{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YNZSS76LIFRBB6LVNLRZW5XDLG","short_pith_number":"pith:YNZSS76L","canonical_record":{"source":{"id":"1407.5029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-07-18T15:10:46Z","cross_cats_sorted":[],"title_canon_sha256":"5f252ae6676c2b02b05242ff24ce8a9089e073510a07e22962d050567c30d51c","abstract_canon_sha256":"e596146c726915abef5f3c2d4e9273df1322c2362d13e9079ef04600733c21a0"},"schema_version":"1.0"},"canonical_sha256":"c373297fcb416210f9756ae39b76e35980d7c84d2ccde95860b1a9560a649082","source":{"kind":"arxiv","id":"1407.5029","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5029","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5029v2","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5029","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"YNZSS76LIFRB","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YNZSS76LIFRBB6LV","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YNZSS76L","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YNZSS76LIFRBB6LVNLRZW5XDLG","target":"record","payload":{"canonical_record":{"source":{"id":"1407.5029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-07-18T15:10:46Z","cross_cats_sorted":[],"title_canon_sha256":"5f252ae6676c2b02b05242ff24ce8a9089e073510a07e22962d050567c30d51c","abstract_canon_sha256":"e596146c726915abef5f3c2d4e9273df1322c2362d13e9079ef04600733c21a0"},"schema_version":"1.0"},"canonical_sha256":"c373297fcb416210f9756ae39b76e35980d7c84d2ccde95860b1a9560a649082","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:13.331492Z","signature_b64":"5YoZFL3tEDNM1QZft82ODv2RpSiorDdIC5nySV8E5dL5oGM+Yd/m7DvltqMQwnICT8Eifcibk4I4i623dwwzDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c373297fcb416210f9756ae39b76e35980d7c84d2ccde95860b1a9560a649082","last_reissued_at":"2026-05-18T00:41:13.330847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:13.330847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.5029","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":"2026-05-18T00:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wYV38S6cL8jOHUAFnBFbP+kkLUL0XQN1EFoaRN/UZPvSfVKWVYNJLfu4BQv8TgtkXeStsc6u+nG9DxUxKqv3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:29:37.934210Z"},"content_sha256":"aeca8e0eaf4b048f595f8f94565a3e384244a2f06ec4096c883d3e97e3179445","schema_version":"1.0","event_id":"sha256:aeca8e0eaf4b048f595f8f94565a3e384244a2f06ec4096c883d3e97e3179445"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YNZSS76LIFRBB6LVNLRZW5XDLG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasisymmetric spheres over Jordan domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jang-Mei Wu, Vyron Vellis","submitted_at":"2014-07-18T15:10:46Z","abstract_excerpt":"Let $\\Omega$ be a planar Jordan domain. We consider double-dome-like surfaces $\\Sigma$ defined by graphs of functions of $dist( \\cdot ,\\partial \\Omega)$ over $\\Omega$. The goal is to find the right conditions on the geometry of the base $\\Omega$ and the growth of the height so that $\\Sigma$ is a quasisphere, or quasisymmetric to $\\mathbb{S}^2$. An internal uniform chord-arc condition on the constant distance sets to $\\partial \\Omega$, coupled with a mild growth condition on the height, gives a close-to-sharp answer. Our method also produces new examples of quasispheres in $\\mathbb{R}^n$, for a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5029","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":"2026-05-18T00:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i293C03Dmn4yI6+bDkaY0o/Im+bwxkjxt2DKhwhiaH8+QV0EvwB50vDdNx1C385zyIxcTaxmjshYnzE0iK7ZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:29:37.934596Z"},"content_sha256":"88b51bd7a8135bb3e3ddccc4488c90f004691a96de684661ce823f6179c9ecee","schema_version":"1.0","event_id":"sha256:88b51bd7a8135bb3e3ddccc4488c90f004691a96de684661ce823f6179c9ecee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YNZSS76LIFRBB6LVNLRZW5XDLG/bundle.json","state_url":"https://pith.science/