{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VDOHYHHSDAWZNLVYSBH3VEN7FF","short_pith_number":"pith:VDOHYHHS","canonical_record":{"source":{"id":"1712.03820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-07T23:54:23Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"680d9bf1d39fda9b217809fb7c2caf64d713aa8132d8bf9082efff128bd18fbe","abstract_canon_sha256":"fdb03c05e6a6fa96585b2e0d5a1043e7d3769e55f18d8dfc87af8cf58f537b8d"},"schema_version":"1.0"},"canonical_sha256":"a8dc7c1cf2182d96aeb8904fba91bf294bab9cdffa00e9af5bda4562a7295837","source":{"kind":"arxiv","id":"1712.03820","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03820","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03820v2","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03820","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"pith_short_12","alias_value":"VDOHYHHSDAWZ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VDOHYHHSDAWZNLVY","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VDOHYHHS","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VDOHYHHSDAWZNLVYSBH3VEN7FF","target":"record","payload":{"canonical_record":{"source":{"id":"1712.03820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-07T23:54:23Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"680d9bf1d39fda9b217809fb7c2caf64d713aa8132d8bf9082efff128bd18fbe","abstract_canon_sha256":"fdb03c05e6a6fa96585b2e0d5a1043e7d3769e55f18d8dfc87af8cf58f537b8d"},"schema_version":"1.0"},"canonical_sha256":"a8dc7c1cf2182d96aeb8904fba91bf294bab9cdffa00e9af5bda4562a7295837","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:01.491060Z","signature_b64":"MimccHuMkV6ckrHi1e2zTzcM67Zg1si7SA7ItcUHGrdr1OcA9MSC7a+23t07HNN60Sr3lANt9FKV2b0KOtSkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8dc7c1cf2182d96aeb8904fba91bf294bab9cdffa00e9af5bda4562a7295837","last_reissued_at":"2026-05-18T00:28:01.490369Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:01.490369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.03820","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":"2026-05-18T00:28:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y55irV1CX2kbKr8Gcn3PRSYyFiiRL5dhuGF3rr9kU6aKnZSh++gZDkMuAZbEp3o9kevtBsnqBgSOwdyalk07AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:59:42.310534Z"},"content_sha256":"5f322139e4eeb9d2a604e1eea933641c3b11b08d13aa91531de2e1f0dd9cb74c","schema_version":"1.0","event_id":"sha256:5f322139e4eeb9d2a604e1eea933641c3b11b08d13aa91531de2e1f0dd9cb74c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VDOHYHHSDAWZNLVYSBH3VEN7FF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smooth solution to higher dimensional complex Plateau problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Rong Du","submitted_at":"2017-12-07T23:54:23Z","abstract_excerpt":"Let $X$ be a compact connected strongly pseudoconvex $CR$ manifold of real dimension $2n-1$ in $\\mathbb{C}^{N}$. For $n\\ge 3$, Yau solved the complex Plateau problem of hypersurface type by checking a bunch of Kohn-Rossi cohomology groups in 1981. In this paper, we generalize Yau's conjecture on some numerical invariant of every isolated surface singularity defined by Yau and the author to any dimension and prove that the conjecture is true for local complete intersection singularities of dimension $n\\ge 3$. As a direct application, we solved complex Plateau problem of hypersurface type for an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03820","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":"2026-05-18T00:28:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0X4ou29blDeSAj/0ltl+SkJGsYNT7ljGQgZFWqJ7kPYM8DgDBXt12rB6M2HHvM6XFRvYn5qQ/kvP8yG+syGpAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:59:42.311136Z"},"content_sha256":"3384f1ee8a62e6a88c591532751bdb3a0eaeeb9334c3347c72865b0a61e01896","schema_version":"1.0","event_id":"sha256:3384f1ee8a62e6a88c591532751bdb3a0eaeeb9334c3347c72865b0a61e01896"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VDOHYHHSDAWZNLVYSBH3VEN7FF/bundle.json","state_url":"https://pith.science