{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B5WZKCBYU6G7U3GEBHG3EEG627","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":"07888d10181378fb4922b0c0a0988f528682087a301c2dea1d91dd7afb14b4c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-18T02:52:34Z","title_canon_sha256":"6b8895c24d86594afcf62eea58ba3cdc054f8f5023a03ad4c60cb40ddb3856f1"},"schema_version":"1.0","source":{"id":"1204.3963","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3963","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3963v1","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3963","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"B5WZKCBYU6G7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B5WZKCBYU6G7U3GE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B5WZKCBY","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:190a2932e2a3f8f661b3e587578c8388bc1d7b44111e4d9fc9972174551f77fa","target":"graph","created_at":"2026-05-18T03:57:38Z","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 prove an extrapolation result for general operators under some weak assumptions on the boundedness of the operator. In particular, we show that if the operator is weakly bounded on some L^{p_{0}}(w), for all \"flat\" weights, w in A_{p_{0}}, 1 < p_{0} <\\infty, then for p in some small neighborhood around p_{0}, and all \"flat\" A_{p} weights, w, the operator is weakly bounded on L^{p}(w), and as a result we get strong type estimates for the operator.","authors_text":"Alexander Volberg, Nicholas Boros, Nikolaos Pattakos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-18T02:52:34Z","title":"Some remarks on extrapolation with \"flat\" weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3963","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":"sha256:9ebcb21dadd2a5d6718efeed8854c686a5219f1e501d8d9ce22e1d005ae7a99e","target":"record","created_at":"2026-05-18T03:57:38Z","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":"07888d10181378fb4922b0c0a0988f528682087a301c2dea1d91dd7afb14b4c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-18T02:52:34Z","title_canon_sha256":"6b8895c24d86594afcf62eea58ba3cdc054f8f5023a03ad4c60cb40ddb3856f1"},"schema_version":"1.0","source":{"id":"1204.3963","kind":"arxiv","version":1}},"canonical_sha256":"0f6d950838a78dfa6cc409cdb210ded7d75c461c3364db10b3bb721c26677400","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f6d950838a78dfa6cc409cdb210ded7d75c461c3364db10b3bb721c26677400","first_computed_at":"2026-05-18T03:57:38.170034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:38.170034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dKEVaXeQlTP7DhAvf5kswmEYzaPvqzrCxKvBQ24YxnIGhKXCP9/S0STn0B4u45OHh4oMoCZXSKurV5eOojBdDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:38.170743Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3963","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ebcb21dadd2a5d6718efeed8854c686a5219f1e501d8d9ce22e1d005ae7a99e","sha256:190a2932e2a3f8f661b3e587578c8388bc1d7b44111e4d9fc9972174551f77fa"],"state_sha256":"582edf2c76e040588bb7593431dd80bd2b1666d6fff532af20f73a190179a18a"}