{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M4ZOSSO3ZQMIVACJR6EHL5GQJS","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":"3edef2a26bdf6178fbf84990e72509be2744217f31981f7e57421763ef38c3dd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-02-05T13:18:42Z","title_canon_sha256":"b7c01e917008314333c9c970f73d20fd78b5baf146543f054c41778e09928eb1"},"schema_version":"1.0","source":{"id":"1502.01530","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01530","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01530v2","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01530","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"M4ZOSSO3ZQMI","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M4ZOSSO3ZQMIVACJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M4ZOSSO3","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:f91e6ae03cbac82dca68a0c5d35feac9b48372163391895af910d420e8dcb74e","target":"graph","created_at":"2026-05-18T00:07:44Z","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 show that the set of Schur idempotents with hyperreflexive range is a Boolean lattice which contains all contractions. We establish a preservation result for sums which implies that the weak* closed span of a hyperreflexive and a ternary masa-bimodule is hyperreflexive, and prove that the weak* closed span of finitely many tensor products of a hyperreflexive space and a hyperreflexive range of a Schur idempotent (respectively, a ternary masa-bimodule) is hyperreflexive.","authors_text":"G. K. Eleftherakis, I. G. Todorov, R. H. Levene","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-02-05T13:18:42Z","title":"Schur idempotents and hyperreflexivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01530","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":"sha256:128ba93629db4f1268a7643c983e54aa92212211ffdd1dcf3429a062b9f7ae4c","target":"record","created_at":"2026-05-18T00:07:44Z","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":"3edef2a26bdf6178fbf84990e72509be2744217f31981f7e57421763ef38c3dd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-02-05T13:18:42Z","title_canon_sha256":"b7c01e917008314333c9c970f73d20fd78b5baf146543f054c41778e09928eb1"},"schema_version":"1.0","source":{"id":"1502.01530","kind":"arxiv","version":2}},"canonical_sha256":"6732e949dbcc188a80498f8875f4d04ca49daaa42e351e054b36cb38be94dd3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6732e949dbcc188a80498f8875f4d04ca49daaa42e351e054b36cb38be94dd3f","first_computed_at":"2026-05-18T00:07:44.161558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:44.161558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iyCgauhQQydlVLxMWQDvuOQOAkDTqUbIevuzpUaBftzhxfWBhXYgcSFQbF19PLtuOj2U8Tcoe9tJKh+40ZObAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:44.162236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01530","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:128ba93629db4f1268a7643c983e54aa92212211ffdd1dcf3429a062b9f7ae4c","sha256:f91e6ae03cbac82dca68a0c5d35feac9b48372163391895af910d420e8dcb74e"],"state_sha256":"b2d2c7d36c11014043aa1a980ae1bebcb57ad70764947f47dc512109bf984263"}