{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MNCC3GPBUYMJE4WLAC5CU4SQ6G","short_pith_number":"pith:MNCC3GPB","schema_version":"1.0","canonical_sha256":"63442d99e1a6189272cb00ba2a7250f19430f44134bbed94f731f511c31fbafb","source":{"kind":"arxiv","id":"1604.03711","version":1},"attestation_state":"computed","paper":{"title":"Nondoubling Calder\\'on-Zygmund theory -a dyadic approach-","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Javier Parcet, Jose M. Conde Alonso","submitted_at":"2016-04-13T10:08:21Z","abstract_excerpt":"Given a measure $\\mu$ of polynomial growth, we refine a deep result by David and Mattila to construct an atomic martingale filtration of $\\mathrm{supp}(\\mu)$ which provides the right framework for a dyadic form of nondoubling harmonic analysis. Despite this filtration being highly irregular, its atoms are comparable to balls in the given metric |which in turn are all doubling| and satisfy a weaker but crucial form of regularity. Our dyadic formulation is effective to address three basic questions:\n  i) A dyadic form of Tolsa's RBMO space which contains it.\n  ii) Lerner's domination and $A_2$-t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1604.03711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-04-13T10:08:21Z","cross_cats_sorted":[],"title_canon_sha256":"f90531dc8ab5f557957fdab981b6c7463817fb2399c5e76d948185a51593ea01","abstract_canon_sha256":"8c469c6447852d58086f441cbc18ee4db3d80f2b75eb19d598349a47ff287092"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:11.869595Z","signature_b64":"+eBAPYTl7hXSwFCki2LxXVILctooQVV/yi9ipEoTGd+Ru6d9++x+6y9y5u7YP0cqhJP+TVTDCsB/CFkGwugRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63442d99e1a6189272cb00ba2a7250f19430f44134bbed94f731f511c31fbafb","last_reissued_at":"2026-05-18T01:17:11.868957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:11.868957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nondoubling Calder\\'on-Zygmund theory -a dyadic approach-","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Javier Parcet, Jose M. Conde Alonso","submitted_at":"2016-04-13T10:08:21Z","abstract_excerpt":"Given a measure $\\mu$ of polynomial growth, we refine a deep result by David and Mattila to construct an atomic martingale filtration of $\\mathrm{supp}(\\mu)$ which provides the right framework for a dyadic form of nondoubling harmonic analysis. Despite this filtration being highly irregular, its atoms are comparable to balls in the given metric |which in turn are all doubling| and satisfy a weaker but crucial form of regularity. Our dyadic formulation is effective to address three basic questions:\n  i) A dyadic form of Tolsa's RBMO space which contains it.\n  ii) Lerner's domination and $A_2$-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03711","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1604.03711","created_at":"2026-05-18T01:17:11.869047+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.03711v1","created_at":"2026-05-18T01:17:11.869047+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03711","created_at":"2026-05-18T01:17:11.869047+00:00"},{"alias_kind":"pith_short_12","alias_value":"MNCC3GPBUYMJ","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MNCC3GPBUYMJE4WL","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MNCC3GPB","created_at":"2026-05-18T12:30:32.724797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MNCC3GPBUYMJE4WLAC5CU4SQ6G","json":"https://pith.science/pith/MNCC3GPBUYMJE4WLAC5CU4SQ6G.json","graph_json":"https://pith.science/api/pith-number/MNCC3GPBUYMJE4WLAC5CU4SQ6G/graph.json","events_json":"https://pith.science/api/pith-number/MNCC3GPBUYMJE4WLAC5CU4SQ6G/events.json","paper":"https://pith.science/paper/MNCC3GPB"},"agent_actions":{"view_html":"https://pith.science/pith/MNCC3GPBUYMJE4WLAC5CU4SQ6G","download_json":"https://pith.science/pith/MNCC3GPBUYMJE4WLAC5CU4SQ6G.json","view_paper":"https://pith.science/paper/MNCC3GPB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.03711&json=true","fetch_graph":"https://pith.science/api/pith-number/MNCC3GPBUYMJE4WLAC5CU4SQ6G/graph.json","fetch_events":"https://pith.science/api/pith-number/MNCC3GPBUYMJE4WLAC5CU4SQ6G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MNCC3GPBUYMJE4WLAC5CU4SQ6G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MNCC3GPBUYMJE4WLAC5CU4SQ6G/action/storage_attestation","attest_author":"https://pith.science/pith/MNCC3GPBUYMJE4WLAC5CU4SQ6G/action/author_attestation","sign_citation":"https://pith.science/pith/MNCC3GPBUYMJE4WLAC5CU4SQ6G/action/citation_signature","submit_replication":"https://pith.science/pith/MNCC3GPBUYMJE4WLAC5CU4SQ6G/action/replication_record"}},"created_at":"2026-05-18T01:17:11.869047+00:00","updated_at":"2026-05-18T01:17:11.869047+00:00"}