{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Q4WYQKESNK66YVCY7HTB6KPY5H","short_pith_number":"pith:Q4WYQKES","canonical_record":{"source":{"id":"1112.4292","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-19T10:35:01Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"0218822ffcb3703a6f544a204c5b40f264b08c8924dc74f7ac1c81170d88a041","abstract_canon_sha256":"08eb6c0d4a5660399e91b72c35544c42af214bfba496e430158c951137bfa3dd"},"schema_version":"1.0"},"canonical_sha256":"872d8828926abdec5458f9e61f29f8e9df49f5d6332b4858a75ff39fe5444273","source":{"kind":"arxiv","id":"1112.4292","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4292","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4292v2","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4292","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"Q4WYQKESNK66","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q4WYQKESNK66YVCY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q4WYQKES","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Q4WYQKESNK66YVCY7HTB6KPY5H","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4292","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-19T10:35:01Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"0218822ffcb3703a6f544a204c5b40f264b08c8924dc74f7ac1c81170d88a041","abstract_canon_sha256":"08eb6c0d4a5660399e91b72c35544c42af214bfba496e430158c951137bfa3dd"},"schema_version":"1.0"},"canonical_sha256":"872d8828926abdec5458f9e61f29f8e9df49f5d6332b4858a75ff39fe5444273","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:49.166151Z","signature_b64":"ja3oGB4Z0VeQzZm4iKemVwoAjYIMBPR2ZP7fqujYrCkfzMQEmsPar1HZV4WltwLUs2NrO+AheV7Xi8HBNI6lDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"872d8828926abdec5458f9e61f29f8e9df49f5d6332b4858a75ff39fe5444273","last_reissued_at":"2026-05-18T03:59:49.165747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:49.165747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4292","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":"2026-05-18T03:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M2fgt3ZnaQBHKZSoWFgChXgybmRFZDKX7CVBKGH6X9IFwPIwnNzR4a6Kdl2wf4Fzgkc8o1utZAIcQ8nBfO7cDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:13:06.036269Z"},"content_sha256":"66f21501bef366b807bc946782f282528181d6b855bdc7facf9f0e7ec5c0986f","schema_version":"1.0","event_id":"sha256:66f21501bef366b807bc946782f282528181d6b855bdc7facf9f0e7ec5c0986f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Q4WYQKESNK66YVCY7HTB6KPY5H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular integral operators on tent spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Christoph Kriegler, Pascal Auscher (LM-Orsay), Pierre Portal (MSI), Sylvie Monniaux (LATP)","submitted_at":"2011-12-19T10:35:01Z","abstract_excerpt":"We extend the recent results concerning boundedness of the maximal regularity operator on tent spaces. This leads us to develop a singular integral operator theory on tent spaces. Such operators have operator-valued kernels. A seemingly appropriate condition on the kernel is time-space decay measured by off-diagonal estimates with various exponents."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4292","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":"2026-05-18T03:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5eN5um5sU30FgRGL7XyNt1fnJXHKdF3kEvkuL6aBe0EGKaF0sRle1ywmvJEWed6/M96vvzfy1o6aehkT9zHrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:13:06.036959Z"},"content_sha256":"7d35268120f4ff29bf8461c66a46a22a16859d79265e4c499926646f696115ab","schema_version":"1.0","event_id":"sha256:7d35268120f4ff29bf8461c66a46a22a16859d79265e4c499926646f696115ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4WYQKESNK66YVCY7HTB6KPY5H/bundle.json","state_url":"https://pith.science/pith/Q4WYQKESNK66YVCY7HTB6KPY5H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4WYQKESNK66YVCY7HTB6KPY5H/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":"2026-06-06T20:13:06Z","links":{"resolver":"https://pith.science/pith/Q4WYQKESNK66YVCY7HTB6KPY5H","bundle":"https://pith.science/pith/Q4WYQKESNK66YVCY7HTB6KPY5H/bundle.json","state":"https://pith.science/pith/Q4WYQKESNK66YVCY7HTB6KPY5H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4WYQKESNK66YVCY7HTB6KPY5H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Q4WYQKESNK66YVCY7HTB6KPY5H","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":"08eb6c0d4a5660399e91b72c35544c42af214bfba496e430158c951137bfa3dd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-19T10:35:01Z","title_canon_sha256":"0218822ffcb3703a6f544a204c5b40f264b08c8924dc74f7ac1c81170d88a041"},"schema_version":"1.0","source":{"id":"1112.4292","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4292","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4292v2","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4292","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"Q4WYQKESNK66","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q4WYQKESNK66YVCY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q4WYQKES","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:7d35268120f4ff29bf8461c66a46a22a16859d79265e4c499926646f696115ab","target":"graph","created_at":"2026-05-18T03:59:49Z","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 extend the recent results concerning boundedness of the maximal regularity operator on tent spaces. This leads us to develop a singular integral operator theory on tent spaces. Such operators have operator-valued kernels. A seemingly appropriate condition on the kernel is time-space decay measured by off-diagonal estimates with various exponents.","authors_text":"Christoph Kriegler, Pascal Auscher (LM-Orsay), Pierre Portal (MSI), Sylvie Monniaux (LATP)","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-19T10:35:01Z","title":"Singular integral operators on tent spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4292","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":"sha256:66f21501bef366b807bc946782f282528181d6b855bdc7facf9f0e7ec5c0986f","target":"record","created_at":"2026-05-18T03:59:49Z","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":"08eb6c0d4a5660399e91b72c35544c42af214bfba496e430158c951137bfa3dd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-19T10:35:01Z","title_canon_sha256":"0218822ffcb3703a6f544a204c5b40f264b08c8924dc74f7ac1c81170d88a041"},"schema_version":"1.0","source":{"id":"1112.4292","kind":"arxiv","version":2}},"canonical_sha256":"872d8828926abdec5458f9e61f29f8e9df49f5d6332b4858a75ff39fe5444273","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"872d8828926abdec5458f9e61f29f8e9df49f5d6332b4858a75ff39fe5444273","first_computed_at":"2026-05-18T03:59:49.165747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:49.165747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ja3oGB4Z0VeQzZm4iKemVwoAjYIMBPR2ZP7fqujYrCkfzMQEmsPar1HZV4WltwLUs2NrO+AheV7Xi8HBNI6lDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:49.166151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4292","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66f21501bef366b807bc946782f282528181d6b855bdc7facf9f0e7ec5c0986f","sha256:7d35268120f4ff29bf8461c66a46a22a16859d79265e4c499926646f696115ab"],"state_sha256":"f54b7836e9991b086e3c6dcfea7aacd1f39a96db66b2f90bc7e801fcbb0650d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3T3uPzOb3jPOwFyVjvQ1j2M2NDvZYdv9fqPx8ef5J6NIY+rhtq7+AOvJMNkZDjPACp44ubCyoMXMg46RhzH4Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:13:06.039580Z","bundle_sha256":"e9a4a97af5d4215cbefba568f8a98cb786c83f4f0b15c2d68089ba5498802d5e"}}