{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LTWHUGVUDE6DQSRLRY2MMVW3PI","short_pith_number":"pith:LTWHUGVU","canonical_record":{"source":{"id":"1410.5547","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T06:12:32Z","cross_cats_sorted":[],"title_canon_sha256":"65d658e52c0dbb15b285d7c768e67676773f6acb89058e9724c7461b11c7dbd0","abstract_canon_sha256":"83ef946c4051e9e5cba05e4c01b7cad9a7e8ef18419cdce2001be83b9fb3ed94"},"schema_version":"1.0"},"canonical_sha256":"5cec7a1ab4193c384a2b8e34c656db7a162f755b75a24e2289dfff02cdb69f2d","source":{"kind":"arxiv","id":"1410.5547","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5547","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5547v2","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5547","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"pith_short_12","alias_value":"LTWHUGVUDE6D","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LTWHUGVUDE6DQSRL","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LTWHUGVU","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LTWHUGVUDE6DQSRLRY2MMVW3PI","target":"record","payload":{"canonical_record":{"source":{"id":"1410.5547","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T06:12:32Z","cross_cats_sorted":[],"title_canon_sha256":"65d658e52c0dbb15b285d7c768e67676773f6acb89058e9724c7461b11c7dbd0","abstract_canon_sha256":"83ef946c4051e9e5cba05e4c01b7cad9a7e8ef18419cdce2001be83b9fb3ed94"},"schema_version":"1.0"},"canonical_sha256":"5cec7a1ab4193c384a2b8e34c656db7a162f755b75a24e2289dfff02cdb69f2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:52.769278Z","signature_b64":"ivnpIRBTWORofam4IJsHiP8qLF1Av9EwsCUhOW5JPrMt/5FhTOoy4RmmSr5GA1X4AlZ94OckIyQRrQB5Pa1nCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cec7a1ab4193c384a2b8e34c656db7a162f755b75a24e2289dfff02cdb69f2d","last_reissued_at":"2026-05-18T02:38:52.768935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:52.768935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.5547","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":"2026-05-18T02:38:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"83QpDONRflYxaMqDsuBH7Nl6tjvaTvr/tlFFHKmT9DT3tpOtILx/4w40n+yVVZ9Bde53Rr4iP2Lu4fK8NO+KCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:42:23.751836Z"},"content_sha256":"bddea1e5e7148536e7b2f9bcaae5442df84305fc6fc059c3b73b62fedefb1cc8","schema_version":"1.0","event_id":"sha256:bddea1e5e7148536e7b2f9bcaae5442df84305fc6fc059c3b73b62fedefb1cc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LTWHUGVUDE6DQSRLRY2MMVW3PI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Radially Symmetric Solutions To The Graphic Willmore Surface Equation","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jingyi Chen, Yuxiang Li","submitted_at":"2014-10-21T06:12:32Z","abstract_excerpt":"We show that a smooth radially symmetric solution $u$ to the graphic Willmore surface equation is either a constant or the defining function of a half sphere in ${\\mathbb R}^3$. In particular, radially symmetric entire Willmore graphs in ${\\mathbb R}^3$ must be flat. When $u$ is a smooth radial solution over a punctured disk $D(\\rho)\\backslash\\{0\\}$ and is in $C^1(D(\\rho))$, we show that there exist a constant $\\lambda$ and a function $\\beta$ in $C^0(D(\\rho))$ such that $u''(r) =\\frac{\\lambda}{2}\\log r+\\beta(r)$; moreover, the graph of $u$ is contained in a graphical region of an inverted cate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5547","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":"2026-05-18T02:38:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lBp0PCBB3B5H8LfN04a8umxwaxE7IPmc9XeuiXcaIdPOLzX5rfeOQTaVAhHYS6wHUNSpZ8GtuRNHvZNaQj/FBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:42:23.752586Z"},"content_sha256":"ba35c11888a1b081ffd9214129f845ceeebe94c03d77e050d447562d90a93ddc","schema_version":"1.0","event_id":"sha256:ba35c11888a1b081ffd9214129f845ceeebe94c03d77e050d447562d90a93ddc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTWHUGVUDE6DQSRLRY2MMVW3PI/bundle.json","state_url":"https://