{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PMNWFG7GYQ7IUK6AFWCDNMGKXK","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":"61ae1492ab4437ca9d65cf3227971e005bc4e2e882c321616824bf3a7ddce56d","cross_cats_sorted":["math-ph","math.MP","math.OA","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-29T15:48:08Z","title_canon_sha256":"25f58bdf932d27bbccdea5f72976ab6a7b732d9a390860104dfa82e5549b458e"},"schema_version":"1.0","source":{"id":"1303.7426","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.7426","created_at":"2026-05-18T02:25:05Z"},{"alias_kind":"arxiv_version","alias_value":"1303.7426v4","created_at":"2026-05-18T02:25:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7426","created_at":"2026-05-18T02:25:05Z"},{"alias_kind":"pith_short_12","alias_value":"PMNWFG7GYQ7I","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PMNWFG7GYQ7IUK6A","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PMNWFG7G","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:00af95620cb858f9232a3cd8811338c01930762b570b515482fd9aae79d8c630","target":"graph","created_at":"2026-05-18T02:25:05Z","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":"For an unbounded self-adjoint operator D on a Hilbert space H and a bounded operator a on H we say that a is weakly D-differentiable if for any pair of vectors x, y in H the function <exp(itD) a exp(-itD)x, y> is differentiable at t =0. We find several conditions which are all equivalent to weak D-differentiability.","authors_text":"Erik Christensen","cross_cats":["math-ph","math.MP","math.OA","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-29T15:48:08Z","title":"On weakly D-differentiable operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7426","kind":"arxiv","version":4},"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":"sha256:63c9e5d15a28883b266ee0704dc7b0216cb33535dea69d32c3889e85635388d2","target":"record","created_at":"2026-05-18T02:25:05Z","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":"61ae1492ab4437ca9d65cf3227971e005bc4e2e882c321616824bf3a7ddce56d","cross_cats_sorted":["math-ph","math.MP","math.OA","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-29T15:48:08Z","title_canon_sha256":"25f58bdf932d27bbccdea5f72976ab6a7b732d9a390860104dfa82e5549b458e"},"schema_version":"1.0","source":{"id":"1303.7426","kind":"arxiv","version":4}},"canonical_sha256":"7b1b629be6c43e8a2bc02d8436b0cababb8578fb8fe211094fd553715a89ef68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b1b629be6c43e8a2bc02d8436b0cababb8578fb8fe211094fd553715a89ef68","first_computed_at":"2026-05-18T02:25:05.009487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:05.009487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2z1AO+uPbCEK/4jTmFxV+1sqm20aHFHJz71xLyx7mG1UbsXet7bYE0cGcjYZnT9zYMEEuN8RhBZeKW51V1peCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:05.009956Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.7426","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63c9e5d15a28883b266ee0704dc7b0216cb33535dea69d32c3889e85635388d2","sha256:00af95620cb858f9232a3cd8811338c01930762b570b515482fd9aae79d8c630"],"state_sha256":"f9540401c9eea41a98d86033881652e6a859ee11b0ec672d9854f61c3eac7da6"}