{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GVIA5UM3IO2DTIL6NCW7YZ2G5Y","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":"3aa11900feb874485ce5b06593098c162816438a1837c251b748a309c3574ea5","cross_cats_sorted":["math.FA","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-17T19:15:40Z","title_canon_sha256":"75e95ad3f8d0cf52a5559eace81e820e81d7c37076e1b2ab4dc79d117fe64907"},"schema_version":"1.0","source":{"id":"1304.4922","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4922","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4922v1","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4922","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"GVIA5UM3IO2D","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GVIA5UM3IO2DTIL6","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GVIA5UM3","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:2692fa81ea6054981d53c26cf2ac879361605cca0e4f79916daa05a4c7ec660e","target":"graph","created_at":"2026-05-18T03:27:43Z","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 article is an introduction to our recent work in harmonic analysis associated with semigroups of operators, in the effort of finding a noncommutative Calder\\'on-Zygmund theory for von Neumann algebras. The classical CZ theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of such metrics -or with very little information on the metric- Markov semigroups of operators appear to be the right substitutes of classical metric/geometric tools in harmonic analysis. Our approach is particularly useful in the noncommutative setting ","authors_text":"Javier Parcet, Marius Junge, Tao Mei","cross_cats":["math.FA","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-17T19:15:40Z","title":"An invitation to harmonic analysis associated with semigroups of operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4922","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":"sha256:53d79b2bee80ee91c6fbccc2975527bd73fb5a42aa47d30ec3f84ea8ebdd05c7","target":"record","created_at":"2026-05-18T03:27:43Z","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":"3aa11900feb874485ce5b06593098c162816438a1837c251b748a309c3574ea5","cross_cats_sorted":["math.FA","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-17T19:15:40Z","title_canon_sha256":"75e95ad3f8d0cf52a5559eace81e820e81d7c37076e1b2ab4dc79d117fe64907"},"schema_version":"1.0","source":{"id":"1304.4922","kind":"arxiv","version":1}},"canonical_sha256":"35500ed19b43b439a17e68adfc6746ee399343e314d1cb539eef44bc84238906","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35500ed19b43b439a17e68adfc6746ee399343e314d1cb539eef44bc84238906","first_computed_at":"2026-05-18T03:27:43.183102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:43.183102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZbiKfpGbry7d8w2Fvwa7JKcfmQPHsHF32rGaPE3VCbw66asovy5Bg2cZJRYnNcQV+BXFupEJmbF0O+qoXN7zCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:43.183826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4922","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53d79b2bee80ee91c6fbccc2975527bd73fb5a42aa47d30ec3f84ea8ebdd05c7","sha256:2692fa81ea6054981d53c26cf2ac879361605cca0e4f79916daa05a4c7ec660e"],"state_sha256":"43c4ec9617341b70fac099a0e98e17abf424a324ec7969f04dda5c7183ab9286"}