{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:STIE2VISFBPMHOKM2PJQE3IMAA","short_pith_number":"pith:STIE2VIS","canonical_record":{"source":{"id":"math/0603640","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2006-03-28T07:58:21Z","cross_cats_sorted":[],"title_canon_sha256":"d6843d80ba834775c00c1242fcfe600109f2c1dc3812321305392ec8b3583f8e","abstract_canon_sha256":"e9b245e81bff5043a97d96a44009aee2ec9a0d027d9ef3519ab1a061c2795989"},"schema_version":"1.0"},"canonical_sha256":"94d04d5512285ec3b94cd3d3026d0c002debc26af6c30b7d2b931bef8e2992f2","source":{"kind":"arxiv","id":"math/0603640","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0603640","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"math/0603640v1","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603640","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"STIE2VISFBPM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"STIE2VISFBPMHOKM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"STIE2VIS","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:STIE2VISFBPMHOKM2PJQE3IMAA","target":"record","payload":{"canonical_record":{"source":{"id":"math/0603640","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2006-03-28T07:58:21Z","cross_cats_sorted":[],"title_canon_sha256":"d6843d80ba834775c00c1242fcfe600109f2c1dc3812321305392ec8b3583f8e","abstract_canon_sha256":"e9b245e81bff5043a97d96a44009aee2ec9a0d027d9ef3519ab1a061c2795989"},"schema_version":"1.0"},"canonical_sha256":"94d04d5512285ec3b94cd3d3026d0c002debc26af6c30b7d2b931bef8e2992f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:42.145099Z","signature_b64":"RLmgoU/HoHyZ04o+ShkjcWf/8cKUOdT1JxP7+HcvORi/ef99ZorjRgIYGCzqWkhg2FVCyyuxT7mOFQhPvOd2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94d04d5512285ec3b94cd3d3026d0c002debc26af6c30b7d2b931bef8e2992f2","last_reissued_at":"2026-05-18T00:03:42.144659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:42.144659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0603640","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":"2026-05-18T00:03:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bc1xnZhI93xDxiINTHVYqvwZqSiJk+V977sLtzgEIwEec6IyBhYFYSH4eNRkwUzslT1Cn72HULY+zzW6rOLbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:27:24.299715Z"},"content_sha256":"8da155981efa14dec25d724ea9cc28d04022371a4fbf4530959333f84851eb53","schema_version":"1.0","event_id":"sha256:8da155981efa14dec25d724ea9cc28d04022371a4fbf4530959333f84851eb53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:STIE2VISFBPMHOKM2PJQE3IMAA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jos\\'e Maria Martell (IMFF), Pascal Auscher (LM-Orsay)","submitted_at":"2006-03-28T07:58:21Z","abstract_excerpt":"This is the first part of a series of four articles. In this work, we are interested in weighted norm estimates. We put the emphasis on two results of different nature: one is based on a good-$\\lambda$ inequality with two-parameters and the other uses Calder\\'on-Zygmund decomposition. These results apply well to singular 'non-integral' operators and their commutators with bounded mean oscillation functions. Singular means that they are of order 0, 'non-integral' that they do not have an integral representation by a kernel with size estimates, even rough, so that they may not be bounded on all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603640","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":"2026-05-18T00:03:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IB/+g3DKAtGILTT4gcDOo1d6qhwctekxKUrJXt2CsPHQRftNMlAPb7vnf9e+90A4iriKIjEMY02hLQhV6VkTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:27:24.300330Z"},"content_sha256":"7080e3965e5ce724e4e882eedb42201942004ef0be007a8db1f668d882dc4798","schema_version":"1.0","event_id":"sha256:7080e3965e5ce724e4e882eedb42201942004ef0be007a8db1f668d882dc4798"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/STIE2VISFBPMHOKM2PJQE3IMAA/bundle.json","state_url":"https://pith.science/pith/STIE2VISFBPMHOKM2PJQE3IMAA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/STIE2VISFBPMHOKM2PJQE3IMAA/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":"2026-06-06T21:27:24Z","links":{"resolver":"https://pith.science/pith/STIE2VISFBPMHOKM2PJQE3IMAA","bundle":"https://pith.science/pith/STIE2VISFBPMHOKM2PJQE3IMAA/bundle.json","state":"https://pith.science/pith/STIE2VISFBPMHOKM2PJQE3IMAA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/STIE2VISFBPMHOKM2PJQE3IMAA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:STIE2VISFBPMHOKM2PJQE3IMAA","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":"e9b245e81bff5043a97d96a44009aee2ec9a0d027d9ef3519ab1a061c2795989","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2006-03-28T07:58:21Z","title_canon_sha256":"d6843d80ba834775c00c1242fcfe600109f2c1dc3812321305392ec8b3583f8e"},"schema_version":"1.0","source":{"id":"math/0603640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0603640","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"math/0603640v1","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603640","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"STIE2VISFBPM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"STIE2VISFBPMHOKM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"STIE2VIS","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:7080e3965e5ce724e4e882eedb42201942004ef0be007a8db1f668d882dc4798","target":"graph","created_at":"2026-05-18T00:03:42Z","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":"This is the first part of a series of four articles. In this work, we are interested in weighted norm estimates. We put the emphasis on two results of different nature: one is based on a good-$\\lambda$ inequality with two-parameters and the other uses Calder\\'on-Zygmund decomposition. These results apply well to singular 'non-integral' operators and their commutators with bounded mean oscillation functions. Singular means that they are of order 0, 'non-integral' that they do not have an integral representation by a kernel with size estimates, even rough, so that they may not be bounded on all ","authors_text":"Jos\\'e Maria Martell (IMFF), Pascal Auscher (LM-Orsay)","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2006-03-28T07:58:21Z","title":"Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603640","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":"sha256:8da155981efa14dec25d724ea9cc28d04022371a4fbf4530959333f84851eb53","target":"record","created_at":"2026-05-18T00:03:42Z","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":"e9b245e81bff5043a97d96a44009aee2ec9a0d027d9ef3519ab1a061c2795989","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2006-03-28T07:58:21Z","title_canon_sha256":"d6843d80ba834775c00c1242fcfe600109f2c1dc3812321305392ec8b3583f8e"},"schema_version":"1.0","source":{"id":"math/0603640","kind":"arxiv","version":1}},"canonical_sha256":"94d04d5512285ec3b94cd3d3026d0c002debc26af6c30b7d2b931bef8e2992f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94d04d5512285ec3b94cd3d3026d0c002debc26af6c30b7d2b931bef8e2992f2","first_computed_at":"2026-05-18T00:03:42.144659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:42.144659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RLmgoU/HoHyZ04o+ShkjcWf/8cKUOdT1JxP7+HcvORi/ef99ZorjRgIYGCzqWkhg2FVCyyuxT7mOFQhPvOd2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:42.145099Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0603640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8da155981efa14dec25d724ea9cc28d04022371a4fbf4530959333f84851eb53","sha256:7080e3965e5ce724e4e882eedb42201942004ef0be007a8db1f668d882dc4798"],"state_sha256":"3e2e83d7df47fd8762002bbf036e11027b26631b84ef4a7c671b1986647c7026"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xxfLEyRpHbN0gOm+sBcV5kAXOWWYRFPeVmNj3XbZygnmPDGUgQIZO1jmtZ1X3NVgZmg0Izu+DUJ78nMK6XhlCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:27:24.303489Z","bundle_sha256":"30e7cb24a85793164b93b7c2bdc1545c7ed798d3a4e9bc8a25be3a17d204440d"}}