04b7e635dacb","target":"record","created_at":"2026-07-01T01:18:01Z","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":"440d1065002fa2c690fc86ed29693bc64ddd11fdf785ea4b19643f0136b5a501","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-30T09:27:37Z","title_canon_sha256":"be5eacaacfc900ddbd6996f76b25eb6e8df6d80b8e1044c1ac5bbbab2f9e5fc4"},"schema_version":"1.0","source":{"id":"2606.31398","kind":"arxiv","version":1}},"canonical_sha256":"1fb8a08e7a17f6ca8df6b297fdffee4bc6a0c3e90197b52e753e5fb3ca2641e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fb8a08e7a17f6ca8df6b297fdffee4bc6a0c3e90197b52e753e5fb3ca2641e5","first_computed_at":"2026-07-01T01:18:01.867700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:18:01.867700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HYifYdV4ONvFVMdKvARBoQMg8LZV740rCAPNgEORW8kRy7LURMbfd8mnRS9vApVo/eNGR2NoAkY/Hh+A++fBBw==","signature_status":"signed_v1","signed_at":"2026-07-01T01:18:01.868098Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.31398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa489266ca16c8af1ae3dc0bc8cdcdef0dde9c8d11455365b97f04b7e635dacb","sha256:e940800d96741ad6e7efa7fad2e55f703c32d9d34c1672f22282d791b086947d"],"state_sha256":"ca68c566729af043604eeaf55207c52c9f72f1b719de77a1ae65f599d577f64f"}