{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TZOQJ2SQ3EQIJAUGNLUBMIFOS3","short_pith_number":"pith:TZOQJ2SQ","canonical_record":{"source":{"id":"1602.08838","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-29T06:39:20Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"89bafcb143d1470d273be665a2df98a32034d161abfd7099aaec5f88f351d963","abstract_canon_sha256":"6adb94ea1a71bee4f20a9f8911bad81b2ef4b5071a1550a73051eee31d9e0639"},"schema_version":"1.0"},"canonical_sha256":"9e5d04ea50d9208482866ae81620ae96cc3d6769323d10acdad242064f75f586","source":{"kind":"arxiv","id":"1602.08838","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08838","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08838v3","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08838","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"TZOQJ2SQ3EQI","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TZOQJ2SQ3EQIJAUG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TZOQJ2SQ","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TZOQJ2SQ3EQIJAUGNLUBMIFOS3","target":"record","payload":{"canonical_record":{"source":{"id":"1602.08838","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-29T06:39:20Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"89bafcb143d1470d273be665a2df98a32034d161abfd7099aaec5f88f351d963","abstract_canon_sha256":"6adb94ea1a71bee4f20a9f8911bad81b2ef4b5071a1550a73051eee31d9e0639"},"schema_version":"1.0"},"canonical_sha256":"9e5d04ea50d9208482866ae81620ae96cc3d6769323d10acdad242064f75f586","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:23.949710Z","signature_b64":"rtbqgLt95ZMnXcUCZWiSSA5Xj//DQM/O3gSg3TBUJ81TACg8RkmnSYzwGKHU0j9z9yjaoBpF7uVGxtf5N/++AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e5d04ea50d9208482866ae81620ae96cc3d6769323d10acdad242064f75f586","last_reissued_at":"2026-05-18T00:33:23.949095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:23.949095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.08838","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P26chgIMEUm8N1KsWUml11dGYAqr9kuTYsWaogqc2INMB3uz4OGFXo7fxSXLuydCuVyCEKA9bxfQtQ+XLk1MCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:02:35.548155Z"},"content_sha256":"497ce8c03750cd2a4dfab649993f263fbd5b2254982223fa80233943ec132262","schema_version":"1.0","event_id":"sha256:497ce8c03750cd2a4dfab649993f263fbd5b2254982223fa80233943ec132262"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TZOQJ2SQ3EQIJAUGNLUBMIFOS3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Fu-Yau equation with negative slope parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.CV","authors_text":"Duong H. Phong, Sebastien Picard, Xiangwen Zhang","submitted_at":"2016-02-29T06:39:20Z","abstract_excerpt":"The Fu-Yau equation is an equation introduced by J. Fu and S.T. Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system, it depends on a slope parameter $\\alpha'$. The equation was solved in dimension $2$ by Fu and Yau in two successive papers for $\\alpha'>0$, and for $\\alpha'<0$. In the present paper, we solve the Fu-Yau equation in arbitrary dimension for $\\alpha'<0$. To our knowledge, these are the first non-trivial solutions of the Fu-Yau equation in any dimension strictly greater than $2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08838","kind":"arxiv","version":3},"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":"2026-05-18T00:33:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VyvwyITKpG0cTYN0qG2QRgK6gKZrG/zFkesgrUEVKrv9TfG8tUKaWcqB3OvBOUCTCSS3aXRufQLwS6b0EAaHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:02:35.548842Z"},"content_sha256":"f0e3c956fe1cdf6aeb543ea7495bdb44f1caf6dd5db035f4d40785f2f2e2c9a4","schema_version":"1.0","event_id":"sha256:f0e3c956fe1cdf6aeb543ea7495bdb44f1caf6dd5db035f4d40785f2f2e2c9a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TZOQJ2SQ3EQIJAUGNLUBMIFOS3/bundle.json","state_url":"https://pith.science/pith/TZOQJ2SQ3EQIJAUGNLUBMIFOS3