{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BPZU476IEC2UBTUXTF4Y6MZ764","short_pith_number":"pith:BPZU476I","canonical_record":{"source":{"id":"1104.3553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-18T18:11:36Z","cross_cats_sorted":["math.CA","math.CV","math.SP"],"title_canon_sha256":"5beee7bc4dc59f7379eab47333ec819ba3cadde8ccd06c295aaa404b4b096e7f","abstract_canon_sha256":"0202f51e61c23d8a3eed758fffa358c52f79bd54a28b66fd62394bf5d210be10"},"schema_version":"1.0"},"canonical_sha256":"0bf34e7fc820b540ce9799798f333ff73f569e7cb1222e36dbb57e1d77ac29e0","source":{"kind":"arxiv","id":"1104.3553","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3553","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3553v1","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3553","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"BPZU476IEC2U","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BPZU476IEC2UBTUX","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BPZU476I","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BPZU476IEC2UBTUXTF4Y6MZ764","target":"record","payload":{"canonical_record":{"source":{"id":"1104.3553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-18T18:11:36Z","cross_cats_sorted":["math.CA","math.CV","math.SP"],"title_canon_sha256":"5beee7bc4dc59f7379eab47333ec819ba3cadde8ccd06c295aaa404b4b096e7f","abstract_canon_sha256":"0202f51e61c23d8a3eed758fffa358c52f79bd54a28b66fd62394bf5d210be10"},"schema_version":"1.0"},"canonical_sha256":"0bf34e7fc820b540ce9799798f333ff73f569e7cb1222e36dbb57e1d77ac29e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:04.505230Z","signature_b64":"A6VF8mdKx3N7MLieP9OPUmrTgS/H8bQcGQ22bo/2svNLwpiq5s/eg9mdimaTRWETZW5o0DyaVgBkto18urDgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bf34e7fc820b540ce9799798f333ff73f569e7cb1222e36dbb57e1d77ac29e0","last_reissued_at":"2026-05-18T04:24:04.504690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:04.504690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.3553","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":"2026-05-18T04:24:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BMGqwhs+/zPSKdxrqMHsrWrxK5ftlT8X6aL0h4wm5uzt7n75N0MkFLRzNp591Kyzm7jI5yDFPLpVB14qD4T7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:43:00.429014Z"},"content_sha256":"1d438074dc0197b4b84c1be2e3467a752c8e145c0d73335c9275267635294c18","schema_version":"1.0","event_id":"sha256:1d438074dc0197b4b84c1be2e3467a752c8e145c0d73335c9275267635294c18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BPZU476IEC2UBTUXTF4Y6MZ764","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimates of operator moduli of continuity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"Aleksei Aleksandrov, Vladimir Peller","submitted_at":"2011-04-18T18:11:36Z","abstract_excerpt":"In \\cite{AP2} we obtained general estimates of the operator moduli of continuity of functions on the real line. In this paper we improve the estimates obtained in \\cite{AP2} for certain special classes of functions.\n  In particular, we improve estimates of Kato \\cite{Ka} and show that $$ \\big\\|\\,|S|-|T|\\,\\big\\|\\le C\\|S-T\\|\\log(2+\\log\\frac{\\|S\\|+\\|T\\|}{\\|S-T\\|}) $$ for every bounded operators $S$ and $T$ on Hilbert space. Here $|S|\\df(S^*S)^{1/2}$. Moreover, we show that this inequality is sharp.\n  We prove in this paper that if $f$ is a nondecreasing continuous function on $\\R$ that vanishes o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3553","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":"2026-05-18T04:24:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m32epzB7XKwLqcgrpeqJW+i4tsoRIHK+uI95fxHY0+gfzZIRcfBgqfiEVH1MUVn3vKmdYJPtHcVtGEN7XVxRCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:43:00.429709Z"},"content_sha256":"65145bf01d3497e5d91929ff65a30f9bc66c7915d0d1bd135d2c81d60d776d28","schema_version":"1.0","event_id":"sha256:65145bf01d3497e5d91929ff65a30f9bc66c7915d0d1bd135d2c81d60d776d28"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BPZU476IEC2UBTUXTF4Y6MZ764/bundle.json","state_url":"https://pith.science/pith