{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IV4GTNQXTPEWQNRWBLWITNBWSE","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":"c3db94c6aae4d63d30e6796aca290d0dd6df4f50472f79595f3bd51b764345b8","cross_cats_sorted":["math.DG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-31T08:30:52Z","title_canon_sha256":"94672a99a395d77f91e078c79243dceeed94408b4cdc574ac38f5937cc8a6dd5"},"schema_version":"1.0","source":{"id":"1508.07716","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07716","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07716v2","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07716","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"IV4GTNQXTPEW","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IV4GTNQXTPEWQNRW","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IV4GTNQX","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:cc8f69b50cac7ee564fc796c7b6f67bb956aa166b60714a7cf91603a8c8a31f5","target":"graph","created_at":"2026-05-18T00:15:24Z","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 extend the Faltings modular heights of abelian varieties to general arithmetic varieties and show direct relations with the Kahler-Einstein geometry, the Minimal Model Program, heights of Bost and Zhang, and give some applications. Along the way, we propose arithmetic Yau-Tian-Donaldson conjecture, an equivalence of a purely arithmetic property of variety and its metrical property, and partially confirm it.","authors_text":"Yuji Odaka","cross_cats":["math.DG","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-31T08:30:52Z","title":"Canonical Kahler metrics and Arithmetics -- Generalising Faltings heights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07716","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:e919f647545c9517c761ebbf488c17479c02bacdcc1ac819d652730cd0ad3425","target":"record","created_at":"2026-05-18T00:15:24Z","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":"c3db94c6aae4d63d30e6796aca290d0dd6df4f50472f79595f3bd51b764345b8","cross_cats_sorted":["math.DG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-31T08:30:52Z","title_canon_sha256":"94672a99a395d77f91e078c79243dceeed94408b4cdc574ac38f5937cc8a6dd5"},"schema_version":"1.0","source":{"id":"1508.07716","kind":"arxiv","version":2}},"canonical_sha256":"457869b6179bc96836360aec89b4369139d764ca0720ea8cc2787d79d87d5c72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"457869b6179bc96836360aec89b4369139d764ca0720ea8cc2787d79d87d5c72","first_computed_at":"2026-05-18T00:15:24.929824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:24.929824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iV0DBxw84P4tVBF2u3LGI9fI2Rq7EjtJu5EwZ+TSBJ7nNFE55c3s6QfQ4aUxHJLS8kBQwtcbspQUBRLZtR6CAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:24.930419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07716","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e919f647545c9517c761ebbf488c17479c02bacdcc1ac819d652730cd0ad3425","sha256:cc8f69b50cac7ee564fc796c7b6f67bb956aa166b60714a7cf91603a8c8a31f5"],"state_sha256":"0149653c64d775cabb6e57a79aade4ef76c4928a5ebf4147330883f96f8674d1"}