{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FVIPLWB52LLV6SGD52YIQVEA4C","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":"304f4c2405e9273fb048ee01343cb881150a6d32169656e25f47b9c83130048c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-26T21:04:00Z","title_canon_sha256":"1ea2631b0b3784fcc34ebd3e36deadf55b27e7d65d7fbe255a0f21416ad2e58a"},"schema_version":"1.0","source":{"id":"1711.09459","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09459","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09459v4","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09459","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"FVIPLWB52LLV","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FVIPLWB52LLV6SGD","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FVIPLWB5","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:2c43cd7ca73e24156711ab87b859acdb6bc19e046844bad203fd8eb7e3050f77","target":"graph","created_at":"2026-05-17T23:41:13Z","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":"Given a tuple $E=(E_1,\\dots,E_g)$ of $d\\times d$ matrices, the collection of those tuples of matrices $X=(X_1,\\dots,X_g)$ (of the same size) such that $\\| \\sum E_j\\otimes X_j\\|\\le 1$ is called a spectraball $\\mathcal B_E$. Likewise, given a tuple $B=(B_1,\\dots,B_g)$ of $e\\times e$ matrices the collection of tuples of matrices $X=(X_1,\\dots,X_g)$ (of the same size) such that $I + \\sum B_j\\otimes X_j +\\sum B_j^* \\otimes X_j^*\\succeq 0$ is a free spectrahedron $\\mathcal D_B$. Assuming $E$ and $B$ are irreducible, plus an additional mild hypothesis, there is a free bianalytic map $p:\\mathcal B_E\\t","authors_text":"Igor Klep, J. William Helton, Meric Augat, Scott McCullough","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-26T21:04:00Z","title":"Free bianalytic maps between spectrahedra and spectraballs in a generic setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09459","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":"sha256:6fd871d39b3c9886f19a0637f6065961a30ba37f916550012cf0324ed24da6f6","target":"record","created_at":"2026-05-17T23:41:13Z","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":"304f4c2405e9273fb048ee01343cb881150a6d32169656e25f47b9c83130048c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-26T21:04:00Z","title_canon_sha256":"1ea2631b0b3784fcc34ebd3e36deadf55b27e7d65d7fbe255a0f21416ad2e58a"},"schema_version":"1.0","source":{"id":"1711.09459","kind":"arxiv","version":4}},"canonical_sha256":"2d50f5d83dd2d75f48c3eeb0885480e086735b3a58b1498f740a32da89441e29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d50f5d83dd2d75f48c3eeb0885480e086735b3a58b1498f740a32da89441e29","first_computed_at":"2026-05-17T23:41:13.388691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:13.388691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nzUZY+dNra1I1dLfCLCEAAneKRgAuDz0SG1fINPo536nLTfctZMCgFlBgGEYlfrNnO2ZKZnVEIBLDJfhjcm0Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:13.389127Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.09459","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fd871d39b3c9886f19a0637f6065961a30ba37f916550012cf0324ed24da6f6","sha256:2c43cd7ca73e24156711ab87b859acdb6bc19e046844bad203fd8eb7e3050f77"],"state_sha256":"3450e1de0c30718a4c783b9a0b31aeab3ec76ce18e086d17a11bb90bb1c83232"}