{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:7HOSDROMN2CAKEVIDAVM2WC2EB","short_pith_number":"pith:7HOSDROM","schema_version":"1.0","canonical_sha256":"f9dd21c5cc6e840512a8182acd585a2048815f924743868e38eca384ebb73449","source":{"kind":"arxiv","id":"1011.0642","version":1},"attestation_state":"computed","paper":{"title":"On general local Tb theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Henri Martikainen, Tuomas Hyt\\\"onen","submitted_at":"2010-11-02T15:29:11Z","abstract_excerpt":"In this paper, local Tb theorems are studied both in the doubling and non-doubling situation. We prove a local Tb theorem for the class of upper doubling measures. With such general measures, scale invariant testing conditions are required (L^{\\infty} or BMO). In the case of doubling measures, we also modify the general non-homogeneous method of proof to yield a new proof of the local Tb theorem with L^2 type testing conditions."},"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":"1011.0642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-02T15:29:11Z","cross_cats_sorted":[],"title_canon_sha256":"e4ebb42233d29e0a46fd64d86853ac6058682255198e5488a22c5b0e44413c1f","abstract_canon_sha256":"b653158d3ddac6ff7564a253eb19000290c211f8e5f5719dfb4b78b325e773d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:37.279777Z","signature_b64":"3kzUnR7E0SMJQDSeZMfUjEOcBBBjKUr30uGmzRWoj5HlymsOOyVhM5udb1CArtnNfjec5ZQhwYP0nho+w04wAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9dd21c5cc6e840512a8182acd585a2048815f924743868e38eca384ebb73449","last_reissued_at":"2026-05-18T03:36:37.279273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:37.279273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On general local Tb theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Henri Martikainen, Tuomas Hyt\\\"onen","submitted_at":"2010-11-02T15:29:11Z","abstract_excerpt":"In this paper, local Tb theorems are studied both in the doubling and non-doubling situation. We prove a local Tb theorem for the class of upper doubling measures. With such general measures, scale invariant testing conditions are required (L^{\\infty} or BMO). In the case of doubling measures, we also modify the general non-homogeneous method of proof to yield a new proof of the local Tb theorem with L^2 type testing conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0642","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":"1011.0642","created_at":"2026-05-18T03:36:37.279355+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.0642v1","created_at":"2026-05-18T03:36:37.279355+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0642","created_at":"2026-05-18T03:36:37.279355+00:00"},{"alias_kind":"pith_short_12","alias_value":"7HOSDROMN2CA","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"7HOSDROMN2CAKEVI","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"7HOSDROM","created_at":"2026-05-18T12:26:04.259169+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/7HOSDROMN2CAKEVIDAVM2WC2EB","json":"https://pith.science/pith/7HOSDROMN2CAKEVIDAVM2WC2EB.json","graph_json":"https://pith.science/api/pith-number/7HOSDROMN2CAKEVIDAVM2WC2EB/graph.json","events_json":"https://pith.science/api/pith-number/7HOSDROMN2CAKEVIDAVM2WC2EB/events.json","paper":"https://pith.science/paper/7HOSDROM"},"agent_actions":{"view_html":"https://pith.science/pith/7HOSDROMN2CAKEVIDAVM2WC2EB","download_json":"https://pith.science/pith/7HOSDROMN2CAKEVIDAVM2WC2EB.json","view_paper":"https://pith.science/paper/7HOSDROM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.0642&json=true","fetch_graph":"https://pith.science/api/pith-number/7HOSDROMN2CAKEVIDAVM2WC2EB/graph.json","fetch_events":"https://pith.science/api/pith-number/7HOSDROMN2CAKEVIDAVM2WC2EB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7HOSDROMN2CAKEVIDAVM2WC2EB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7HOSDROMN2CAKEVIDAVM2WC2EB/action/storage_attestation","attest_author":"https://pith.science/pith/7HOSDROMN2CAKEVIDAVM2WC2EB/action/author_attestation","sign_citation":"https://pith.science/pith/7HOSDROMN2CAKEVIDAVM2WC2EB/action/citation_signature","submit_replication":"https://pith.science/pith/7HOSDROMN2CAKEVIDAVM2WC2EB/action/replication_record"}},"created_at":"2026-05-18T03:36:37.279355+00:00","updated_at":"2026-05-18T03:36:37.279355+00:00"}