{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KSIIQPH2SOOP2KONEO455INBPQ","short_pith_number":"pith:KSIIQPH2","canonical_record":{"source":{"id":"1801.09842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-30T03:38:08Z","cross_cats_sorted":["math.AP","math.CV"],"title_canon_sha256":"c1a03cce4c095c915bb73db474f60b47ae37506fe38721ed53cbe5457ccce3bd","abstract_canon_sha256":"082dc8e55a869ba0791b7e0e3076c2defa7af8b79fcba996f36b2f28ec9eb6ef"},"schema_version":"1.0"},"canonical_sha256":"5490883cfa939cfd29cd23b9dea1a17c146a8bc92218cb40d0fa3b141c018800","source":{"kind":"arxiv","id":"1801.09842","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09842","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09842v1","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09842","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"pith_short_12","alias_value":"KSIIQPH2SOOP","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KSIIQPH2SOOP2KON","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KSIIQPH2","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KSIIQPH2SOOP2KONEO455INBPQ","target":"record","payload":{"canonical_record":{"source":{"id":"1801.09842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-30T03:38:08Z","cross_cats_sorted":["math.AP","math.CV"],"title_canon_sha256":"c1a03cce4c095c915bb73db474f60b47ae37506fe38721ed53cbe5457ccce3bd","abstract_canon_sha256":"082dc8e55a869ba0791b7e0e3076c2defa7af8b79fcba996f36b2f28ec9eb6ef"},"schema_version":"1.0"},"canonical_sha256":"5490883cfa939cfd29cd23b9dea1a17c146a8bc92218cb40d0fa3b141c018800","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:46.611567Z","signature_b64":"+WDHLTYlH5lzeoyUpxBsE33jwHHgrj6yI00WS7F8C8myFiTcMm1HnRXPE9HvRd5DFAcblrtc5w53KLbV2bZSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5490883cfa939cfd29cd23b9dea1a17c146a8bc92218cb40d0fa3b141c018800","last_reissued_at":"2026-05-18T00:24:46.611055Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:46.611055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.09842","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2AN53uYCw+gv/z8vTVzuZa+BZId9Le8FiJb+qwhjik1wejjr8TCycmTTekZ3CweUFDToeU96s10iaw8hnwpQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:14:29.067300Z"},"content_sha256":"e8b8e3e106fd2b85995e52194c66c8c45fea941926a19ac3324df301235567b4","schema_version":"1.0","event_id":"sha256:e8b8e3e106fd2b85995e52194c66c8c45fea941926a19ac3324df301235567b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KSIIQPH2SOOP2KONEO455INBPQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fu-Yau Hessian Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CV"],"primary_cat":"math.DG","authors_text":"Duong H. Phong, Sebastien Picard, Xiangwen Zhang","submitted_at":"2018-01-30T03:38:08Z","abstract_excerpt":"We solve the Fu-Yau equation for arbitrary dimension and arbitrary slope $\\alpha'$. Actually we obtain at the same time a solution of the open case $\\alpha'>0$, an improved solution of the known case $\\alpha'<0$, and solutions for a family of Hessian equations which includes the Fu-Yau equation as a special case. The method is based on the introduction of a more stringent ellipticity condition than the usual $\\Gamma_k$ admissible cone condition, and which can be shown to be preserved by precise estimates with scale."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09842","kind":"arxiv","version":1},"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":"2026-05-18T00:24:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QeEixSARzT93Ho+c5Ka6Z97578kjzCWA0FfhVyDK103BVPbF0/b8cOII/kHV3h/l5vOOjZGxjnIWmv7tVKsRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:14:29.068011Z"},"content_sha256":"5a4feb5fcb0c8eafe4925813ef8cd9805ab30be735c287047f31c674c202a7fb","schema_version":"1.0","event_id":"sha256:5a4feb5fcb0c8eafe4925813ef8cd9805ab30be735c287047f31c674c202a7fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KSIIQPH2SOOP2KONEO455INBPQ/bundle.json","state_url":"https://pith.science/pith/