{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZU7EXBZFNJQU2TNL66CJUE4W3F","short_pith_number":"pith:ZU7EXBZF","canonical_record":{"source":{"id":"1601.06852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-25T23:58:25Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c01146e0899ffa3772f478aaa974f5478562b4be2bed4c9a1f63147a483e7bf7","abstract_canon_sha256":"c3716943f9c4beefe3d5ba863c26c88b952dd2c294a1afc8bc366fd31f207a77"},"schema_version":"1.0"},"canonical_sha256":"cd3e4b87256a614d4dabf7849a1396d95893b274c3df8f90982c780d9e85a5da","source":{"kind":"arxiv","id":"1601.06852","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06852","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06852v2","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06852","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZU7EXBZFNJQU","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZU7EXBZFNJQU2TNL","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZU7EXBZF","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZU7EXBZFNJQU2TNL66CJUE4W3F","target":"record","payload":{"canonical_record":{"source":{"id":"1601.06852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-25T23:58:25Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c01146e0899ffa3772f478aaa974f5478562b4be2bed4c9a1f63147a483e7bf7","abstract_canon_sha256":"c3716943f9c4beefe3d5ba863c26c88b952dd2c294a1afc8bc366fd31f207a77"},"schema_version":"1.0"},"canonical_sha256":"cd3e4b87256a614d4dabf7849a1396d95893b274c3df8f90982c780d9e85a5da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:21.562943Z","signature_b64":"69dMcWh1tSmvQH/TezOmwXW0QaXuKWdflZOpN6x3gPWEgME5iwsA5dMjre/pEADRKqA++UBL9HhqA+Wh1ajCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd3e4b87256a614d4dabf7849a1396d95893b274c3df8f90982c780d9e85a5da","last_reissued_at":"2026-05-18T01:04:21.562476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:21.562476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.06852","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":"2026-05-18T01:04:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fHNhPo3QLD92y73SGK6jou32PMgssj3duf1rehub1njnTJi1iYvelSO26vzQQUpF0paVtaJWaueL1Y8by80oCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:20:42.889899Z"},"content_sha256":"55625b015789edac16d6b93a6d629c9b9a05e0900c372ed4b99941456a72e57f","schema_version":"1.0","event_id":"sha256:55625b015789edac16d6b93a6d629c9b9a05e0900c372ed4b99941456a72e57f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZU7EXBZFNJQU2TNL66CJUE4W3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification theorems for solutions of higher order boundary conformally invariant problems, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Jingang Xiong, Liming Sun","submitted_at":"2016-01-25T23:58:25Z","abstract_excerpt":"In this paper, we prove that nonnegative polyharmonic functions on the upper half space satisfying a conformally invariant nonlinear boundary condition have to be the \"\\emph{polynomials} plus \\emph{bubbles}\" form. The nonlinear problem is motivated by the recent studies of boundary GJMS operators and the $Q$-curvature in conformal geometry. The result implies that in the conformal class of the unit Euclidean ball there exist metrics with a single singular boundary point which have flat $Q$-curvature and constant boundary $Q$-curvature. Moreover, all of such metrics are classified. This phenome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06852","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":"2026-05-18T01:04:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0lLCvXZsO6i1M253VZe1KXV61JKwAGG56SuhcWY5gMlu/bBF3hJH0y6rXK06Jly/OvanGM+HnkG058nnXZNbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:20:42.890631Z"},"content_sha256":"2d1e26eea481860484b342b12e79879f41bc87d438c817af582bdde1a3b42210","schema_version":"1.0","event_id":"sha256:2d1e26eea481860484b342b12e79879f41bc87d438c817af582bdde1a3b42210"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZU7EXBZFNJQU2TNL66CJUE4W3F/bundle.json","state_url":"https://pith.science/pith/ZU7EXBZFNJQU2TNL66CJUE4W3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZU7EXBZFNJQU2TNL66CJUE4W3F/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":"2026-05-26T18:20:42Z","links":{"resolver":"https://pith.science/pith/ZU7EXBZFNJQU2TNL66CJUE4W3F","bundle":"https://pith.science/pith/ZU7EXBZFNJQU2TNL66CJUE4W3F/bundle.json","state":"https://pith.science/pith/ZU7EXBZFNJQU2TNL66CJUE4W3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZU7EXBZFNJQU2TNL66CJUE4W3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZU7EXBZFNJQU2TNL66CJUE4W3F","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":"c3716943f9c4beefe3d5ba863c26c88b952dd2c294a1afc8bc366fd31f207a77","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-25T23:58:25Z","title_canon_sha256":"c01146e0899ffa3772f478aaa974f5478562b4be2bed4c9a1f63147a483e7bf7"},"schema_version":"1.0","source":{"id":"1601.06852","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06852","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06852v2","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06852","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZU7EXBZFNJQU","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZU7EXBZFNJQU2TNL","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZU7EXBZF","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:2d1e26eea481860484b342b12e79879f41bc87d438c817af582bdde1a3b42210","target":"graph","created_at":"2026-05-18T01:04:21Z","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 this paper, we prove that nonnegative polyharmonic functions on the upper half space satisfying a conformally invariant nonlinear boundary condition have to be the \"\\emph{polynomials} plus \\emph{bubbles}\" form. The nonlinear problem is motivated by the recent studies of boundary GJMS operators and the $Q$-curvature in conformal geometry. The result implies that in the conformal class of the unit Euclidean ball there exist metrics with a single singular boundary point which have flat $Q$-curvature and constant boundary $Q$-curvature. Moreover, all of such metrics are classified. This phenome","authors_text":"Jingang Xiong, Liming Sun","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-25T23:58:25Z","title":"Classification theorems for solutions of higher order boundary conformally invariant problems, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06852","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":"sha256:55625b015789edac16d6b93a6d629c9b9a05e0900c372ed4b99941456a72e57f","target":"record","created_at":"2026-05-18T01:04:21Z","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":"c3716943f9c4beefe3d5ba863c26c88b952dd2c294a1afc8bc366fd31f207a77","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-25T23:58:25Z","title_canon_sha256":"c01146e0899ffa3772f478aaa974f5478562b4be2bed4c9a1f63147a483e7bf7"},"schema_version":"1.0","source":{"id":"1601.06852","kind":"arxiv","version":2}},"canonical_sha256":"cd3e4b87256a614d4dabf7849a1396d95893b274c3df8f90982c780d9e85a5da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd3e4b87256a614d4dabf7849a1396d95893b274c3df8f90982c780d9e85a5da","first_computed_at":"2026-05-18T01:04:21.562476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:21.562476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"69dMcWh1tSmvQH/TezOmwXW0QaXuKWdflZOpN6x3gPWEgME5iwsA5dMjre/pEADRKqA++UBL9HhqA+Wh1ajCBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:21.562943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06852","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55625b015789edac16d6b93a6d629c9b9a05e0900c372ed4b99941456a72e57f","sha256:2d1e26eea481860484b342b12e79879f41bc87d438c817af582bdde1a3b42210"],"state_sha256":"8ed89e4f14dfb106d31a8643cf5382cb92a139298fb9675652ae56b8c30f21ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4cACepq6smEBxMxDSU4g1ktI3430Mg0kN/dVv2OjRk+0+6cnFJeaKJ2t7yJOtCjgxlo+73LcS7AAg5+a6H8qCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:20:42.894434Z","bundle_sha256":"8150a7c934e6f5290165333aade26ef6d9402d6f39186d598825ef996437275e"}}