{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6FRQ5DGYSZN4OMYBIIAA7R4KKO","short_pith_number":"pith:6FRQ5DGY","canonical_record":{"source":{"id":"1712.10289","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-12-29T17:44:32Z","cross_cats_sorted":[],"title_canon_sha256":"955048e5b16bba71012f518f6e3cc6e281f649c45c1f2730863c4dde99ab38a9","abstract_canon_sha256":"708deb07cf04e163722fd5d7fc0e50b41a43d6825ce498c3b58ea4638bb65ad9"},"schema_version":"1.0"},"canonical_sha256":"f1630e8cd8965bc7330142000fc78a53a9171884a991cbd79e7ded8cab4691b5","source":{"kind":"arxiv","id":"1712.10289","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.10289","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"1712.10289v2","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.10289","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"6FRQ5DGYSZN4","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6FRQ5DGYSZN4OMYB","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6FRQ5DGY","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6FRQ5DGYSZN4OMYBIIAA7R4KKO","target":"record","payload":{"canonical_record":{"source":{"id":"1712.10289","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-12-29T17:44:32Z","cross_cats_sorted":[],"title_canon_sha256":"955048e5b16bba71012f518f6e3cc6e281f649c45c1f2730863c4dde99ab38a9","abstract_canon_sha256":"708deb07cf04e163722fd5d7fc0e50b41a43d6825ce498c3b58ea4638bb65ad9"},"schema_version":"1.0"},"canonical_sha256":"f1630e8cd8965bc7330142000fc78a53a9171884a991cbd79e7ded8cab4691b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:39.456699Z","signature_b64":"eNlWMho6vuXeskjMetR/QPKYtiqdiNSyXTP8GHp/FJ+Gc24AcnkwFOjR/m9Uhg7T2ik9jb4qJCeH/ZvVynnnDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1630e8cd8965bc7330142000fc78a53a9171884a991cbd79e7ded8cab4691b5","last_reissued_at":"2026-05-18T00:05:39.456320Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:39.456320Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.10289","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L9Fa+xYlDphB4fMzljeDCNS+QaLB0mOyWxhinfPO582Y4IdujWt+3eLdLS9CAcW+hn6gttEmIVG8i3PjF+8IBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:54:55.611856Z"},"content_sha256":"0d4deda3ff6cb9e20846d9492eefce8ea5845ee6c69d7f688948cd8f490d0114","schema_version":"1.0","event_id":"sha256:0d4deda3ff6cb9e20846d9492eefce8ea5845ee6c69d7f688948cd8f490d0114"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6FRQ5DGYSZN4OMYBIIAA7R4KKO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher order $\\Sc^2$-differentiability and application to Koplienko trace formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anna Skripka, Christian Le Merdy, Cl\\'ement Coine, Fedor Sukochev","submitted_at":"2017-12-29T17:44:32Z","abstract_excerpt":"Let $A$ be a selfadjoint operator in a separable Hilbert space, $K$ a selfadjoint Hilbert-Schmidt operator, and $f\\in C^n(\\mathbb{R})$. We establish that $\\varphi(t)=f(A+tK)-f(A)$ is $n$-times continuously differentiable on $\\mathbb{R}$ in the Hilbert-Schmidt norm, provided either $A$ is bounded or the derivatives $f^{(i)}$, $i=1,\\ldots,n$, are bounded. As an application of the second order $\\Sc^2$-differentiability, we extend the Koplienko trace formula from the Besov class $B_{\\infty1}^2(\\R)$ to functions $f$ for which the divided difference $f^{[2]}$ admits a certain Hilbert space factoriza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10289","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXenwGYmVhbFO8pmUGMPhVLGVnqDKvn9OqQU6nmPrnYIRCCZIXvQ0Z3r/JioQdqVOvzKWZCQYv3TXB2rqvCTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:54:55.612520Z"},"content_sha256":"af6d753e2b8c0305e69da9f07e15b2e4a361b257937ef3f818deac4fa756d919","schema_version":"1.0","event_id":"sha256:af6d753e2b8c0305e69da9f07e15b2e4a361b257937ef3f818deac4fa756d919"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6FRQ5DGYSZN4OMYBIIAA7R4KKO/bundle.json","state_url":"https://pith.science/pith/6FRQ5DGYSZN4OMYBIIAA7R4KKO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