{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EYTMIJEJFVLVVP3JZDAMVSIIAK","short_pith_number":"pith:EYTMIJEJ","canonical_record":{"source":{"id":"1710.01588","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CV","submitted_at":"2017-10-04T13:12:39Z","cross_cats_sorted":[],"title_canon_sha256":"00d96e10862003b07f355045f921a0010556717590cb8761815ba30388711488","abstract_canon_sha256":"07b2e981fe368ab7d199a137d1d8bac00e2aeb778579ab64d13d078044dd6aa2"},"schema_version":"1.0"},"canonical_sha256":"2626c424892d575abf69c8c0cac90802a749a142b4fbea9938e1ef07595099c4","source":{"kind":"arxiv","id":"1710.01588","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01588","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01588v2","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01588","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"pith_short_12","alias_value":"EYTMIJEJFVLV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EYTMIJEJFVLVVP3J","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EYTMIJEJ","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EYTMIJEJFVLVVP3JZDAMVSIIAK","target":"record","payload":{"canonical_record":{"source":{"id":"1710.01588","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CV","submitted_at":"2017-10-04T13:12:39Z","cross_cats_sorted":[],"title_canon_sha256":"00d96e10862003b07f355045f921a0010556717590cb8761815ba30388711488","abstract_canon_sha256":"07b2e981fe368ab7d199a137d1d8bac00e2aeb778579ab64d13d078044dd6aa2"},"schema_version":"1.0"},"canonical_sha256":"2626c424892d575abf69c8c0cac90802a749a142b4fbea9938e1ef07595099c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:36.662951Z","signature_b64":"0RBrU9r10B+VDpljbIQd5GEDDD1PJPQClcVaqkPmO7GfyrC2A5oBaMocTjynJC8/nHMmszOiBPl727g4j80uCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2626c424892d575abf69c8c0cac90802a749a142b4fbea9938e1ef07595099c4","last_reissued_at":"2026-05-18T00:29:36.662355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:36.662355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.01588","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":"2026-05-18T00:29:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zCBeWIm1+X3AFvekJP9NXX/IiH4311wMfqDbuhz3FWb6NK84++2jVAv08IQq42ewET76edBzueiDnAmaic7EAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:25:00.754197Z"},"content_sha256":"2ba44df3a0b45c24c365e41b8de2ef7d49c89e5c48b8c5f6c1216ab8a938544d","schema_version":"1.0","event_id":"sha256:2ba44df3a0b45c24c365e41b8de2ef7d49c89e5c48b8c5f6c1216ab8a938544d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EYTMIJEJFVLVVP3JZDAMVSIIAK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"BMO-Teichm\\\"uller spaces revisited","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Huaying Wei, Michel Zinsmeister","submitted_at":"2017-10-04T13:12:39Z","abstract_excerpt":"In a paper of Cui and Zinsmeister the equivalence among three definitions of BMO-Teichm\\\"uller spaces associated with a Fuchsian group was proven using the Douady-Earle extension operator. In this paper, we show that these equivalences are actually biholomorphisms. It was further shown in the above quoted paper that the Douady-Earle extension operator is continuous at the origin. We improve this result by showing G\\^ateaux-differentiability at this point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01588","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":"2026-05-18T00:29:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJ08UPj2z05s2ECTjZv4HsBnPTvg5MmpA61vc4eBBhQeW1i1xDKJkhc8XyZnbv2LbxABs6UdyzpqKw5KmMYeBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:25:00.754557Z"},"content_sha256":"6c39982c27447b265af87d945448d3fb0cceb0fea45663ed38875d05c24c503e","schema_version":"1.0","event_id":"sha256:6c39982c27447b265af87d945448d3fb0cceb0fea45663ed38875d05c24c503e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EYTMIJEJFVLVVP3JZDAMVSIIAK/bundle.json","state_url":"https://pith.science/pith/EYTMIJEJFVLVVP3JZDAMVSIIAK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EYTMIJEJFVLVVP3JZDAMVSIIAK/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":"2026-06-23T22:25:00Z","links":{"resolver":"https://pith.science/pith/EYTMIJEJFVLVVP3JZDAMVSIIAK","bundle":"https://pith.science/pith/EYTMIJEJFVLVVP3JZDAMVSIIAK/bundle.json","state":"https://pith.science/pith/EYTMIJEJFVLVVP3JZDAMVSIIAK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EYTMIJEJFVLVVP3JZDAMVSIIAK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EYTMIJEJFVLVVP3JZDAMVSIIAK","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":"07b2e981fe368ab7d199a137d1d8bac00e2aeb778579ab64d13d078044dd6aa2","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CV","submitted_at":"2017-10-04T13:12:39Z","title_canon_sha256":"00d96e10862003b07f355045f921a0010556717590cb8761815ba30388711488"},"schema_version":"1.0","source":{"id":"1710.01588","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01588","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01588v2","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01588","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"pith_short_12","alias_value":"EYTMIJEJFVLV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EYTMIJEJFVLVVP3J","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EYTMIJEJ","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:6c39982c27447b265af87d945448d3fb0cceb0fea45663ed38875d05c24c503e","target":"graph","created_at":"2026-05-18T00:29:36Z","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":"In a paper of Cui and Zinsmeister the equivalence among three definitions of BMO-Teichm\\\"uller spaces associated with a Fuchsian group was proven using the Douady-Earle extension operator. In this paper, we show that these equivalences are actually biholomorphisms. It was further shown in the above quoted paper that the Douady-Earle extension operator is continuous at the origin. We improve this result by showing G\\^ateaux-differentiability at this point.","authors_text":"Huaying Wei, Michel Zinsmeister","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CV","submitted_at":"2017-10-04T13:12:39Z","title":"BMO-Teichm\\\"uller spaces revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01588","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":"sha256:2ba44df3a0b45c24c365e41b8de2ef7d49c89e5c48b8c5f6c1216ab8a938544d","target":"record","created_at":"2026-05-18T00:29:36Z","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":"07b2e981fe368ab7d199a137d1d8bac00e2aeb778579ab64d13d078044dd6aa2","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CV","submitted_at":"2017-10-04T13:12:39Z","title_canon_sha256":"00d96e10862003b07f355045f921a0010556717590cb8761815ba30388711488"},"schema_version":"1.0","source":{"id":"1710.01588","kind":"arxiv","version":2}},"canonical_sha256":"2626c424892d575abf69c8c0cac90802a749a142b4fbea9938e1ef07595099c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2626c424892d575abf69c8c0cac90802a749a142b4fbea9938e1ef07595099c4","first_computed_at":"2026-05-18T00:29:36.662355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:36.662355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0RBrU9r10B+VDpljbIQd5GEDDD1PJPQClcVaqkPmO7GfyrC2A5oBaMocTjynJC8/nHMmszOiBPl727g4j80uCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:36.662951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.01588","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ba44df3a0b45c24c365e41b8de2ef7d49c89e5c48b8c5f6c1216ab8a938544d","sha256:6c39982c27447b265af87d945448d3fb0cceb0fea45663ed38875d05c24c503e"],"state_sha256":"b646dd840690860beb8a74e1d9eb1fa17731c37ccca2e62ce9228a2cc3b8be94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k+kk8U/7RhtnTHkTI+K5FdHqG4ZBtzRGF1R/oOqF/vy1KAkbR1r3RGEdWZATrZdtks2aRBxKFWbDTeSV5HVOBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T22:25:00.756503Z","bundle_sha256":"64964b449b2eb191a5d7819d9f4a5c70b7d53cd857acfa395fc02f831d969345"}}