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TZOQJ2SQ3EQIJAUGNLUBMIFOS3/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":"2026-05-25T14:02:35Z","links":{"resolver":"https://pith.science/pith/TZOQJ2SQ3EQIJAUGNLUBMIFOS3","bundle":"https://pith.science/pith/TZOQJ2SQ3EQIJAUGNLUBMIFOS3/bundle.json","state":"https://pith.science/pith/TZOQJ2SQ3EQIJAUGNLUBMIFOS3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TZOQJ2SQ3EQIJAUGNLUBMIFOS3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TZOQJ2SQ3EQIJAUGNLUBMIFOS3","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":"6adb94ea1a71bee4f20a9f8911bad81b2ef4b5071a1550a73051eee31d9e0639","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-29T06:39:20Z","title_canon_sha256":"89bafcb143d1470d273be665a2df98a32034d161abfd7099aaec5f88f351d963"},"schema_version":"1.0","source":{"id":"1602.08838","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08838","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08838v3","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08838","created_at":"2026-05-18T00:33:23Z"},{"alias_kind":"pith_short_12","alias_value":"TZOQJ2SQ3EQI","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TZOQJ2SQ3EQIJAUG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TZOQJ2SQ","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:f0e3c956fe1cdf6aeb543ea7495bdb44f1caf6dd5db035f4d40785f2f2e2c9a4","target":"graph","created_at":"2026-05-18T00:33:23Z","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":"The Fu-Yau equation is an equation introduced by J. Fu and S.T. Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system, it depends on a slope parameter $\\alpha'$. The equation was solved in dimension $2$ by Fu and Yau in two successive papers for $\\alpha'>0$, and for $\\alpha'<0$. In the present paper, we solve the Fu-Yau equation in arbitrary dimension for $\\alpha'<0$. To our knowledge, these are the first non-trivial solutions of the Fu-Yau equation in any dimension strictly greater than $2$.","authors_text":"Duong H. Phong, Sebastien Picard, Xiangwen Zhang","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-29T06:39:20Z","title":"The Fu-Yau equation with negative slope parameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08838","kind":"arxiv","version":3},"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":"sha256:497ce8c03750cd2a4dfab649993f263fbd5b2254982223fa80233943ec132262","target":"record","created_at":"2026-05-18T00:33:23Z","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":"6adb94ea1a71bee4f20a9f8911bad81b2ef4b5071a1550a73051eee31d9e0639","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-29T06:39:20Z","title_canon_sha256":"89bafcb143d1470d273be665a2df98a32034d161abfd7099aaec5f88f351d963"},"schema_version":"1.0","source":{"id":"1602.08838","kind":"arxiv","version":3}},"canonical_sha256":"9e5d04ea50d9208482866ae81620ae96cc3d6769323d10acdad242064f75f586","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e5d04ea50d9208482866ae81620ae96cc3d6769323d10acdad242064f75f586","first_computed_at":"2026-05-18T00:33:23.949095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:23.949095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rtbqgLt95ZMnXcUCZWiSSA5Xj//DQM/O3gSg3TBUJ81TACg8RkmnSYzwGKHU0j9z9yjaoBpF7uVGxtf5N/++AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:23.949710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.08838","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:497ce8c03750cd2a4dfab649993f263fbd5b2254982223fa80233943ec132262","sha256:f0e3c956fe1cdf6aeb543ea7495bdb44f1caf6dd5db035f4d40785f2f2e2c9a4"],"state_sha256":"71e6a7e3aa5ef4ef893deb243e71dd704d787d50e1500ba32dd0504437292223"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"swNGRdTFhhx0JC0uz2EypCLWLXfFN0ziwlyXoUrefVViLnwIGJJOo2xbYmbfd8LIOGXTuO81rRX+aLCblGlCAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:02:35.552501Z","bundle_sha256":"e8b922ff6f1d6d9f575c5b312ac0ccb612c46aaaf558453e1933e426e1cbc2eb"}}