{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VE6W7GUUF6HROBMAX6IIHAOO4I","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":"98f058273497e9fece00c27cf282acea41ae4eca93445a552c049863bb2be468","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-02T16:21:23Z","title_canon_sha256":"32764477b416da3481cfb284bfe41d2fc5ce3b6f776ac93e7d614e7ddced3c3f"},"schema_version":"1.0","source":{"id":"1203.0509","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0509","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0509v1","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0509","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"pith_short_12","alias_value":"VE6W7GUUF6HR","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VE6W7GUUF6HROBMA","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VE6W7GUU","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:1a8538280c0c9e537f9b853675b67a88840f2f1fcd2458951d9f8b31aaa385b5","target":"graph","created_at":"2026-05-18T03:43:28Z","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 continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the scope of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algeb","authors_text":"C. Trapani, G. Bellomonte, J-P. Antoine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-02T16:21:23Z","title":"Fully representable and *-semisimple topological partial *-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0509","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":"sha256:040330ec4efb1eeae2e98cbe11ec187b80db36a18d77a7ad5d772d54b9e7f0f5","target":"record","created_at":"2026-05-18T03:43:28Z","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":"98f058273497e9fece00c27cf282acea41ae4eca93445a552c049863bb2be468","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-02T16:21:23Z","title_canon_sha256":"32764477b416da3481cfb284bfe41d2fc5ce3b6f776ac93e7d614e7ddced3c3f"},"schema_version":"1.0","source":{"id":"1203.0509","kind":"arxiv","version":1}},"canonical_sha256":"a93d6f9a942f8f170580bf908381cee22115a1a6c88464a47425cae2843bb4ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a93d6f9a942f8f170580bf908381cee22115a1a6c88464a47425cae2843bb4ec","first_computed_at":"2026-05-18T03:43:28.504494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:28.504494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z9vxaOHYm520OaClHLhNwL7IsnvszBeb8QvX5zMN8WUhzNyNb51dws9ddMJ3wCGUx1CoZUtWmqjsMw1/dbhgCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:28.504981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0509","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:040330ec4efb1eeae2e98cbe11ec187b80db36a18d77a7ad5d772d54b9e7f0f5","sha256:1a8538280c0c9e537f9b853675b67a88840f2f1fcd2458951d9f8b31aaa385b5"],"state_sha256":"c96937deab72c318a3103cc7d1e5bf7945915f2a9134fac0e45846969c0e5492"}