{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VZ43ZRLAGL5DLTYP3FC2N7QZSO","short_pith_number":"pith:VZ43ZRLA","canonical_record":{"source":{"id":"1304.3873","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-14T02:59:09Z","cross_cats_sorted":[],"title_canon_sha256":"2ff2c5935d045e20e34c563f0ed311005b0d94f2893fd64d423057a42ccc20f5","abstract_canon_sha256":"84559dd41cb01fb33f2f496b2a0d29f34200a4e2a474db02be92047020949b07"},"schema_version":"1.0"},"canonical_sha256":"ae79bcc56032fa35cf0fd945a6fe199390f63a4b5928aee5a831c623403ea479","source":{"kind":"arxiv","id":"1304.3873","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3873","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3873v2","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3873","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"VZ43ZRLAGL5D","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VZ43ZRLAGL5DLTYP","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VZ43ZRLA","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VZ43ZRLAGL5DLTYP3FC2N7QZSO","target":"record","payload":{"canonical_record":{"source":{"id":"1304.3873","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-14T02:59:09Z","cross_cats_sorted":[],"title_canon_sha256":"2ff2c5935d045e20e34c563f0ed311005b0d94f2893fd64d423057a42ccc20f5","abstract_canon_sha256":"84559dd41cb01fb33f2f496b2a0d29f34200a4e2a474db02be92047020949b07"},"schema_version":"1.0"},"canonical_sha256":"ae79bcc56032fa35cf0fd945a6fe199390f63a4b5928aee5a831c623403ea479","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:21.459949Z","signature_b64":"pNLqGO2Wa3HEQPpPdkRPXlSolHaHjlAErl/KjPXjSkwLf0G3UPQJ4L+qeOuQfHvEQ9iVYhdcsNh0u2GmmQCnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae79bcc56032fa35cf0fd945a6fe199390f63a4b5928aee5a831c623403ea479","last_reissued_at":"2026-05-18T01:02:21.459256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:21.459256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.3873","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":"2026-05-18T01:02:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7eQ43IKIKUy3XCzjNJPso/QKqQTRVbajwYanRPA6dmFmPDkDxdPKyzz+RfqRf8Iu0XCN4pVDRSp3ZbM/FxDEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:06:43.150677Z"},"content_sha256":"872cda015edde5d5458846e9474c9a830155068a9855c4aa03dac87e69f4fdb8","schema_version":"1.0","event_id":"sha256:872cda015edde5d5458846e9474c9a830155068a9855c4aa03dac87e69f4fdb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VZ43ZRLAGL5DLTYP3FC2N7QZSO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on weak convergence of singular integrals in metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mariusz Urba\\'nski, Vasilis Chousionis","submitted_at":"2013-04-14T02:59:09Z","abstract_excerpt":"We prove that in any metric space $(X,d)$ the singular integral operators {equation*} T^k_{\\mu,\\ve}(f)(x)=\\int_{X\\setminus B(x,\\varepsilon)}k(x,y)f(y)d\\mu (y).{equation*} converge weakly in some dense subspaces of $L^2(\\mu)$ under minimal regularity assumptions for the measures and the kernels."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3873","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":"2026-05-18T01:02:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hU3kszt9NMC9mKs9ZHK0HMXm3fH8xIOHObyL0gg7fb9V2svWveulnOVLYkk4DP5pNEfwUBJF5cVo3JBrSHlqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:06:43.151181Z"},"content_sha256":"7f484dab81b070448d64e20e9903c5e17a626e7efd4f2cf2102a67841f23b69b","schema_version":"1.0","event_id":"sha256:7f484dab81b070448d64e20e9903c5e17a626e7efd4f2cf2102a67841f23b69b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZ43ZRLAGL5DLTYP3FC2N7QZSO/bundle.json","state_url":"https://pith.science/pith/VZ43ZRLAGL5DLTYP3FC2N7QZSO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZ43ZRLAGL5DLTYP3FC2N7QZSO/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":"2026-06-08T03:06:43Z","links":{"resolver":"https://pith.science/pith/VZ43ZRLAGL5DLTYP3FC2N7QZSO","bundle":"https://pith.science/pith/VZ43ZRLAGL5DLTYP3FC2N7QZSO/bundle.json","state":"https://pith.science/pith/VZ43ZRLAGL5DLTYP3FC2N7QZSO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZ43ZRLAGL5DLTYP3FC2N7QZSO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VZ43ZRLAGL5DLTYP3FC2N7QZSO","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":"84559dd41cb01fb33f2f496b2a0d29f34200a4e2a474db02be92047020949b07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-14T02:59:09Z","title_canon_sha256":"2ff2c5935d045e20e34c563f0ed311005b0d94f2893fd64d423057a42ccc20f5"},"schema_version":"1.0","source":{"id":"1304.3873","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3873","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3873v2","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3873","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"VZ43ZRLAGL5D","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VZ43ZRLAGL5DLTYP","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VZ43ZRLA","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:7f484dab81b070448d64e20e9903c5e17a626e7efd4f2cf2102a67841f23b69b","target":"graph","created_at":"2026-05-18T01:02:21Z","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":"We prove that in any metric space $(X,d)$ the singular integral operators {equation*} T^k_{\\mu,\\ve}(f)(x)=\\int_{X\\setminus B(x,\\varepsilon)}k(x,y)f(y)d\\mu (y).{equation*} converge weakly in some dense subspaces of $L^2(\\mu)$ under minimal regularity assumptions for the measures and the kernels.","authors_text":"Mariusz Urba\\'nski, Vasilis Chousionis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-14T02:59:09Z","title":"A note on weak convergence of singular integrals in metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3873","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":"sha256:872cda015edde5d5458846e9474c9a830155068a9855c4aa03dac87e69f4fdb8","target":"record","created_at":"2026-05-18T01:02:21Z","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":"84559dd41cb01fb33f2f496b2a0d29f34200a4e2a474db02be92047020949b07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-14T02:59:09Z","title_canon_sha256":"2ff2c5935d045e20e34c563f0ed311005b0d94f2893fd64d423057a42ccc20f5"},"schema_version":"1.0","source":{"id":"1304.3873","kind":"arxiv","version":2}},"canonical_sha256":"ae79bcc56032fa35cf0fd945a6fe199390f63a4b5928aee5a831c623403ea479","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae79bcc56032fa35cf0fd945a6fe199390f63a4b5928aee5a831c623403ea479","first_computed_at":"2026-05-18T01:02:21.459256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:21.459256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pNLqGO2Wa3HEQPpPdkRPXlSolHaHjlAErl/KjPXjSkwLf0G3UPQJ4L+qeOuQfHvEQ9iVYhdcsNh0u2GmmQCnCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:21.459949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.3873","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:872cda015edde5d5458846e9474c9a830155068a9855c4aa03dac87e69f4fdb8","sha256:7f484dab81b070448d64e20e9903c5e17a626e7efd4f2cf2102a67841f23b69b"],"state_sha256":"594fb637c192a4658fbf57d4d6461345e6a61d001f03194002a152b02e173621"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZzffM/O2gIUevTpDhk0lmZ+CxHKMxkQyNteLTTuNPBiYCnB4tIAs5crLFf1DY1YBRgB8aXzIAD3tX94qLCX1Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T03:06:43.153398Z","bundle_sha256":"0397fec02e8cdf434816c1e2abe11cc1f8d17bdb945f719d3dd7d25359363053"}}