/pith/VDOHYHHSDAWZNLVYSBH3VEN7FF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VDOHYHHSDAWZNLVYSBH3VEN7FF/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":"2026-05-27T17:59:42Z","links":{"resolver":"https://pith.science/pith/VDOHYHHSDAWZNLVYSBH3VEN7FF","bundle":"https://pith.science/pith/VDOHYHHSDAWZNLVYSBH3VEN7FF/bundle.json","state":"https://pith.science/pith/VDOHYHHSDAWZNLVYSBH3VEN7FF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VDOHYHHSDAWZNLVYSBH3VEN7FF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VDOHYHHSDAWZNLVYSBH3VEN7FF","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":"fdb03c05e6a6fa96585b2e0d5a1043e7d3769e55f18d8dfc87af8cf58f537b8d","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-07T23:54:23Z","title_canon_sha256":"680d9bf1d39fda9b217809fb7c2caf64d713aa8132d8bf9082efff128bd18fbe"},"schema_version":"1.0","source":{"id":"1712.03820","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03820","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03820v2","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03820","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"pith_short_12","alias_value":"VDOHYHHSDAWZ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VDOHYHHSDAWZNLVY","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VDOHYHHS","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:3384f1ee8a62e6a88c591532751bdb3a0eaeeb9334c3347c72865b0a61e01896","target":"graph","created_at":"2026-05-18T00:28:01Z","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 $X$ be a compact connected strongly pseudoconvex $CR$ manifold of real dimension $2n-1$ in $\\mathbb{C}^{N}$. For $n\\ge 3$, Yau solved the complex Plateau problem of hypersurface type by checking a bunch of Kohn-Rossi cohomology groups in 1981. In this paper, we generalize Yau's conjecture on some numerical invariant of every isolated surface singularity defined by Yau and the author to any dimension and prove that the conjecture is true for local complete intersection singularities of dimension $n\\ge 3$. As a direct application, we solved complex Plateau problem of hypersurface type for an","authors_text":"Rong Du","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-07T23:54:23Z","title":"Smooth solution to higher dimensional complex Plateau problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03820","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":"sha256:5f322139e4eeb9d2a604e1eea933641c3b11b08d13aa91531de2e1f0dd9cb74c","target":"record","created_at":"2026-05-18T00:28:01Z","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":"fdb03c05e6a6fa96585b2e0d5a1043e7d3769e55f18d8dfc87af8cf58f537b8d","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-07T23:54:23Z","title_canon_sha256":"680d9bf1d39fda9b217809fb7c2caf64d713aa8132d8bf9082efff128bd18fbe"},"schema_version":"1.0","source":{"id":"1712.03820","kind":"arxiv","version":2}},"canonical_sha256":"a8dc7c1cf2182d96aeb8904fba91bf294bab9cdffa00e9af5bda4562a7295837","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8dc7c1cf2182d96aeb8904fba91bf294bab9cdffa00e9af5bda4562a7295837","first_computed_at":"2026-05-18T00:28:01.490369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:01.490369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MimccHuMkV6ckrHi1e2zTzcM67Zg1si7SA7ItcUHGrdr1OcA9MSC7a+23t07HNN60Sr3lANt9FKV2b0KOtSkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:01.491060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.03820","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f322139e4eeb9d2a604e1eea933641c3b11b08d13aa91531de2e1f0dd9cb74c","sha256:3384f1ee8a62e6a88c591532751bdb3a0eaeeb9334c3347c72865b0a61e01896"],"state_sha256":"e88e844534951d6eecb14f51d6dc6f58de19ff19ca2b16e6af273cf869949a52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Blw2t4fi9gJMxoueRaN2QdpXuQblPqhaNQ+upZlQ3jC4wZJXMWObqGgnqHBPMaJ3kPwsKkpFHsLWnh+lOlS0Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T17:59:42.314189Z","bundle_sha256":"429740dd8d3f2a2b38f6cca26e2191e3b4bdebb7fe90f236dcd829a3456157cc"}}