{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4KNFZ356NKHWH5X5VBYTHOXXKM","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":"038e3196f551e1a5b7a9d378d662f30fe68e2317b39f488bd31fd369b4f61969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-27T15:23:26Z","title_canon_sha256":"6bfa93912c831b053e07653994977148919528d2af2aabab5098935972abea27"},"schema_version":"1.0","source":{"id":"1406.7208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7208","created_at":"2026-05-18T02:28:22Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7208v1","created_at":"2026-05-18T02:28:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7208","created_at":"2026-05-18T02:28:22Z"},{"alias_kind":"pith_short_12","alias_value":"4KNFZ356NKHW","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4KNFZ356NKHWH5X5","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4KNFZ356","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:2ac9eaf3397628fa936bdfeb7ebbc5a75ea0a8adf77c9fe6d35dd415db652b5f","target":"graph","created_at":"2026-05-18T02:28:22Z","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 consider Hilbert algebras with a supplementary Fr\\'echet topology and get various extensions of the algebraic structure by using duality techniques. In particular we obtain optimal multiplier-type involutive algebras, which in applications are large enough to be of significant practical use. The setting covers many situations arising from quantization rules, as those involving square-integrable families of bounded operators.","authors_text":"M. Mantoiu, R. Purice","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-27T15:23:26Z","title":"On Fr\\'echet-Hilbert Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7208","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":"sha256:52108fb25bdab54e72cdc39828370e3fdd0975fe180f8d0fad436437e71f9a78","target":"record","created_at":"2026-05-18T02:28:22Z","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":"038e3196f551e1a5b7a9d378d662f30fe68e2317b39f488bd31fd369b4f61969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-27T15:23:26Z","title_canon_sha256":"6bfa93912c831b053e07653994977148919528d2af2aabab5098935972abea27"},"schema_version":"1.0","source":{"id":"1406.7208","kind":"arxiv","version":1}},"canonical_sha256":"e29a5cefbe6a8f63f6fda87133baf753223b7560945ee621ffcce2c2b1828a23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e29a5cefbe6a8f63f6fda87133baf753223b7560945ee621ffcce2c2b1828a23","first_computed_at":"2026-05-18T02:28:22.964687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:22.964687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PlVCjhvwESD7y8DNPZBI/josDI2L4tTcf5zLIMPYxNfAxFWfj3ZSVUiamKiJ8F400j3xFUDTooitO8VqyJdyBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:22.965175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52108fb25bdab54e72cdc39828370e3fdd0975fe180f8d0fad436437e71f9a78","sha256:2ac9eaf3397628fa936bdfeb7ebbc5a75ea0a8adf77c9fe6d35dd415db652b5f"],"state_sha256":"02dc7b329e14cdefa5f379fa5bc260b6bd9f8683a0cfd08e2ea9dd3b017fecca"}