{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:PKB2PYQB7RKLWX6HFC5Z3RYHFU","short_pith_number":"pith:PKB2PYQB","canonical_record":{"source":{"id":"1004.3176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-19T12:44:00Z","cross_cats_sorted":[],"title_canon_sha256":"c84f582db3a329d15cdc3cdb3f7bc5d95cde63e57aeb1c0c0bf59162bd40bbc2","abstract_canon_sha256":"d2e5f0d78de08d8e7a0dea6d9bc052ec69fac68ff42253cfb5825066d2a211a5"},"schema_version":"1.0"},"canonical_sha256":"7a83a7e201fc54bb5fc728bb9dc7072d019a5415a3ac4dd0e4028d1854e4a4dd","source":{"kind":"arxiv","id":"1004.3176","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3176","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3176v1","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3176","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"PKB2PYQB7RKL","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PKB2PYQB7RKLWX6H","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PKB2PYQB","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:PKB2PYQB7RKLWX6HFC5Z3RYHFU","target":"record","payload":{"canonical_record":{"source":{"id":"1004.3176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-19T12:44:00Z","cross_cats_sorted":[],"title_canon_sha256":"c84f582db3a329d15cdc3cdb3f7bc5d95cde63e57aeb1c0c0bf59162bd40bbc2","abstract_canon_sha256":"d2e5f0d78de08d8e7a0dea6d9bc052ec69fac68ff42253cfb5825066d2a211a5"},"schema_version":"1.0"},"canonical_sha256":"7a83a7e201fc54bb5fc728bb9dc7072d019a5415a3ac4dd0e4028d1854e4a4dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:37.345465Z","signature_b64":"Zz7rF98AfZEfN7Cj/uF8GmxrzTZ10n3fywKkrBH4ktSGlZZwyhjacXC9tFSVPCXamHxANLq81yJfB66nrLJlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a83a7e201fc54bb5fc728bb9dc7072d019a5415a3ac4dd0e4028d1854e4a4dd","last_reissued_at":"2026-05-18T03:36:37.344843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:37.344843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.3176","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":"2026-05-18T03:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5khdNwEyg3Bkv5fIlsuZTRJrsF0s0wY/v2nxVbn3afDmylBS+BFPy3n5qtQ4UaybEZzjS3WXFyvckdqRMPpKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:29:28.539181Z"},"content_sha256":"fd9c305750777f3d0d22111943852eba46c99163362ec00e1b019932c514fee5","schema_version":"1.0","event_id":"sha256:fd9c305750777f3d0d22111943852eba46c99163362ec00e1b019932c514fee5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:PKB2PYQB7RKLWX6HFC5Z3RYHFU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector-valued non-homogeneous Tb theorem on metric measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Henri Martikainen","submitted_at":"2010-04-19T12:44:00Z","abstract_excerpt":"We prove a vector-valued non-homogeneous Tb theorem on certain quasimetric spaces equipped with what we call an upper doubling measure. Essentially, we merge recent techniques from the domain and range side of things, achieving a Tb theorem which is quite general with respect to both of them."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3176","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":"2026-05-18T03:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJjnUrS3kKKRKoJW7vlONFoaL4vwsU3oMBXOt0j6SGcuZEKba3pAtqH02F6HyuS0fv7pVfxmfhf1csh7/+niCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:29:28.539864Z"},"content_sha256":"45fa91155a2b81326bd5b59f7fe75f481d7910417aa0009395bdad6e3c6deb36","schema_version":"1.0","event_id":"sha256:45fa91155a2b81326bd5b59f7fe75f481d7910417aa0009395bdad6e3c6deb36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PKB2PYQB7RKLWX6HFC5Z3RYHFU/bundle.json","state_url":"https://pith.science/pith/PKB2PYQB7RKLWX6HFC5Z3RYHFU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PKB2PYQB7RKLWX6HFC5Z3RYHFU/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":"2026-05-27T18:29:28Z","links":{"resolver":"https://pith.science/pith/PKB2PYQB7RKLWX6HFC5Z3RYHFU","bundle":"https://pith.science/pith/PKB2PYQB7RKLWX6HFC5Z3RYHFU/bundle.json","state":"https://pith.science/pith/PKB2PYQB7RKLWX6HFC5Z3RYHFU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PKB2PYQB7RKLWX6HFC5Z3RYHFU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PKB2PYQB7RKLWX6HFC5Z3RYHFU","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":"d2e5f0d78de08d8e7a0dea6d9bc052ec69fac68ff42253cfb5825066d2a211a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-19T12:44:00Z","title_canon_sha256":"c84f582db3a329d15cdc3cdb3f7bc5d95cde63e57aeb1c0c0bf59162bd40bbc2"},"schema_version":"1.0","source":{"id":"1004.3176","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3176","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3176v1","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3176","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"PKB2PYQB7RKL","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PKB2PYQB7RKLWX6H","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PKB2PYQB","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:45fa91155a2b81326bd5b59f7fe75f481d7910417aa0009395bdad6e3c6deb36","target":"graph","created_at":"2026-05-18T03:36:37Z","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 a vector-valued non-homogeneous Tb theorem on certain quasimetric spaces equipped with what we call an upper doubling measure. Essentially, we merge recent techniques from the domain and range side of things, achieving a Tb theorem which is quite general with respect to both of them.","authors_text":"Henri Martikainen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-19T12:44:00Z","title":"Vector-valued non-homogeneous Tb theorem on metric measure spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3176","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:fd9c305750777f3d0d22111943852eba46c99163362ec00e1b019932c514fee5","target":"record","created_at":"2026-05-18T03:36:37Z","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":"d2e5f0d78de08d8e7a0dea6d9bc052ec69fac68ff42253cfb5825066d2a211a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-19T12:44:00Z","title_canon_sha256":"c84f582db3a329d15cdc3cdb3f7bc5d95cde63e57aeb1c0c0bf59162bd40bbc2"},"schema_version":"1.0","source":{"id":"1004.3176","kind":"arxiv","version":1}},"canonical_sha256":"7a83a7e201fc54bb5fc728bb9dc7072d019a5415a3ac4dd0e4028d1854e4a4dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a83a7e201fc54bb5fc728bb9dc7072d019a5415a3ac4dd0e4028d1854e4a4dd","first_computed_at":"2026-05-18T03:36:37.344843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:37.344843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zz7rF98AfZEfN7Cj/uF8GmxrzTZ10n3fywKkrBH4ktSGlZZwyhjacXC9tFSVPCXamHxANLq81yJfB66nrLJlDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:37.345465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3176","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd9c305750777f3d0d22111943852eba46c99163362ec00e1b019932c514fee5","sha256:45fa91155a2b81326bd5b59f7fe75f481d7910417aa0009395bdad6e3c6deb36"],"state_sha256":"eb48e849d2ba40b70c1f14900ca263cce1ef12cee6cab95cfd85012b400aa05f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NH7tmHBoYELZ9odlmKuqo8T8aing3IetMyK+HxJGOzYn3Sg6qdf/+gGIEIXdiSprTWZxM7QbZ9vGrcYHOC6ADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:29:28.543271Z","bundle_sha256":"5b7775763c495cfdca8be4f213cd573c72c3de5b201eb310e3cb927078b12bf2"}}