KSIIQPH2SOOP2KONEO455INBPQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KSIIQPH2SOOP2KONEO455INBPQ/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":"2026-05-25T21:14:29Z","links":{"resolver":"https://pith.science/pith/KSIIQPH2SOOP2KONEO455INBPQ","bundle":"https://pith.science/pith/KSIIQPH2SOOP2KONEO455INBPQ/bundle.json","state":"https://pith.science/pith/KSIIQPH2SOOP2KONEO455INBPQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KSIIQPH2SOOP2KONEO455INBPQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KSIIQPH2SOOP2KONEO455INBPQ","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":"082dc8e55a869ba0791b7e0e3076c2defa7af8b79fcba996f36b2f28ec9eb6ef","cross_cats_sorted":["math.AP","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-30T03:38:08Z","title_canon_sha256":"c1a03cce4c095c915bb73db474f60b47ae37506fe38721ed53cbe5457ccce3bd"},"schema_version":"1.0","source":{"id":"1801.09842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09842","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09842v1","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09842","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"pith_short_12","alias_value":"KSIIQPH2SOOP","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KSIIQPH2SOOP2KON","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KSIIQPH2","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:5a4feb5fcb0c8eafe4925813ef8cd9805ab30be735c287047f31c674c202a7fb","target":"graph","created_at":"2026-05-18T00:24:46Z","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 solve the Fu-Yau equation for arbitrary dimension and arbitrary slope $\\alpha'$. Actually we obtain at the same time a solution of the open case $\\alpha'>0$, an improved solution of the known case $\\alpha'<0$, and solutions for a family of Hessian equations which includes the Fu-Yau equation as a special case. The method is based on the introduction of a more stringent ellipticity condition than the usual $\\Gamma_k$ admissible cone condition, and which can be shown to be preserved by precise estimates with scale.","authors_text":"Duong H. Phong, Sebastien Picard, Xiangwen Zhang","cross_cats":["math.AP","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-30T03:38:08Z","title":"Fu-Yau Hessian Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09842","kind":"arxiv","version":1},"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:e8b8e3e106fd2b85995e52194c66c8c45fea941926a19ac3324df301235567b4","target":"record","created_at":"2026-05-18T00:24:46Z","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":"082dc8e55a869ba0791b7e0e3076c2defa7af8b79fcba996f36b2f28ec9eb6ef","cross_cats_sorted":["math.AP","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-30T03:38:08Z","title_canon_sha256":"c1a03cce4c095c915bb73db474f60b47ae37506fe38721ed53cbe5457ccce3bd"},"schema_version":"1.0","source":{"id":"1801.09842","kind":"arxiv","version":1}},"canonical_sha256":"5490883cfa939cfd29cd23b9dea1a17c146a8bc92218cb40d0fa3b141c018800","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5490883cfa939cfd29cd23b9dea1a17c146a8bc92218cb40d0fa3b141c018800","first_computed_at":"2026-05-18T00:24:46.611055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:46.611055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+WDHLTYlH5lzeoyUpxBsE33jwHHgrj6yI00WS7F8C8myFiTcMm1HnRXPE9HvRd5DFAcblrtc5w53KLbV2bZSDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:46.611567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8b8e3e106fd2b85995e52194c66c8c45fea941926a19ac3324df301235567b4","sha256:5a4feb5fcb0c8eafe4925813ef8cd9805ab30be735c287047f31c674c202a7fb"],"state_sha256":"fe41063056ba45a3f80f7587b5f9f9a148458e56649d8fb9de0bfe8e5e5d09cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SCPSFtSnLl6ytLJQ7m/67cMjgeXLI9GxU+mmgxaayjyMwnleT6wncKw1TjnAm1HAZytOfmkPT0wu061XNbXmCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:14:29.071575Z","bundle_sha256":"7fce053e92f330d380b706a31ab04d2ff1e0ef4bfe5d5e3c67af71e46c139c94"}}