{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MHRXFZEE6QDCBDMRO4T7E3WDDI","short_pith_number":"pith:MHRXFZEE","canonical_record":{"source":{"id":"1508.04702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-19T16:44:42Z","cross_cats_sorted":["math.CA","math.CV","math.SP"],"title_canon_sha256":"d691fd35816bfb56aa534d36f5fc227f470c8f018fbd9f262c5fa10b5179de4b","abstract_canon_sha256":"a310c6b2ada39a48df550a099f1c9cda879db6ffb78ed0532a8116d6d396a03f"},"schema_version":"1.0"},"canonical_sha256":"61e372e484f406208d917727f26ec31a2b41f63c8674cef8e73ff7de6a5a74bf","source":{"kind":"arxiv","id":"1508.04702","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04702","created_at":"2026-05-18T01:35:02Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04702v1","created_at":"2026-05-18T01:35:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04702","created_at":"2026-05-18T01:35:02Z"},{"alias_kind":"pith_short_12","alias_value":"MHRXFZEE6QDC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MHRXFZEE6QDCBDMR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MHRXFZEE","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MHRXFZEE6QDCBDMRO4T7E3WDDI","target":"record","payload":{"canonical_record":{"source":{"id":"1508.04702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-19T16:44:42Z","cross_cats_sorted":["math.CA","math.CV","math.SP"],"title_canon_sha256":"d691fd35816bfb56aa534d36f5fc227f470c8f018fbd9f262c5fa10b5179de4b","abstract_canon_sha256":"a310c6b2ada39a48df550a099f1c9cda879db6ffb78ed0532a8116d6d396a03f"},"schema_version":"1.0"},"canonical_sha256":"61e372e484f406208d917727f26ec31a2b41f63c8674cef8e73ff7de6a5a74bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:02.050633Z","signature_b64":"Ju9LC32zPdRE9RfHLEfIpOJcdPdkRCJvq4Lloj82BLA7NstOBZy+F/OoRcHkWDi+0kJwLe0I/T43N+Vd7PTCAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61e372e484f406208d917727f26ec31a2b41f63c8674cef8e73ff7de6a5a74bf","last_reissued_at":"2026-05-18T01:35:02.049936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:02.049936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.04702","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:35:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"epTMa2kDgH1oDlkmQ9n/Ks9ar1G4SJubQDbXKgtjPkojH85r0xeNVpJE+ojVUmXcsmt0/TwYYR7mSDtzEJilBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:22:24.740902Z"},"content_sha256":"37c7c68cc583494d8a37b1179adbee7f795a762649d638713901b4905d9e2f9d","schema_version":"1.0","event_id":"sha256:37c7c68cc583494d8a37b1179adbee7f795a762649d638713901b4905d9e2f9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MHRXFZEE6QDCBDMRO4T7E3WDDI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functions of almost commuting operators and an extension of the Helton-Howe trace formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"Alexei Aleksandrov, Vladimir Peller","submitted_at":"2015-08-19T16:44:42Z","abstract_excerpt":"Let $A$ and $B$ be almost commuting (i.e., the commutator $AB-BA$ belongs to trace class) self-adjoint operators. We construct a functional calculus $\\varphi\\mapsto\\varphi(A,B)$ for functions $\\varphi$ in the Besov class $B_{\\infty,1}^1({\\Bbb R}^2)$. This functional calculus is linear, the operators $\\varphi(A,B)$ and $\\psi(A,B)$ almost commute for $\\varphi,\\,\\psi\\in B_{\\infty,1}^1({\\Bbb R}^2)$, and $\\varphi(A,B)=u(A)v(B)$ whenever $\\varphi(s,t)=u(s)v(t)$. We extend the Helton--Howe trace formula for arbitrary functions in $B_{\\infty,1}^1({\\Bbb R}^2)$. The main tool is triple operator integral"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04702","kind":"arxiv","version":1},"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":"2026-05-18T01:35:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pHtOpnBedbit1CdJAMFhcPVBF/OV/d4aweYj42qPzc0cJq9ccvJD4PjZ1jnm1H4JJPFL59BS7xK3hWgnaEouAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:22:24.741645Z"},"content_sha256":"36590da4da4af1435a903489f4ec6c0b4a8516ae56b3ce9cb6bd22dc0d617844","schema_version":"1.0","event_id":"sha256:36590da4da4af1435a903489f4ec6c0b4a8516ae56b3ce9cb6bd22dc0d617844"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHRXFZEE6QDCBDMRO4T7E3WDDI/bundle.json","state_url":"https://