{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IV4GTNQXTPEWQNRWBLWITNBWSE","short_pith_number":"pith:IV4GTNQX","canonical_record":{"source":{"id":"1508.07716","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-31T08:30:52Z","cross_cats_sorted":["math.DG","math.NT"],"title_canon_sha256":"94672a99a395d77f91e078c79243dceeed94408b4cdc574ac38f5937cc8a6dd5","abstract_canon_sha256":"c3db94c6aae4d63d30e6796aca290d0dd6df4f50472f79595f3bd51b764345b8"},"schema_version":"1.0"},"canonical_sha256":"457869b6179bc96836360aec89b4369139d764ca0720ea8cc2787d79d87d5c72","source":{"kind":"arxiv","id":"1508.07716","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IV4GTNQXTPEWQNRWBLWITNBWSE","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07716","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-31T08:30:52Z","cross_cats_sorted":["math.DG","math.NT"],"title_canon_sha256":"94672a99a395d77f91e078c79243dceeed94408b4cdc574ac38f5937cc8a6dd5","abstract_canon_sha256":"c3db94c6aae4d63d30e6796aca290d0dd6df4f50472f79595f3bd51b764345b8"},"schema_version":"1.0"},"canonical_sha256":"457869b6179bc96836360aec89b4369139d764ca0720ea8cc2787d79d87d5c72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:24.930419Z","signature_b64":"iV0DBxw84P4tVBF2u3LGI9fI2Rq7EjtJu5EwZ+TSBJ7nNFE55c3s6QfQ4aUxHJLS8kBQwtcbspQUBRLZtR6CAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"457869b6179bc96836360aec89b4369139d764ca0720ea8cc2787d79d87d5c72","last_reissued_at":"2026-05-18T00:15:24.929824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:24.929824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07716","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":"2026-05-18T00:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCXmuLU3d9Hgj8dby0QYt8tPXxZOMbpgT8nCeciPYHyTYeXZrZiQ9UGVk/EqgqsVXE4ywM9VvfdaAy7EucYXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:08:49.297532Z"},"content_sha256":"e919f647545c9517c761ebbf488c17479c02bacdcc1ac819d652730cd0ad3425","schema_version":"1.0","event_id":"sha256:e919f647545c9517c761ebbf488c17479c02bacdcc1ac819d652730cd0ad3425"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IV4GTNQXTPEWQNRWBLWITNBWSE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Canonical Kahler metrics and Arithmetics -- Generalising Faltings heights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.NT"],"primary_cat":"math.AG","authors_text":"Yuji Odaka","submitted_at":"2015-08-31T08:30:52Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07716","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":"2026-05-18T00:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uLD38r6osc3wYd6sESR3H0COSSCOzjrZbEsvcJPNimMcP3BPX6+0IIz4k6M31xDT2wlnxyQm9liA7uzrDi4QAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:08:49.298201Z"},"content_sha256":"cc8f69b50cac7ee564fc796c7b6f67bb956aa166b60714a7cf91603a8c8a31f5","schema_version":"1.0","event_id":"sha256:cc8f69b50cac7ee564fc796c7b6f67bb956aa166b60714a7cf91603a8c8a31f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IV4GTNQXTPEWQNRWBLWITNBWSE/bundle.json","state_url":"https://pith.science/pith/IV4GTNQXTPEWQNRWBLWITNBWSE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IV4GTNQXTPEWQNRWBLWITNBWSE/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":"2026-05-26T19:08:49Z","links":{"resolver":"https://pith.science/pith/IV4GTNQXTPEWQNRWBLWITNBWSE","bundle":"https://pith.science/pith/IV4GTNQXTPEWQNRWBLWITNBWSE/bundle.json","state":"https://pith.science/pith/IV4GTNQXTPEWQNRWBLWITNBWSE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IV4GTNQXTPEWQNRWBLWITNBWSE/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7y96UVrwJZVe2Je+ICPqerYLq+YLhq7ORwtZMe5ta9p58bJ7jizPq+RYEDpxqDtgALeO1xRiXKb3mkbGDUplDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:08:49.301952Z","bundle_sha256":"0e563869f6e7e7efab737d2a73e463412a5c9aff76c47d4892bcd970cbc7c96b"}}