{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EH2QEC3IEDUJ2ATZ67BM25F3DC","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":"0b0ca76368843f9bde409238c67887f2f3dc5eb5a8453de398e5c519d0fd2b71","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-10-31T17:34:54Z","title_canon_sha256":"6d09b7415bc569144ecc77c49e27eb3b82d358ac234f5ee7488c01e00858d270"},"schema_version":"1.0","source":{"id":"2510.27670","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.27670","created_at":"2026-05-18T03:09:33Z"},{"alias_kind":"arxiv_version","alias_value":"2510.27670v2","created_at":"2026-05-18T03:09:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.27670","created_at":"2026-05-18T03:09:33Z"},{"alias_kind":"pith_short_12","alias_value":"EH2QEC3IEDUJ","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"EH2QEC3IEDUJ2ATZ","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"EH2QEC3I","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:63eac87fb56ec9a9ef6eb01b7d3a78c54e54d00c8459de4c07f30656e0f6a2c3","target":"graph","created_at":"2026-05-18T03:09:33Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Fifteen possible classes regarding the numbers of non-elliptic faces in the boundary of W are identified and an explicit example is presented for each class. A nonempty intersection of three mutually distinct one-dimensional faces is a corner point."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The analysis assumes that varying only the number of non-elliptic faces fully captures all possible non-generic boundary structures for three Hermitian 4x4 matrices without additional geometric features or degeneracies arising, as implied by the identification of exactly fifteen classes in the abstract."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Classifies non-generic joint numerical ranges of three Hermitian 4x4 matrices into 15 classes with examples, proves corner points from face intersections, and compares the separable numerical range boundary for entanglement analysis."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The joint numerical range of three Hermitian 4x4 matrices has non-generic boundaries classifiable into fifteen types based on non-elliptic faces."}],"snapshot_sha256":"9de2e237d544232c9fba57f29caffcb53bf426897ca2549e01f66ebd8d7a365e"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"90fd9df962dcbf30fced2238a231408677f4f50e5c5ae3e474df80a58e4a96d0"},"paper":{"abstract_excerpt":"We analyze the joint numerical range $W$ of three hermitian matrices of order four. In the generic case, this three-dimensional convex set has a smooth boundary. We analyze non-generic structures. Fifteen possible classes regarding the numbers of non-elliptic faces in the boundary of $W$ are identified and an explicit example is presented for each class. Secondly, it is shown that a nonempty intersection of three mutually distinct one-dimensional faces is a corner point. Thirdly, introducing a tensor product structure into $\\mathbb C^4=\\mathbb C^2\\otimes\\mathbb C^2$, one defines the separable ","authors_text":"Ilya Spitkovsky, Karol \\.Zyczkowski, Konrad Szyma\\'nski, Piotr Pikul, Stephan Weis","cross_cats":[],"headline":"The joint numerical range of three Hermitian 4x4 matrices has non-generic boundaries classifiable into fifteen types based on non-elliptic faces.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-10-31T17:34:54Z","title":"The joint numerical range of three hermitian $4\\times 4$ matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.27670","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-18T02:42:59.509916Z","id":"4576030c-bc1e-4ed7-8175-de083007f681","model_set":{"reader":"grok-4.3"},"one_line_summary":"Classifies non-generic joint numerical ranges of three Hermitian 4x4 matrices into 15 classes with examples, proves corner points from face intersections, and compares the separable numerical range boundary for entanglement analysis.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The joint numerical range of three Hermitian 4x4 matrices has non-generic boundaries classifiable into fifteen types based on non-elliptic faces.","strongest_claim":"Fifteen possible classes regarding the numbers of non-elliptic faces in the boundary of W are identified and an explicit example is presented for each class. A nonempty intersection of three mutually distinct one-dimensional faces is a corner point.","weakest_assumption":"The analysis assumes that varying only the number of non-elliptic faces fully captures all possible non-generic boundary structures for three Hermitian 4x4 matrices without additional geometric features or degeneracies arising, as implied by the identification of exactly fifteen classes in the abstract."}},"verdict_id":"4576030c-bc1e-4ed7-8175-de083007f681"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:438fc26c497618e93335fc8ceeabd946253085685214068a91ca242fe6abfbef","target":"record","created_at":"2026-05-18T03:09:33Z","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":"0b0ca76368843f9bde409238c67887f2f3dc5eb5a8453de398e5c519d0fd2b71","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-10-31T17:34:54Z","title_canon_sha256":"6d09b7415bc569144ecc77c49e27eb3b82d358ac234f5ee7488c01e00858d270"},"schema_version":"1.0","source":{"id":"2510.27670","kind":"arxiv","version":2}},"canonical_sha256":"21f5020b6820e89d0279f7c2cd74bb18bf4e2c645dcd5f6640d54b8551b340cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21f5020b6820e89d0279f7c2cd74bb18bf4e2c645dcd5f6640d54b8551b340cb","first_computed_at":"2026-05-18T03:09:33.693262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:33.693262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z6JVosggUvR8IPwzfdTFZAE5sOa0MrHg46hGObsfY4HOXvZ7ZUoaNP8q4BZEsXfrvS2gbqX742Q9ODddDjWIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:33.693754Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.27670","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:438fc26c497618e93335fc8ceeabd946253085685214068a91ca242fe6abfbef","sha256:63eac87fb56ec9a9ef6eb01b7d3a78c54e54d00c8459de4c07f30656e0f6a2c3"],"state_sha256":"8287a017f0ef92b8fec7013ae0d641e7ff6bb931799fea38fbd0db66b83d64e7"}