pith.science/pith/LTWHUGVUDE6DQSRLRY2MMVW3PI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTWHUGVUDE6DQSRLRY2MMVW3PI/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":"2026-06-11T11:42:23Z","links":{"resolver":"https://pith.science/pith/LTWHUGVUDE6DQSRLRY2MMVW3PI","bundle":"https://pith.science/pith/LTWHUGVUDE6DQSRLRY2MMVW3PI/bundle.json","state":"https://pith.science/pith/LTWHUGVUDE6DQSRLRY2MMVW3PI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTWHUGVUDE6DQSRLRY2MMVW3PI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LTWHUGVUDE6DQSRLRY2MMVW3PI","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":"83ef946c4051e9e5cba05e4c01b7cad9a7e8ef18419cdce2001be83b9fb3ed94","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T06:12:32Z","title_canon_sha256":"65d658e52c0dbb15b285d7c768e67676773f6acb89058e9724c7461b11c7dbd0"},"schema_version":"1.0","source":{"id":"1410.5547","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5547","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5547v2","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5547","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"pith_short_12","alias_value":"LTWHUGVUDE6D","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LTWHUGVUDE6DQSRL","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LTWHUGVU","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:ba35c11888a1b081ffd9214129f845ceeebe94c03d77e050d447562d90a93ddc","target":"graph","created_at":"2026-05-18T02:38:52Z","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 show that a smooth radially symmetric solution $u$ to the graphic Willmore surface equation is either a constant or the defining function of a half sphere in ${\\mathbb R}^3$. In particular, radially symmetric entire Willmore graphs in ${\\mathbb R}^3$ must be flat. When $u$ is a smooth radial solution over a punctured disk $D(\\rho)\\backslash\\{0\\}$ and is in $C^1(D(\\rho))$, we show that there exist a constant $\\lambda$ and a function $\\beta$ in $C^0(D(\\rho))$ such that $u''(r) =\\frac{\\lambda}{2}\\log r+\\beta(r)$; moreover, the graph of $u$ is contained in a graphical region of an inverted cate","authors_text":"Jingyi Chen, Yuxiang Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T06:12:32Z","title":"Radially Symmetric Solutions To The Graphic Willmore Surface Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5547","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:bddea1e5e7148536e7b2f9bcaae5442df84305fc6fc059c3b73b62fedefb1cc8","target":"record","created_at":"2026-05-18T02:38:52Z","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":"83ef946c4051e9e5cba05e4c01b7cad9a7e8ef18419cdce2001be83b9fb3ed94","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T06:12:32Z","title_canon_sha256":"65d658e52c0dbb15b285d7c768e67676773f6acb89058e9724c7461b11c7dbd0"},"schema_version":"1.0","source":{"id":"1410.5547","kind":"arxiv","version":2}},"canonical_sha256":"5cec7a1ab4193c384a2b8e34c656db7a162f755b75a24e2289dfff02cdb69f2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cec7a1ab4193c384a2b8e34c656db7a162f755b75a24e2289dfff02cdb69f2d","first_computed_at":"2026-05-18T02:38:52.768935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:52.768935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ivnpIRBTWORofam4IJsHiP8qLF1Av9EwsCUhOW5JPrMt/5FhTOoy4RmmSr5GA1X4AlZ94OckIyQRrQB5Pa1nCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:52.769278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5547","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bddea1e5e7148536e7b2f9bcaae5442df84305fc6fc059c3b73b62fedefb1cc8","sha256:ba35c11888a1b081ffd9214129f845ceeebe94c03d77e050d447562d90a93ddc"],"state_sha256":"6a200765ba0292317854708d5ef23c52de3b59bbc682215d2ed7c41f9fc7a936"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BReKQLhH9m+k6Xa1PFfEk2fwM7kWlZeXLkmGFhyJOhBgKSDJudEwggLrA0Wjo7OYyCgs7Xn1lXUvihtn8dVPDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:42:23.756350Z","bundle_sha256":"7fe9d779383f9a82b518915644d19467ee2e428ab90b0452bfb373823106824a"}}