{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LER6FZSK4LLUHIRKPBQVJ4NOOW","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":"fcf77bdb9efb1e76c6be70e833700b6d1cddd2e53597659e99731ca114098fa4","cross_cats_sorted":["cs.SC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-12-29T22:18:37Z","title_canon_sha256":"fe4a6afa7a3b5baf13188ebb73930a98210115669505c9f0df3433a04d18d18e"},"schema_version":"1.0","source":{"id":"2401.00089","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.00089","created_at":"2026-05-22T01:03:39Z"},{"alias_kind":"arxiv_version","alias_value":"2401.00089v4","created_at":"2026-05-22T01:03:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.00089","created_at":"2026-05-22T01:03:39Z"},{"alias_kind":"pith_short_12","alias_value":"LER6FZSK4LLU","created_at":"2026-05-22T01:03:39Z"},{"alias_kind":"pith_short_16","alias_value":"LER6FZSK4LLUHIRK","created_at":"2026-05-22T01:03:39Z"},{"alias_kind":"pith_short_8","alias_value":"LER6FZSK","created_at":"2026-05-22T01:03:39Z"}],"graph_snapshots":[{"event_id":"sha256:ec837c19155d207da62d7bf65716d8ebf811b7255186d905c46bbe075243126c","target":"graph","created_at":"2026-05-22T01:03:39Z","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/2401.00089/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given two real symmetric matrices, their eigenvalue configuration is the relative arrangement of their eigenvalues on the real line. In this paper, we consider the following problem: given two parametric real symmetric matrices and an eigenvalue configuration, find a simple condition on the parameters such that their eigenvalues have the given configuration. We give an algorithm which expresses the eigenvalue configuration problem as a real root counting problem of certain symmetric polynomials, whose roots can be counted using the Fundamental Theorem of Symmetric Polynomials and Descartes' ru","authors_text":"Daniel Profili, Hoon Hong, J. Rafael Sendra","cross_cats":["cs.SC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-12-29T22:18:37Z","title":"Conditions for eigenvalue configurations of two real symmetric matrices (symmetric polynomial approach)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.00089","kind":"arxiv","version":4},"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:d52270c814aa31e27d3f1f22216062be3fe919fd29bde221e4e50c2078fb3ff3","target":"record","created_at":"2026-05-22T01:03:39Z","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":"fcf77bdb9efb1e76c6be70e833700b6d1cddd2e53597659e99731ca114098fa4","cross_cats_sorted":["cs.SC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2023-12-29T22:18:37Z","title_canon_sha256":"fe4a6afa7a3b5baf13188ebb73930a98210115669505c9f0df3433a04d18d18e"},"schema_version":"1.0","source":{"id":"2401.00089","kind":"arxiv","version":4}},"canonical_sha256":"5923e2e64ae2d743a22a786154f1ae75b9392bdc2eb9d26e018e2481872afef5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5923e2e64ae2d743a22a786154f1ae75b9392bdc2eb9d26e018e2481872afef5","first_computed_at":"2026-05-22T01:03:39.074770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:03:39.074770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cnTMTEWATcntZLnISgu0v+s5Cpu76SCGqYGmq+GMN1NVUuDRu94p7SXvG/H/fokZIo36oN+G1aamIBONtxR/Ag==","signature_status":"signed_v1","signed_at":"2026-05-22T01:03:39.075481Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.00089","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d52270c814aa31e27d3f1f22216062be3fe919fd29bde221e4e50c2078fb3ff3","sha256:ec837c19155d207da62d7bf65716d8ebf811b7255186d905c46bbe075243126c"],"state_sha256":"0c947b5efe62175242606dbfb8f13c999aa342e5705b31f736cfed23a9525750"}