pith.science/pith/MHRXFZEE6QDCBDMRO4T7E3WDDI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHRXFZEE6QDCBDMRO4T7E3WDDI/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":"2026-05-31T05:22:24Z","links":{"resolver":"https://pith.science/pith/MHRXFZEE6QDCBDMRO4T7E3WDDI","bundle":"https://pith.science/pith/MHRXFZEE6QDCBDMRO4T7E3WDDI/bundle.json","state":"https://pith.science/pith/MHRXFZEE6QDCBDMRO4T7E3WDDI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHRXFZEE6QDCBDMRO4T7E3WDDI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MHRXFZEE6QDCBDMRO4T7E3WDDI","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":"a310c6b2ada39a48df550a099f1c9cda879db6ffb78ed0532a8116d6d396a03f","cross_cats_sorted":["math.CA","math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-19T16:44:42Z","title_canon_sha256":"d691fd35816bfb56aa534d36f5fc227f470c8f018fbd9f262c5fa10b5179de4b"},"schema_version":"1.0","source":{"id":"1508.04702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04702","created_at":"2026-05-18T01:35:02Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04702v1","created_at":"2026-05-18T01:35:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04702","created_at":"2026-05-18T01:35:02Z"},{"alias_kind":"pith_short_12","alias_value":"MHRXFZEE6QDC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MHRXFZEE6QDCBDMR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MHRXFZEE","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:36590da4da4af1435a903489f4ec6c0b4a8516ae56b3ce9cb6bd22dc0d617844","target":"graph","created_at":"2026-05-18T01:35:02Z","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 $A$ and $B$ be almost commuting (i.e., the commutator $AB-BA$ belongs to trace class) self-adjoint operators. We construct a functional calculus $\\varphi\\mapsto\\varphi(A,B)$ for functions $\\varphi$ in the Besov class $B_{\\infty,1}^1({\\Bbb R}^2)$. This functional calculus is linear, the operators $\\varphi(A,B)$ and $\\psi(A,B)$ almost commute for $\\varphi,\\,\\psi\\in B_{\\infty,1}^1({\\Bbb R}^2)$, and $\\varphi(A,B)=u(A)v(B)$ whenever $\\varphi(s,t)=u(s)v(t)$. We extend the Helton--Howe trace formula for arbitrary functions in $B_{\\infty,1}^1({\\Bbb R}^2)$. The main tool is triple operator integral","authors_text":"Alexei Aleksandrov, Vladimir Peller","cross_cats":["math.CA","math.CV","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-19T16:44:42Z","title":"Functions of almost commuting operators and an extension of the Helton-Howe trace formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04702","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":"sha256:37c7c68cc583494d8a37b1179adbee7f795a762649d638713901b4905d9e2f9d","target":"record","created_at":"2026-05-18T01:35:02Z","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":"a310c6b2ada39a48df550a099f1c9cda879db6ffb78ed0532a8116d6d396a03f","cross_cats_sorted":["math.CA","math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-19T16:44:42Z","title_canon_sha256":"d691fd35816bfb56aa534d36f5fc227f470c8f018fbd9f262c5fa10b5179de4b"},"schema_version":"1.0","source":{"id":"1508.04702","kind":"arxiv","version":1}},"canonical_sha256":"61e372e484f406208d917727f26ec31a2b41f63c8674cef8e73ff7de6a5a74bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61e372e484f406208d917727f26ec31a2b41f63c8674cef8e73ff7de6a5a74bf","first_computed_at":"2026-05-18T01:35:02.049936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:02.049936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ju9LC32zPdRE9RfHLEfIpOJcdPdkRCJvq4Lloj82BLA7NstOBZy+F/OoRcHkWDi+0kJwLe0I/T43N+Vd7PTCAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:02.050633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37c7c68cc583494d8a37b1179adbee7f795a762649d638713901b4905d9e2f9d","sha256:36590da4da4af1435a903489f4ec6c0b4a8516ae56b3ce9cb6bd22dc0d617844"],"state_sha256":"731c8d547a0236504bb1a41612315241a7694fe4abe40864cc44d6cd44ff804d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xYagJCF2o/Q2LPWxBkAWVdTKbTJxdhc6L34XU9HurwGHDs18GDirEwXkRk9WYJRBBHAJugRn4FceDL+YZH3pAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:22:24.745477Z","bundle_sha256":"ab5cde3ee0a43e88d0295acd1698e8132bf5a2ee2cbf60f08efa368a61211e30"}}