{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:5NUTXIKPFQ27EGHM45VTOJ4DB6","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":"6f7a75827ea75dbbfb603b7a916dfdd61ef028a4d7712ecf6dde75e35af54938","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-07-01T06:38:15Z","title_canon_sha256":"26877713da28dbceb3f6beffd15d35479c7ffe1170018ed327db697ddf5da79f"},"schema_version":"1.0","source":{"id":"2007.00269","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.00269","created_at":"2026-07-05T01:15:30Z"},{"alias_kind":"arxiv_version","alias_value":"2007.00269v1","created_at":"2026-07-05T01:15:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.00269","created_at":"2026-07-05T01:15:30Z"},{"alias_kind":"pith_short_12","alias_value":"5NUTXIKPFQ27","created_at":"2026-07-05T01:15:30Z"},{"alias_kind":"pith_short_16","alias_value":"5NUTXIKPFQ27EGHM","created_at":"2026-07-05T01:15:30Z"},{"alias_kind":"pith_short_8","alias_value":"5NUTXIKP","created_at":"2026-07-05T01:15:30Z"}],"graph_snapshots":[{"event_id":"sha256:9a2539aed1e540595d7d2a9aadb541989c15d7d38cc992f14ea8ba76e0691780","target":"graph","created_at":"2026-07-05T01:15:30Z","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/2007.00269/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For an (indefinite) scalar product $[x,y]_B = x^HBy$ for $B= \\pm B^H \\in Gl_n(\\mathbb{C})$ on $\\mathbb{C}^n \\times \\mathbb{C}^n$ we show that the set of diagonalizable matrices is dense in the set of all $B$-selfadjoint, $B$-skewadjoint, $B$-unitary and $B$-normal matrices.","authors_text":"Philip Saltenberger, Ralph John de la Cruz","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-07-01T06:38:15Z","title":"Density of diagonalizable matrices in sets of structured matrices defined from indefinite scalar products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.00269","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":"sha256:0a0a9ea535985b5b7ebe89c581b6da04c18c42d6ff052d69cb307259cf5a9d07","target":"record","created_at":"2026-07-05T01:15:30Z","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":"6f7a75827ea75dbbfb603b7a916dfdd61ef028a4d7712ecf6dde75e35af54938","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-07-01T06:38:15Z","title_canon_sha256":"26877713da28dbceb3f6beffd15d35479c7ffe1170018ed327db697ddf5da79f"},"schema_version":"1.0","source":{"id":"2007.00269","kind":"arxiv","version":1}},"canonical_sha256":"eb693ba14f2c35f218ece76b3727830f8d4df6635b64b476a8cadab677df3010","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb693ba14f2c35f218ece76b3727830f8d4df6635b64b476a8cadab677df3010","first_computed_at":"2026-07-05T01:15:30.154248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:15:30.154248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RQ134x2pSz7Gs5nAqm6XP7Bzrr2rN29ZkV+VG3m67U9YP3eS8j7+8US2YCPsSzYmu4w/wFKbgjk8/12z86u8BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:15:30.154679Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.00269","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a0a9ea535985b5b7ebe89c581b6da04c18c42d6ff052d69cb307259cf5a9d07","sha256:9a2539aed1e540595d7d2a9aadb541989c15d7d38cc992f14ea8ba76e0691780"],"state_sha256":"ddcdd301669664502749cb652a80be19642295a10efbf1cc9a65c1d850eacbbc"}