{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:XHQMCRBPPEXMNSBQZ76IJVR6F3","short_pith_number":"pith:XHQMCRBP","canonical_record":{"source":{"id":"0810.3073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-10-17T06:58:30Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"dd2f27e4f7fab99f66caddff1c8c9de5cfce3edb836427f4de0b615c512dd5c6","abstract_canon_sha256":"87266f1663f09f8e6fc74b86d5d94fdf2fdf5648beed94f23ec2f42b6cb1a1e2"},"schema_version":"1.0"},"canonical_sha256":"b9e0c1442f792ec6c830cffc84d63e2eefc60928b33d5ccb8bd28bad74115e5e","source":{"kind":"arxiv","id":"0810.3073","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.3073","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"0810.3073v1","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.3073","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"XHQMCRBPPEXM","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"XHQMCRBPPEXMNSBQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"XHQMCRBP","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:XHQMCRBPPEXMNSBQZ76IJVR6F3","target":"record","payload":{"canonical_record":{"source":{"id":"0810.3073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-10-17T06:58:30Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"dd2f27e4f7fab99f66caddff1c8c9de5cfce3edb836427f4de0b615c512dd5c6","abstract_canon_sha256":"87266f1663f09f8e6fc74b86d5d94fdf2fdf5648beed94f23ec2f42b6cb1a1e2"},"schema_version":"1.0"},"canonical_sha256":"b9e0c1442f792ec6c830cffc84d63e2eefc60928b33d5ccb8bd28bad74115e5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:50.775027Z","signature_b64":"SCR3iZtwryh+O1Q+9OEJfjVcGcUKfVPZ3ytCyhk8V141oNQ0GowMkxOaUDBVfUzdIIaLRw7pVwz62vYnajpSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9e0c1442f792ec6c830cffc84d63e2eefc60928b33d5ccb8bd28bad74115e5e","last_reissued_at":"2026-05-18T00:03:50.774391Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:50.774391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.3073","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":"2026-05-18T00:03:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"379GdcyjeqXzV8RhgfW3IF9bBm0PtNQwO6X4atsXtLIDV2YTmK3aSYlgfd7VfYz3nY2SwZae4BN0kltpmmS2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T00:09:08.624484Z"},"content_sha256":"3cc9ef535ce4c0b0e9811120b2b5054546ad9ea01dd5c5f7b32f73519397aa7e","schema_version":"1.0","event_id":"sha256:3cc9ef535ce4c0b0e9811120b2b5054546ad9ea01dd5c5f7b32f73519397aa7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:XHQMCRBPPEXMNSBQZ76IJVR6F3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted norm inequalities, off-diagonal estimates and elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.CA","authors_text":"Jos\\'e Maria Martell (IMFF), Pascal Auscher (LM-Orsay)","submitted_at":"2008-10-17T06:58:30Z","abstract_excerpt":"We give an overview of the generalized Calder\\'on-Zygmund theory for \"non-integral\" singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted estimates for such operators and their commutators with $\\BMO$ functions. $L^p-L^q$ off-diagonal estimates when $p\\le q$ play an important role and we present them. They are particularly well suited to the semigroups generated by second order elliptic operators and the range of exponents $(p,q)$ rules the $L^p$ theory for many operators constructed from the semi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.3073","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":"2026-05-18T00:03:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXCQOJcMiAuygi7RlK89YWZ+3qg5v1dHb9lreCirmbb99Gm61dMO7b+DCAPdFxvIGghZ4+8ei+pT8Ih5w1zVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T00:09:08.625157Z"},"content_sha256":"9b1297e2ee8e2e05f6c4c8005c50465f3189b08d29fbcdc5571b8b6d00d4a6fe","schema_version":"1.0","event_id":"sha256:9b1297e2ee8e2e05f6c4c8005c50465f3189b08d29fbcdc5571b8b6d00d4a6fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XHQMCRBPPEXMNSBQZ76IJVR6F3/bundle.json","state_url":"https://pith.science