{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JDLHO4DG4DP5BSTYT6R2NPUJJB","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":"9c2ebd19935e7f3b41bf0729f20a47ce8c770b3b6fff4a8caca63c3762cc04f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-22T18:38:38Z","title_canon_sha256":"3c65c3eabbc85f967e976581c3a91448b2e6a50251459883167ec5ede5506fb7"},"schema_version":"1.0","source":{"id":"1511.07049","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07049","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07049v2","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07049","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"JDLHO4DG4DP5","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JDLHO4DG4DP5BSTY","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JDLHO4DG","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:8b346d05b183609910ee92dd2978a2cb32d667c443c5202a135a471476ea45d4","target":"graph","created_at":"2026-05-18T00:07:12Z","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 partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their domains. We use these results to study the problem of extending a positive definite function defined on a symmetric subset of a locally compact group to a positive definite function defined on the whole group.","authors_text":"Ivan G. Todorov, Rupert H. Levene, Ying-Fen Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-22T18:38:38Z","title":"Positive extensions of Schur multipliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07049","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":"sha256:611861cb1976ce04f659e029411ca8038f766d31d5bb09a9a4923c9963ebb1b0","target":"record","created_at":"2026-05-18T00:07:12Z","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":"9c2ebd19935e7f3b41bf0729f20a47ce8c770b3b6fff4a8caca63c3762cc04f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-22T18:38:38Z","title_canon_sha256":"3c65c3eabbc85f967e976581c3a91448b2e6a50251459883167ec5ede5506fb7"},"schema_version":"1.0","source":{"id":"1511.07049","kind":"arxiv","version":2}},"canonical_sha256":"48d6777066e0dfd0ca789fa3a6be894863df6c388fa02d028c32ae5ce5d4abd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48d6777066e0dfd0ca789fa3a6be894863df6c388fa02d028c32ae5ce5d4abd3","first_computed_at":"2026-05-18T00:07:12.649991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:12.649991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4FgLVGmOQSzFYtDkbQA3aTHfNBsi6Wn0wT8sXebO8ZsHlBRgBM3yfhJrV+F8ObvWAVl/wtlxexQvNJPHGtgnAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:12.650590Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07049","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:611861cb1976ce04f659e029411ca8038f766d31d5bb09a9a4923c9963ebb1b0","sha256:8b346d05b183609910ee92dd2978a2cb32d667c443c5202a135a471476ea45d4"],"state_sha256":"d0726ff773808651b2c8f774ca37ed7651294b2db63f0203287c8114a06cb577"}