{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UGO43NFLCUUPSCD3AYN4X3XKO6","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":"973f1864a242f704bb3dd25e749c494ae22697397b53d65cf3e6f11d5ac76c5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-06-23T23:42:44Z","title_canon_sha256":"f74edeba503fbae2a2147146b7f2726a9babcb4fbb5a369f37c6da7e1ab83252"},"schema_version":"1.0","source":{"id":"1806.09053","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09053","created_at":"2026-07-05T03:59:19Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09053v2","created_at":"2026-07-05T03:59:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09053","created_at":"2026-07-05T03:59:19Z"},{"alias_kind":"pith_short_12","alias_value":"UGO43NFLCUUP","created_at":"2026-07-05T03:59:19Z"},{"alias_kind":"pith_short_16","alias_value":"UGO43NFLCUUPSCD3","created_at":"2026-07-05T03:59:19Z"},{"alias_kind":"pith_short_8","alias_value":"UGO43NFL","created_at":"2026-07-05T03:59:19Z"}],"graph_snapshots":[{"event_id":"sha256:8ae04287fbd8ffdcc86951f37c38a63ccfcd938182c6c21fd662e269b6afb7be","target":"graph","created_at":"2026-07-05T03:59:19Z","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/1806.09053/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $ SM_n(\\mathbb{R})^g$ denote $g$-tuples of $n \\times n$ real symmetric matrices. Given tuples $X=(X_1, \\dots, X_g) \\in SM_{n_1}(\\mathbb{R})^g$ and $Y=(Y_1, \\dots, Y_g) \\in SM_{n_2}(\\mathbb{R})^g$, a matrix convex combination of $X$ and $Y$ is a sum of the form \\[ V_1^* XV_1+V_2^* Y V_2 \\quad \\quad \\quad V_1^* V_1+V_2^* V_2=I_n \\] where $V_1:\\mathbb{R}^n \\to \\mathbb{R}^{n_1}$ and $V_2:\\mathbb{R}^n \\to \\mathbb{R}^{n_2}$ are contractions. Matrix convex sets are sets which are closed under matrix convex combinations. A key feature of matrix convex combinations is that the $g$-tuples $X, Y$, an","authors_text":"Eric Evert, J. William Helton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-06-23T23:42:44Z","title":"Arveson extreme points span free spectrahedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09053","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:d1d6b1473892bdb8425bd474b0dd40d34d06b7fb3907f9e5aabf0ea14c0114e1","target":"record","created_at":"2026-07-05T03:59:19Z","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":"973f1864a242f704bb3dd25e749c494ae22697397b53d65cf3e6f11d5ac76c5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-06-23T23:42:44Z","title_canon_sha256":"f74edeba503fbae2a2147146b7f2726a9babcb4fbb5a369f37c6da7e1ab83252"},"schema_version":"1.0","source":{"id":"1806.09053","kind":"arxiv","version":2}},"canonical_sha256":"a19dcdb4ab1528f9087b061bcbeeea779197b0ea3e825e295dd31d4a547701fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a19dcdb4ab1528f9087b061bcbeeea779197b0ea3e825e295dd31d4a547701fe","first_computed_at":"2026-07-05T03:59:19.783647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:59:19.783647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PvWK9q774zZ8VffOJaL6eJPxZ9gCVA/aNf+qqS7IICPuMXUqDtQQ7C0X4ySCB9ywjQWU4NtJd3vhU2HbyionBg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:59:19.784154Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.09053","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1d6b1473892bdb8425bd474b0dd40d34d06b7fb3907f9e5aabf0ea14c0114e1","sha256:8ae04287fbd8ffdcc86951f37c38a63ccfcd938182c6c21fd662e269b6afb7be"],"state_sha256":"1d3c0b66ad7bc057e9227d1655b2011590c792499bdefe825959ac7312265380"}