/pith/XHQMCRBPPEXMNSBQZ76IJVR6F3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XHQMCRBPPEXMNSBQZ76IJVR6F3/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":"2026-06-07T00:09:08Z","links":{"resolver":"https://pith.science/pith/XHQMCRBPPEXMNSBQZ76IJVR6F3","bundle":"https://pith.science/pith/XHQMCRBPPEXMNSBQZ76IJVR6F3/bundle.json","state":"https://pith.science/pith/XHQMCRBPPEXMNSBQZ76IJVR6F3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XHQMCRBPPEXMNSBQZ76IJVR6F3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:XHQMCRBPPEXMNSBQZ76IJVR6F3","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":"87266f1663f09f8e6fc74b86d5d94fdf2fdf5648beed94f23ec2f42b6cb1a1e2","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-10-17T06:58:30Z","title_canon_sha256":"dd2f27e4f7fab99f66caddff1c8c9de5cfce3edb836427f4de0b615c512dd5c6"},"schema_version":"1.0","source":{"id":"0810.3073","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.3073","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"0810.3073v1","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.3073","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"XHQMCRBPPEXM","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"XHQMCRBPPEXMNSBQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"XHQMCRBP","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:9b1297e2ee8e2e05f6c4c8005c50465f3189b08d29fbcdc5571b8b6d00d4a6fe","target":"graph","created_at":"2026-05-18T00:03:50Z","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 give an overview of the generalized Calder\\'on-Zygmund theory for \"non-integral\" singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted estimates for such operators and their commutators with $\\BMO$ functions. $L^p-L^q$ off-diagonal estimates when $p\\le q$ play an important role and we present them. They are particularly well suited to the semigroups generated by second order elliptic operators and the range of exponents $(p,q)$ rules the $L^p$ theory for many operators constructed from the semi","authors_text":"Jos\\'e Maria Martell (IMFF), Pascal Auscher (LM-Orsay)","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-10-17T06:58:30Z","title":"Weighted norm inequalities, off-diagonal estimates and elliptic operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.3073","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":"sha256:3cc9ef535ce4c0b0e9811120b2b5054546ad9ea01dd5c5f7b32f73519397aa7e","target":"record","created_at":"2026-05-18T00:03:50Z","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":"87266f1663f09f8e6fc74b86d5d94fdf2fdf5648beed94f23ec2f42b6cb1a1e2","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-10-17T06:58:30Z","title_canon_sha256":"dd2f27e4f7fab99f66caddff1c8c9de5cfce3edb836427f4de0b615c512dd5c6"},"schema_version":"1.0","source":{"id":"0810.3073","kind":"arxiv","version":1}},"canonical_sha256":"b9e0c1442f792ec6c830cffc84d63e2eefc60928b33d5ccb8bd28bad74115e5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9e0c1442f792ec6c830cffc84d63e2eefc60928b33d5ccb8bd28bad74115e5e","first_computed_at":"2026-05-18T00:03:50.774391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:50.774391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SCR3iZtwryh+O1Q+9OEJfjVcGcUKfVPZ3ytCyhk8V141oNQ0GowMkxOaUDBVfUzdIIaLRw7pVwz62vYnajpSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:50.775027Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.3073","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cc9ef535ce4c0b0e9811120b2b5054546ad9ea01dd5c5f7b32f73519397aa7e","sha256:9b1297e2ee8e2e05f6c4c8005c50465f3189b08d29fbcdc5571b8b6d00d4a6fe"],"state_sha256":"2c1e1b17f9cc95c34d76ff793ce2fd2e9de4ddbace777b3e430d55a1815c8f6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Cgvo9bMvQbDv6MPb6rsUoEpti7uEdHWwaZ4b9aH4m7+M/Oovi8IQ9j0lFH0TUci6thoW95k0YsQZq2Ntu95Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T00:09:08.628889Z","bundle_sha256":"2a917c4a0c045bcbea5aff318286d70ca829c7d5dcbd1adbde62d9237b6ca88e"}}