{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UAI76XSD2ZGKF3D6UUKFRBQUFQ","short_pith_number":"pith:UAI76XSD","canonical_record":{"source":{"id":"1810.03788","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-09T03:10:17Z","cross_cats_sorted":[],"title_canon_sha256":"69dbebf640e07da3b8a27c372f823bcb849fdb29eae2a6c27cf3433eb7d0e0d1","abstract_canon_sha256":"c4c6f48b6958bd1555abd5ebc064caa3ffcdb848602a03d164c7367b7195562b"},"schema_version":"1.0"},"canonical_sha256":"a011ff5e43d64ca2ec7ea5145886142c2054ddecc161cde3d5dd86329b47d39a","source":{"kind":"arxiv","id":"1810.03788","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03788","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03788v2","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03788","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"pith_short_12","alias_value":"UAI76XSD2ZGK","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UAI76XSD2ZGKF3D6","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UAI76XSD","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UAI76XSD2ZGKF3D6UUKFRBQUFQ","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03788","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-09T03:10:17Z","cross_cats_sorted":[],"title_canon_sha256":"69dbebf640e07da3b8a27c372f823bcb849fdb29eae2a6c27cf3433eb7d0e0d1","abstract_canon_sha256":"c4c6f48b6958bd1555abd5ebc064caa3ffcdb848602a03d164c7367b7195562b"},"schema_version":"1.0"},"canonical_sha256":"a011ff5e43d64ca2ec7ea5145886142c2054ddecc161cde3d5dd86329b47d39a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:48.942951Z","signature_b64":"ODkA2WVAvkx6/Veh2IR7D9g2yP/ZqvOw7FfiR4aVYlJPOM700LGcLhEyX9cWGUKbPocffgYVM6UPEoGe7FAtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a011ff5e43d64ca2ec7ea5145886142c2054ddecc161cde3d5dd86329b47d39a","last_reissued_at":"2026-05-18T00:02:48.942456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:48.942456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03788","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":"2026-05-18T00:02:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YIqUrbV4+4Jmag7doDafnleTlvpNMuwgRBod0Em7MtC7rm0siG99smLkifwM92gM86qVHQx5q3Mpw9XIIL4LCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:33:01.215901Z"},"content_sha256":"1da0d0f2e10caa498d5bc5ff89af5fb7bd9c29a284d41e742cc5b83c8ae59e76","schema_version":"1.0","event_id":"sha256:1da0d0f2e10caa498d5bc5ff89af5fb7bd9c29a284d41e742cc5b83c8ae59e76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UAI76XSD2ZGKF3D6UUKFRBQUFQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Atomic decomposition of product Hardy spaces via wavelet bases on spaces of homogeneous type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ji Li, Lesley A. Ward, M. Cristina Pereyra, Yongsheng Han","submitted_at":"2018-10-09T03:10:17Z","abstract_excerpt":"We provide an atomic decomposition of the product Hardy spaces $H^p(\\widetilde{X})$ which were recently developed by Han, Li, and Ward in the setting of product spaces of homogeneous type $\\widetilde{X} = X_1 \\times X_2$. Here each factor $(X_i,d_i,\\mu_i)$, for $i = 1$, $2$, is a space of homogeneous type in the sense of Coifman and Weiss.\n  These Hardy spaces make use of the orthogonal wavelet bases of Auscher and Hyt\\\"onen and their underlying reference dyadic grids.\n  However, no additional assumptions on the quasi-metric or on the doubling measure for each factor space are made. To carry o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03788","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":"2026-05-18T00:02:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mvIKuM+KDw2em4E7IHcamnY1aQz3T3PuCvQ2AK1tbMDlZzzF4JWPY9BN2EKWQCvrbycyGtSt2I/TKsJHESYaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:33:01.216253Z"},"content_sha256":"671bdbcd50fa8f38c2c95e73b5dc97f38a7f1e09de742cf94d2c9447d991b5e6","schema_version":"1.0","event_id":"sha256:671bdbcd50fa8f38c2c95e73b5dc97f38a7f1e09de742cf94d2c9447d991b5e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UAI76XSD2ZGKF3D6UUKFRBQUFQ/bundle.json","state_url":"https://pith.science/pith/UAI76XSD2ZGKF3D6UUKFRBQUFQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UAI76XSD2ZGKF3D6UUKFRBQUFQ/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":"2026-06-04T19:33:01Z","links":{"resolver":"https://pith.science/pith/UAI76XSD2ZGKF3D6UUKFRBQUFQ","bundle":"https://pith.science/pith/UAI76XSD2ZGKF3D6UUKFRBQUFQ/bundle.json","state":"https://pith.science/pith/UAI76XSD2ZGKF3D6UUKFRBQUFQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UAI76XSD2ZGKF3D6UUKFRBQUFQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UAI76XSD2ZGKF3D6UUKFRBQUFQ","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":"c4c6f48b6958bd1555abd5ebc064caa3ffcdb848602a03d164c7367b7195562b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-09T03:10:17Z","title_canon_sha256":"69dbebf640e07da3b8a27c372f823bcb849fdb29eae2a6c27cf3433eb7d0e0d1"},"schema_version":"1.0","source":{"id":"1810.03788","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03788","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03788v2","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03788","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"pith_short_12","alias_value":"UAI76XSD2ZGK","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UAI76XSD2ZGKF3D6","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UAI76XSD","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:671bdbcd50fa8f38c2c95e73b5dc97f38a7f1e09de742cf94d2c9447d991b5e6","target":"graph","created_at":"2026-05-18T00:02:48Z","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 provide an atomic decomposition of the product Hardy spaces $H^p(\\widetilde{X})$ which were recently developed by Han, Li, and Ward in the setting of product spaces of homogeneous type $\\widetilde{X} = X_1 \\times X_2$. Here each factor $(X_i,d_i,\\mu_i)$, for $i = 1$, $2$, is a space of homogeneous type in the sense of Coifman and Weiss.\n  These Hardy spaces make use of the orthogonal wavelet bases of Auscher and Hyt\\\"onen and their underlying reference dyadic grids.\n  However, no additional assumptions on the quasi-metric or on the doubling measure for each factor space are made. To carry o","authors_text":"Ji Li, Lesley A. Ward, M. Cristina Pereyra, Yongsheng Han","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-09T03:10:17Z","title":"Atomic decomposition of product Hardy spaces via wavelet bases on spaces of homogeneous type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03788","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":"sha256:1da0d0f2e10caa498d5bc5ff89af5fb7bd9c29a284d41e742cc5b83c8ae59e76","target":"record","created_at":"2026-05-18T00:02:48Z","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":"c4c6f48b6958bd1555abd5ebc064caa3ffcdb848602a03d164c7367b7195562b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-09T03:10:17Z","title_canon_sha256":"69dbebf640e07da3b8a27c372f823bcb849fdb29eae2a6c27cf3433eb7d0e0d1"},"schema_version":"1.0","source":{"id":"1810.03788","kind":"arxiv","version":2}},"canonical_sha256":"a011ff5e43d64ca2ec7ea5145886142c2054ddecc161cde3d5dd86329b47d39a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a011ff5e43d64ca2ec7ea5145886142c2054ddecc161cde3d5dd86329b47d39a","first_computed_at":"2026-05-18T00:02:48.942456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:48.942456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ODkA2WVAvkx6/Veh2IR7D9g2yP/ZqvOw7FfiR4aVYlJPOM700LGcLhEyX9cWGUKbPocffgYVM6UPEoGe7FAtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:48.942951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03788","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1da0d0f2e10caa498d5bc5ff89af5fb7bd9c29a284d41e742cc5b83c8ae59e76","sha256:671bdbcd50fa8f38c2c95e73b5dc97f38a7f1e09de742cf94d2c9447d991b5e6"],"state_sha256":"30866133ada36a3b15152328e840ee3ec441d7d85f4da901f08f067715372a98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D9JzaZShwIjDRm4XWF/2+bYWp5sV9K6A+jSaQc741iILMZMqMuNA/XbtgEiTWv8gX6Vpu0UCyzJT0iZJaAZdBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:33:01.218258Z","bundle_sha256":"b66e1f3df5b71b2d2980d37135fd1b41d7bed832fdc79ade20fe9a9626b51ebd"}}