6FRQ5DGYSZN4OMYBIIAA7R4KKO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T11:54:55Z","links":{"resolver":"https://pith.science/pith/6FRQ5DGYSZN4OMYBIIAA7R4KKO","bundle":"https://pith.science/pith/6FRQ5DGYSZN4OMYBIIAA7R4KKO/bundle.json","state":"https://pith.science/pith/6FRQ5DGYSZN4OMYBIIAA7R4KKO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6FRQ5DGYSZN4OMYBIIAA7R4KKO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6FRQ5DGYSZN4OMYBIIAA7R4KKO","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":"708deb07cf04e163722fd5d7fc0e50b41a43d6825ce498c3b58ea4638bb65ad9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-12-29T17:44:32Z","title_canon_sha256":"955048e5b16bba71012f518f6e3cc6e281f649c45c1f2730863c4dde99ab38a9"},"schema_version":"1.0","source":{"id":"1712.10289","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.10289","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"1712.10289v2","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.10289","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"6FRQ5DGYSZN4","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6FRQ5DGYSZN4OMYB","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6FRQ5DGY","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:af6d753e2b8c0305e69da9f07e15b2e4a361b257937ef3f818deac4fa756d919","target":"graph","created_at":"2026-05-18T00:05:39Z","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 $A$ be a selfadjoint operator in a separable Hilbert space, $K$ a selfadjoint Hilbert-Schmidt operator, and $f\\in C^n(\\mathbb{R})$. We establish that $\\varphi(t)=f(A+tK)-f(A)$ is $n$-times continuously differentiable on $\\mathbb{R}$ in the Hilbert-Schmidt norm, provided either $A$ is bounded or the derivatives $f^{(i)}$, $i=1,\\ldots,n$, are bounded. As an application of the second order $\\Sc^2$-differentiability, we extend the Koplienko trace formula from the Besov class $B_{\\infty1}^2(\\R)$ to functions $f$ for which the divided difference $f^{[2]}$ admits a certain Hilbert space factoriza","authors_text":"Anna Skripka, Christian Le Merdy, Cl\\'ement Coine, Fedor Sukochev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-12-29T17:44:32Z","title":"Higher order $\\Sc^2$-differentiability and application to Koplienko trace formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10289","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":"sha256:0d4deda3ff6cb9e20846d9492eefce8ea5845ee6c69d7f688948cd8f490d0114","target":"record","created_at":"2026-05-18T00:05:39Z","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":"708deb07cf04e163722fd5d7fc0e50b41a43d6825ce498c3b58ea4638bb65ad9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-12-29T17:44:32Z","title_canon_sha256":"955048e5b16bba71012f518f6e3cc6e281f649c45c1f2730863c4dde99ab38a9"},"schema_version":"1.0","source":{"id":"1712.10289","kind":"arxiv","version":2}},"canonical_sha256":"f1630e8cd8965bc7330142000fc78a53a9171884a991cbd79e7ded8cab4691b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1630e8cd8965bc7330142000fc78a53a9171884a991cbd79e7ded8cab4691b5","first_computed_at":"2026-05-18T00:05:39.456320Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:39.456320Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eNlWMho6vuXeskjMetR/QPKYtiqdiNSyXTP8GHp/FJ+Gc24AcnkwFOjR/m9Uhg7T2ik9jb4qJCeH/ZvVynnnDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:39.456699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.10289","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d4deda3ff6cb9e20846d9492eefce8ea5845ee6c69d7f688948cd8f490d0114","sha256:af6d753e2b8c0305e69da9f07e15b2e4a361b257937ef3f818deac4fa756d919"],"state_sha256":"4d1cdd0b45fb7fc2720f63c1d33a755b1574cc6d1e62dc6e7d729a1ce36ba4af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+0LlaR2rLp88PjtRFgWN7m2lceccacPRd4FlAESED+ics7JvocMYE4GtCK3VPazxS6ywoMm9frHNu/4fv4u0Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:54:55.616455Z","bundle_sha256":"905d7b001c2dec3673f59f2b38f67c6d4cb29d083eb885833506711d7657dbfb"}}