/BPZU476IEC2UBTUXTF4Y6MZ764/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BPZU476IEC2UBTUXTF4Y6MZ764/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":"2026-05-31T00:43:00Z","links":{"resolver":"https://pith.science/pith/BPZU476IEC2UBTUXTF4Y6MZ764","bundle":"https://pith.science/pith/BPZU476IEC2UBTUXTF4Y6MZ764/bundle.json","state":"https://pith.science/pith/BPZU476IEC2UBTUXTF4Y6MZ764/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BPZU476IEC2UBTUXTF4Y6MZ764/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BPZU476IEC2UBTUXTF4Y6MZ764","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":"0202f51e61c23d8a3eed758fffa358c52f79bd54a28b66fd62394bf5d210be10","cross_cats_sorted":["math.CA","math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-18T18:11:36Z","title_canon_sha256":"5beee7bc4dc59f7379eab47333ec819ba3cadde8ccd06c295aaa404b4b096e7f"},"schema_version":"1.0","source":{"id":"1104.3553","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3553","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3553v1","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3553","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"BPZU476IEC2U","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BPZU476IEC2UBTUX","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BPZU476I","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:65145bf01d3497e5d91929ff65a30f9bc66c7915d0d1bd135d2c81d60d776d28","target":"graph","created_at":"2026-05-18T04:24:04Z","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":"In \\cite{AP2} we obtained general estimates of the operator moduli of continuity of functions on the real line. In this paper we improve the estimates obtained in \\cite{AP2} for certain special classes of functions.\n  In particular, we improve estimates of Kato \\cite{Ka} and show that $$ \\big\\|\\,|S|-|T|\\,\\big\\|\\le C\\|S-T\\|\\log(2+\\log\\frac{\\|S\\|+\\|T\\|}{\\|S-T\\|}) $$ for every bounded operators $S$ and $T$ on Hilbert space. Here $|S|\\df(S^*S)^{1/2}$. Moreover, we show that this inequality is sharp.\n  We prove in this paper that if $f$ is a nondecreasing continuous function on $\\R$ that vanishes o","authors_text":"Aleksei 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":"2011-04-18T18:11:36Z","title":"Estimates of operator moduli of continuity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3553","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":"sha256:1d438074dc0197b4b84c1be2e3467a752c8e145c0d73335c9275267635294c18","target":"record","created_at":"2026-05-18T04:24:04Z","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":"0202f51e61c23d8a3eed758fffa358c52f79bd54a28b66fd62394bf5d210be10","cross_cats_sorted":["math.CA","math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-18T18:11:36Z","title_canon_sha256":"5beee7bc4dc59f7379eab47333ec819ba3cadde8ccd06c295aaa404b4b096e7f"},"schema_version":"1.0","source":{"id":"1104.3553","kind":"arxiv","version":1}},"canonical_sha256":"0bf34e7fc820b540ce9799798f333ff73f569e7cb1222e36dbb57e1d77ac29e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bf34e7fc820b540ce9799798f333ff73f569e7cb1222e36dbb57e1d77ac29e0","first_computed_at":"2026-05-18T04:24:04.504690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:04.504690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A6VF8mdKx3N7MLieP9OPUmrTgS/H8bQcGQ22bo/2svNLwpiq5s/eg9mdimaTRWETZW5o0DyaVgBkto18urDgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:04.505230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3553","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d438074dc0197b4b84c1be2e3467a752c8e145c0d73335c9275267635294c18","sha256:65145bf01d3497e5d91929ff65a30f9bc66c7915d0d1bd135d2c81d60d776d28"],"state_sha256":"349090271bfea0a054307a16ed875bd541676e292cf6f83d4ef9a95194854b98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ydxJWP0+3Kx4g/erkDSurV1jqRRQDQfLf6i9x4gxK6ZbpV+NI4+G8l6zPvmNn3AL9LwunYgKPVWMJHeHu50bDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:43:00.433050Z","bundle_sha256":"8d61ec9b00f0cd6d827e7c9607e5c79558b571bdda367572b0e4ef9199a1c82a"}}