{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IOUFXID34Q7BRJ2NJS5PGXYXX7","short_pith_number":"pith:IOUFXID3","canonical_record":{"source":{"id":"1212.3684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-15T13:57:34Z","cross_cats_sorted":[],"title_canon_sha256":"41d26e343ef3a2bb231aeeb70a43e0a76a1885dc9cd4e3f3b4fb75428e6e79fd","abstract_canon_sha256":"2b21833dbc81db77eaa45d298f4875cfc4e480518590c34300516708556f0734"},"schema_version":"1.0"},"canonical_sha256":"43a85ba07be43e18a74d4cbaf35f17bfd9eae33d4a3d81597150050f548d7e82","source":{"kind":"arxiv","id":"1212.3684","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3684","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3684v1","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3684","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"IOUFXID34Q7B","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IOUFXID34Q7BRJ2N","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IOUFXID3","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IOUFXID34Q7BRJ2NJS5PGXYXX7","target":"record","payload":{"canonical_record":{"source":{"id":"1212.3684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-15T13:57:34Z","cross_cats_sorted":[],"title_canon_sha256":"41d26e343ef3a2bb231aeeb70a43e0a76a1885dc9cd4e3f3b4fb75428e6e79fd","abstract_canon_sha256":"2b21833dbc81db77eaa45d298f4875cfc4e480518590c34300516708556f0734"},"schema_version":"1.0"},"canonical_sha256":"43a85ba07be43e18a74d4cbaf35f17bfd9eae33d4a3d81597150050f548d7e82","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:17.459453Z","signature_b64":"rSHBwHNO2/ahyabPxNVZQuHJxIRfyjiHPhnlTtCQ1TJhO+Q/Wp9nZ+Eo2ftPyoeti5MeZkN/ygnlWX3cBL7cDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43a85ba07be43e18a74d4cbaf35f17bfd9eae33d4a3d81597150050f548d7e82","last_reissued_at":"2026-05-18T02:38:17.458755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:17.458755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.3684","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fKIDZljGgjoHjrl4O5s0cmDJtUV6vXTw8uNLNFOiEMUixZlf4AP0l+a/C6JQJYoSYLLoWbds2D9V0wtefXsNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:33:31.374420Z"},"content_sha256":"ba4892260c2f2a6fd09a34828ac7ba5b1cee2951e49d2a93fec33393367a85b4","schema_version":"1.0","event_id":"sha256:ba4892260c2f2a6fd09a34828ac7ba5b1cee2951e49d2a93fec33393367a85b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IOUFXID34Q7BRJ2NJS5PGXYXX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Square functions with general measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Henri Martikainen, Mihalis Mourgoglou","submitted_at":"2012-12-15T13:57:34Z","abstract_excerpt":"We characterize the boundedness of square functions in the upper half-space with general measures. The short proof is based on an averaging identity over good Whitney regions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3684","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UIR2QCUjHeQVEufiTV5ajMDJ3WkW1J5tzMeUbkDtAt+4cBNDcBCUdsptmOwTsBJnH58V28Cs/a0vTyBmyi+PDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:33:31.374809Z"},"content_sha256":"83d0d12d1e96b5ede12da69fc628408dd4f54710c37ce8facf6555710c57dcc1","schema_version":"1.0","event_id":"sha256:83d0d12d1e96b5ede12da69fc628408dd4f54710c37ce8facf6555710c57dcc1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOUFXID34Q7BRJ2NJS5PGXYXX7/bundle.json","state_url":"https://pith.science/pith/IOUFXID34Q7BRJ2NJS5PGXYXX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOUFXID34Q7BRJ2NJS5PGXYXX7/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":"2026-05-28T01:33:31Z","links":{"resolver":"https://pith.science/pith/IOUFXID34Q7BRJ2NJS5PGXYXX7","bundle":"https://pith.science/pith/IOUFXID34Q7BRJ2NJS5PGXYXX7/bundle.json","state":"https://pith.science/pith/IOUFXID34Q7BRJ2NJS5PGXYXX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOUFXID34Q7BRJ2NJS5PGXYXX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IOUFXID34Q7BRJ2NJS5PGXYXX7","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":"2b21833dbc81db77eaa45d298f4875cfc4e480518590c34300516708556f0734","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-15T13:57:34Z","title_canon_sha256":"41d26e343ef3a2bb231aeeb70a43e0a76a1885dc9cd4e3f3b4fb75428e6e79fd"},"schema_version":"1.0","source":{"id":"1212.3684","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3684","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3684v1","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3684","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"IOUFXID34Q7B","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IOUFXID34Q7BRJ2N","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IOUFXID3","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:83d0d12d1e96b5ede12da69fc628408dd4f54710c37ce8facf6555710c57dcc1","target":"graph","created_at":"2026-05-18T02:38:17Z","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 characterize the boundedness of square functions in the upper half-space with general measures. The short proof is based on an averaging identity over good Whitney regions.","authors_text":"Henri Martikainen, Mihalis Mourgoglou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-15T13:57:34Z","title":"Square functions with general measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3684","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:ba4892260c2f2a6fd09a34828ac7ba5b1cee2951e49d2a93fec33393367a85b4","target":"record","created_at":"2026-05-18T02:38:17Z","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":"2b21833dbc81db77eaa45d298f4875cfc4e480518590c34300516708556f0734","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-12-15T13:57:34Z","title_canon_sha256":"41d26e343ef3a2bb231aeeb70a43e0a76a1885dc9cd4e3f3b4fb75428e6e79fd"},"schema_version":"1.0","source":{"id":"1212.3684","kind":"arxiv","version":1}},"canonical_sha256":"43a85ba07be43e18a74d4cbaf35f17bfd9eae33d4a3d81597150050f548d7e82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43a85ba07be43e18a74d4cbaf35f17bfd9eae33d4a3d81597150050f548d7e82","first_computed_at":"2026-05-18T02:38:17.458755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:17.458755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rSHBwHNO2/ahyabPxNVZQuHJxIRfyjiHPhnlTtCQ1TJhO+Q/Wp9nZ+Eo2ftPyoeti5MeZkN/ygnlWX3cBL7cDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:17.459453Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3684","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba4892260c2f2a6fd09a34828ac7ba5b1cee2951e49d2a93fec33393367a85b4","sha256:83d0d12d1e96b5ede12da69fc628408dd4f54710c37ce8facf6555710c57dcc1"],"state_sha256":"9e3c87e2de4c047249acaac2f6aa5ae4dbc5591499dd7409cfc739171d689e32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dAkh8JuLMrqLCQEXTk5TAOPrQ+Tw6y2ECgEXmJxfEWnaev+KPM07wOwKKP/DYOpDTPtKuQRAqQY/xWoeRDJvBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:33:31.376930Z","bundle_sha256":"15becbcca874afeb731542d60966a8ade56827d901c43a5ab5786f4317b75337"}}