{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U3PGSBHBGDLHRFTNTIQ3SCU7N7","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":"c187572b70494a070789e85d1c098eed098ad0d2b8bce2db0ce9c1b5bb26621f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-09T01:41:30Z","title_canon_sha256":"c51bb671b795ef77f823a6c6d0b9d39b57691329265d40c2deb3e2339a910805"},"schema_version":"1.0","source":{"id":"1803.03350","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03350","created_at":"2026-05-18T00:19:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03350v2","created_at":"2026-05-18T00:19:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03350","created_at":"2026-05-18T00:19:50Z"},{"alias_kind":"pith_short_12","alias_value":"U3PGSBHBGDLH","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U3PGSBHBGDLHRFTN","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U3PGSBHB","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:81829bd07b594b3a1cc92fe3e6adc7533d53897f93311dee0a25f334be7d64b4","target":"graph","created_at":"2026-05-18T00:19:50Z","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"},"paper":{"abstract_excerpt":"The Hermitian eigenvalue problem asks for the possible eigenvalues of a sum of Hermitian matrices given the eigenvalues of the summands. This is a problem about the Lie algebra of the maximal compact subgroup of $G=\\operatorname{SL}(n)$ . There is a polyhedral cone (the \"eigencone\") determining the possible answers to the problem. These eigencones can be defined for arbitrary semisimple groups $G$, and also control the (suitably stabilized) problem of existence of non-zero invariants in tensor products of irreducible representations of $G$.\n  We give a description of the extremal rays of the e","authors_text":"Joshua Kiers, Prakash Belkale","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-09T01:41:30Z","title":"Extremal rays in the Hermitian eigenvalue problem for arbitrary types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03350","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":"sha256:02984a701f431aafb663beef50860e2d2729df2c75753f3b34680911d94039d4","target":"record","created_at":"2026-05-18T00:19:50Z","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":"c187572b70494a070789e85d1c098eed098ad0d2b8bce2db0ce9c1b5bb26621f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-09T01:41:30Z","title_canon_sha256":"c51bb671b795ef77f823a6c6d0b9d39b57691329265d40c2deb3e2339a910805"},"schema_version":"1.0","source":{"id":"1803.03350","kind":"arxiv","version":2}},"canonical_sha256":"a6de6904e130d678966d9a21b90a9f6fee3a80ceb60e8a5e935efab7f7767ba4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6de6904e130d678966d9a21b90a9f6fee3a80ceb60e8a5e935efab7f7767ba4","first_computed_at":"2026-05-18T00:19:50.658553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:50.658553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i+7IzsQtpCTRHxaqfCnBGu/YYU5lrf7ya7dKORQai2epK34ScThRjV58SNTdtcAO/B0MmBSrS993HkGbHvFoDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:50.659198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03350","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02984a701f431aafb663beef50860e2d2729df2c75753f3b34680911d94039d4","sha256:81829bd07b594b3a1cc92fe3e6adc7533d53897f93311dee0a25f334be7d64b4"],"state_sha256":"3ee0ef0972a5569dabc34220bf78487bdde66ecb017040fd343a3c09975fefa6"}