{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UI2SJYNB3M6QMPA3PLBQU4XMJM","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":"424a2e24532025216bd4d5efa49a70e6ab91d787096f6ecbe507beb0e6076b83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-30T23:19:38Z","title_canon_sha256":"294980d9b1a10944dad7b04df750bf8070877766dfc54f7ad0a5ed5d884037c7"},"schema_version":"1.0","source":{"id":"1612.00075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00075","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00075v1","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00075","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"pith_short_12","alias_value":"UI2SJYNB3M6Q","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UI2SJYNB3M6QMPA3","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UI2SJYNB","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:43fde85cded1ba5cbb5db963e72134a07a3b80b467ccbb89bd9cd142a2176604","target":"graph","created_at":"2026-05-18T00:56:06Z","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":"This is the first paper in a series to develop a linear and nonlinear theory for elliptic and parabolic equations on K\\\"ahler varieties with mild singularities. Donaldson has established a Schauder estimate for linear and complex Monge-Amp\\`ere equations when the background K\\\"ahler metrics on $\\mathbb{C}^n$ have cone singularities along a smooth complex hypersurface. We prove a sharp pointwise Schauder estimate for linear elliptic and parabolic equations on $\\mathbb{C}^n$ with background metric $g_\\beta= \\sqrt{-1} ( dz_1 \\wedge d\\bar{z_1} + \\ldots + \\beta^2|z_n|^{-2(1-\\beta)} dz_n \\wedge d\\ba","authors_text":"Bin Guo, Jian Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-30T23:19:38Z","title":"Schauder estimates for equations with cone metrics, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00075","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:f8c9aa78b136b792029859d264834aa10ed2f1894e156ee16525cdb440f3c921","target":"record","created_at":"2026-05-18T00:56:06Z","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":"424a2e24532025216bd4d5efa49a70e6ab91d787096f6ecbe507beb0e6076b83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-30T23:19:38Z","title_canon_sha256":"294980d9b1a10944dad7b04df750bf8070877766dfc54f7ad0a5ed5d884037c7"},"schema_version":"1.0","source":{"id":"1612.00075","kind":"arxiv","version":1}},"canonical_sha256":"a23524e1a1db3d063c1b7ac30a72ec4b0777e09a0f31f56667e2ce613202cef8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a23524e1a1db3d063c1b7ac30a72ec4b0777e09a0f31f56667e2ce613202cef8","first_computed_at":"2026-05-18T00:56:06.898465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:06.898465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zzRykXXEyYFte/Y7u48gVmCj5994NTPmPxFCBZYLxprENwm8cZzMpTCAnvjI1ZBNUS031Wo7vETryOWA2BC0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:06.898971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8c9aa78b136b792029859d264834aa10ed2f1894e156ee16525cdb440f3c921","sha256:43fde85cded1ba5cbb5db963e72134a07a3b80b467ccbb89bd9cd142a2176604"],"state_sha256":"b084055650608bfece64222e23b0666783d276b216f4c93b3d441452fcfd25e7"}