{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:O5W3OJKGEJYOYE2HWY6MUIAVQ5","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":"db06b50bbddd99365dc00910136cdd6d52015dc32bf6c570e02b4afc2e37c22b","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-14T12:41:25Z","title_canon_sha256":"1acdde0f6fe0fd5dc08749e4876350904b44b073f7ee1459b185bb8cdeb1a712"},"schema_version":"1.0","source":{"id":"1504.03521","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03521","created_at":"2026-05-18T01:37:07Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03521v2","created_at":"2026-05-18T01:37:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03521","created_at":"2026-05-18T01:37:07Z"},{"alias_kind":"pith_short_12","alias_value":"O5W3OJKGEJYO","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O5W3OJKGEJYOYE2H","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O5W3OJKG","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:0a886cf04aa3947f681bfeedb0d7d73faf38905e09b4e16c8076e809920a6420","target":"graph","created_at":"2026-05-18T01:37:07Z","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":"Let D be a self-adjoint operator on a Hilbert space H and x a bounded operator on H. We say that x is n-times weakly D-differentiable, if for any pair of vectors a, b from H the function < exp(itD)x exp(-itD) a, b> is n-times differentiable. We give several characterizations of this property, among which one is original. The results are used to show, that for a von Neumann algebra M on H, the sub-algebra of n-times weakly D-differentiable operators has a representation as a reflexive algebra of operators on a bigger Hilbert space.","authors_text":"Erik Christensen","cross_cats":["math-ph","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-14T12:41:25Z","title":"Higher Weak Derivatives and Reflexive Algebras of Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03521","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:fa42469b13e7586e0b1b3e6b246966fa2b0d63ccef2ed9516f58ebfaab5c3893","target":"record","created_at":"2026-05-18T01:37:07Z","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":"db06b50bbddd99365dc00910136cdd6d52015dc32bf6c570e02b4afc2e37c22b","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-14T12:41:25Z","title_canon_sha256":"1acdde0f6fe0fd5dc08749e4876350904b44b073f7ee1459b185bb8cdeb1a712"},"schema_version":"1.0","source":{"id":"1504.03521","kind":"arxiv","version":2}},"canonical_sha256":"776db725462270ec1347b63cca2015877332de30a405b51c9e1e8639ad9c791c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"776db725462270ec1347b63cca2015877332de30a405b51c9e1e8639ad9c791c","first_computed_at":"2026-05-18T01:37:07.388515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:07.388515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gPPf+3x4IedQ45ELLGhB9f38eBH4VQQIEOWQpL38OBty6aUkoMFeZsU9/OTPr7/OhbkBtYBGpW/D2sVGUXx/BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:07.389059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03521","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa42469b13e7586e0b1b3e6b246966fa2b0d63ccef2ed9516f58ebfaab5c3893","sha256:0a886cf04aa3947f681bfeedb0d7d73faf38905e09b4e16c8076e809920a6420"],"state_sha256":"3ec74d04f619493273a2ec451b4370d390265b84e6f2752bcc866e57399018dd"}