{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:STFT2GH42WTP64HYHRXEOMXQHS","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":"e1889e2d446ffd352ed2c12eeb99141ae42cea83076ccc408a86bc16223f45ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-04T15:37:39Z","title_canon_sha256":"c60399e5aa9fcf36f3041b2ad84101de19614dc17e2092c59284f4d6eb3c69d8"},"schema_version":"1.0","source":{"id":"1503.01344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01344","created_at":"2026-05-18T02:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01344v1","created_at":"2026-05-18T02:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01344","created_at":"2026-05-18T02:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"STFT2GH42WTP","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"STFT2GH42WTP64HY","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"STFT2GH4","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:6b07ed0d41decd407983cdf062adbb91067399cb7a8b79e3067655ef0eef004a","target":"graph","created_at":"2026-05-18T02:25:34Z","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":"We introduce and study the class of extremally rich JB$^*$-triples. We establish new results to determine the distance from an element $a$ in an extremally rich JB$^*$-triple $E$ to the set $\\partial_{e} (E_1)$ of all extreme points of the closed unit ball of $E$. More concretely, we prove that $$\\hbox{dist} (a,\\partial_e (E_1)) =\\max \\{ 1, \\|a\\|-1\\},$$ for every $a\\in E$ which is not Brown-Pedersen quasi-invertible. As a consequence, we determine the form of the $\\lambda$-function of Aron and Lohman on the open unit ball of an extremally rich JB$^*$-triple $E$, by showing that $\\lambda (a)= \\","authors_text":"Akhlaq A. Siddiqui, Antonio M. Peralta, Fatmah B. Jamjoom, Haifa M. Tahlawi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-04T15:37:39Z","title":"Quadratic Conorm and extremally rich JB*-triples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01344","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:ccc695aa893b8518e82466564a064f977b11a70d706b8c89a5ae0e157edf1d7c","target":"record","created_at":"2026-05-18T02:25:34Z","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":"e1889e2d446ffd352ed2c12eeb99141ae42cea83076ccc408a86bc16223f45ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-04T15:37:39Z","title_canon_sha256":"c60399e5aa9fcf36f3041b2ad84101de19614dc17e2092c59284f4d6eb3c69d8"},"schema_version":"1.0","source":{"id":"1503.01344","kind":"arxiv","version":1}},"canonical_sha256":"94cb3d18fcd5a6ff70f83c6e4732f03cbb48116ec635b76102a95e1eb2cf9d92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94cb3d18fcd5a6ff70f83c6e4732f03cbb48116ec635b76102a95e1eb2cf9d92","first_computed_at":"2026-05-18T02:25:34.736368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:34.736368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cH+OWwNH1eCdNLqW0sc0vKV9v5pvHmGUEqzyBW0TNscI0KzRobMKq54Nn8ycG1CdvXT3/ar3OM5nyTR4qwSJBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:34.736800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccc695aa893b8518e82466564a064f977b11a70d706b8c89a5ae0e157edf1d7c","sha256:6b07ed0d41decd407983cdf062adbb91067399cb7a8b79e3067655ef0eef004a"],"state_sha256":"ef395d7847b6ba906ec0d1e3e85a8768c063244e560859493ac5bd91e34abdc2"}