pith/YNZSS76LIFRBB6LVNLRZW5XDLG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YNZSS76LIFRBB6LVNLRZW5XDLG/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":"2026-06-02T05:29:37Z","links":{"resolver":"https://pith.science/pith/YNZSS76LIFRBB6LVNLRZW5XDLG","bundle":"https://pith.science/pith/YNZSS76LIFRBB6LVNLRZW5XDLG/bundle.json","state":"https://pith.science/pith/YNZSS76LIFRBB6LVNLRZW5XDLG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YNZSS76LIFRBB6LVNLRZW5XDLG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YNZSS76LIFRBB6LVNLRZW5XDLG","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":"e596146c726915abef5f3c2d4e9273df1322c2362d13e9079ef04600733c21a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-07-18T15:10:46Z","title_canon_sha256":"5f252ae6676c2b02b05242ff24ce8a9089e073510a07e22962d050567c30d51c"},"schema_version":"1.0","source":{"id":"1407.5029","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5029","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5029v2","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5029","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"YNZSS76LIFRB","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YNZSS76LIFRBB6LV","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YNZSS76L","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:88b51bd7a8135bb3e3ddccc4488c90f004691a96de684661ce823f6179c9ecee","target":"graph","created_at":"2026-05-18T00:41:13Z","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":"Let $\\Omega$ be a planar Jordan domain. We consider double-dome-like surfaces $\\Sigma$ defined by graphs of functions of $dist( \\cdot ,\\partial \\Omega)$ over $\\Omega$. The goal is to find the right conditions on the geometry of the base $\\Omega$ and the growth of the height so that $\\Sigma$ is a quasisphere, or quasisymmetric to $\\mathbb{S}^2$. An internal uniform chord-arc condition on the constant distance sets to $\\partial \\Omega$, coupled with a mild growth condition on the height, gives a close-to-sharp answer. Our method also produces new examples of quasispheres in $\\mathbb{R}^n$, for a","authors_text":"Jang-Mei Wu, Vyron Vellis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-07-18T15:10:46Z","title":"Quasisymmetric spheres over Jordan domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5029","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:aeca8e0eaf4b048f595f8f94565a3e384244a2f06ec4096c883d3e97e3179445","target":"record","created_at":"2026-05-18T00:41:13Z","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":"e596146c726915abef5f3c2d4e9273df1322c2362d13e9079ef04600733c21a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-07-18T15:10:46Z","title_canon_sha256":"5f252ae6676c2b02b05242ff24ce8a9089e073510a07e22962d050567c30d51c"},"schema_version":"1.0","source":{"id":"1407.5029","kind":"arxiv","version":2}},"canonical_sha256":"c373297fcb416210f9756ae39b76e35980d7c84d2ccde95860b1a9560a649082","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c373297fcb416210f9756ae39b76e35980d7c84d2ccde95860b1a9560a649082","first_computed_at":"2026-05-18T00:41:13.330847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:13.330847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5YoZFL3tEDNM1QZft82ODv2RpSiorDdIC5nySV8E5dL5oGM+Yd/m7DvltqMQwnICT8Eifcibk4I4i623dwwzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:13.331492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5029","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeca8e0eaf4b048f595f8f94565a3e384244a2f06ec4096c883d3e97e3179445","sha256:88b51bd7a8135bb3e3ddccc4488c90f004691a96de684661ce823f6179c9ecee"],"state_sha256":"1ba0dbf3e599d9909d1ac7a9babb107ec626235cb61a756dfced4d832fb6602d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sN5BkkcjeganBzc1nGD/CgFtm+wl+ffCkOiNJmFOV7zyMnpz+t3Ndgf2vXtYq0CrMMISHDzvK33EN6QH+cGmCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:29:37.937084Z","bundle_sha256":"65dd2c3af6abe24f03b6c6531fc9582e93ccf026924471f69529d7ad5e4441ef"}}