{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z4IQVHKASVEVICELROTYUDDLWR","short_pith_number":"pith:Z4IQVHKA","canonical_record":{"source":{"id":"1503.02899","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2015-03-10T13:41:37Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"22dd47651fc6f250472615013ceabb80b5532d7c1c811213ce62e25b6bdabfe1","abstract_canon_sha256":"4035f575cbb72afc4a01bdd697f4d33936a05044cda6df7fa0ab60b27db131b1"},"schema_version":"1.0"},"canonical_sha256":"cf110a9d40954954088b8ba78a0c6bb473d4ab3a97ce0cf4527590aad5278a1c","source":{"kind":"arxiv","id":"1503.02899","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02899","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02899v2","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02899","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"pith_short_12","alias_value":"Z4IQVHKASVEV","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z4IQVHKASVEVICEL","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z4IQVHKA","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z4IQVHKASVEVICELROTYUDDLWR","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02899","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2015-03-10T13:41:37Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"22dd47651fc6f250472615013ceabb80b5532d7c1c811213ce62e25b6bdabfe1","abstract_canon_sha256":"4035f575cbb72afc4a01bdd697f4d33936a05044cda6df7fa0ab60b27db131b1"},"schema_version":"1.0"},"canonical_sha256":"cf110a9d40954954088b8ba78a0c6bb473d4ab3a97ce0cf4527590aad5278a1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:01.570499Z","signature_b64":"bCNcMhveVkNspcehWQni9jkks6rBhf+MeQTU0Pa/Y/btdFtlx/URTZ1tMTgCIOqB+U59p4KYzm5d5anPwftcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf110a9d40954954088b8ba78a0c6bb473d4ab3a97ce0cf4527590aad5278a1c","last_reissued_at":"2026-05-18T01:25:01.569753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:01.569753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02899","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":"2026-05-18T01:25:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8uo117cb5vOBCv202TanZf6lgEt6MklV7LB2yHofl7TwZZOcAt8w3Jn9nDVHqAzcPY4+fIaz/xq7AvzCaiSWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:17:23.465907Z"},"content_sha256":"9d9b3a3d8b1d38eaae3f09780bc6ef8d24e3974891f5a3383809af195bac21f7","schema_version":"1.0","event_id":"sha256:9d9b3a3d8b1d38eaae3f09780bc6ef8d24e3974891f5a3383809af195bac21f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z4IQVHKASVEVICELROTYUDDLWR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calabi-Yau metrics and string compactification","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"hep-th","authors_text":"Michael R. Douglas","submitted_at":"2015-03-10T13:41:37Z","abstract_excerpt":"Yau proved an existence theorem for Ricci-flat K\\\"ahler metrics in the 1970's, but we still have no closed form expressions for them. Nevertheless there are several ways to get approximate expressions, both numerical and analytical. We survey some of this work and explain how it can be used to obtain physical predictions from superstring theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02899","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":"2026-05-18T01:25:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4U1HXeps4EH6KBhisIsTrk6F1xW5tYOl/oUTq6AqCpEtGD1x6foml8xoRrcUefNqsvPtESHTzW7fQP67VbK9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:17:23.466349Z"},"content_sha256":"e7616246f7da266dd8f1f11d3a0e1c79e8b51deb7e8acfa34fb6b4fcb4552229","schema_version":"1.0","event_id":"sha256:e7616246f7da266dd8f1f11d3a0e1c79e8b51deb7e8acfa34fb6b4fcb4552229"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4IQVHKASVEVICELROTYUDDLWR/bundle.json","state_url":"https://pith.science/pith/Z4IQVHKASVEVICELROTYUDDLWR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4IQVHKASVEVICELROTYUDDLWR/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":"2026-08-13T09:17:23Z","links":{"resolver":"https://pith.science/pith/Z4IQVHKASVEVICELROTYUDDLWR","bundle":"https://pith.science/pith/Z4IQVHKASVEVICELROTYUDDLWR/bundle.json","state":"https://pith.science/pith/Z4IQVHKASVEVICELROTYUDDLWR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4IQVHKASVEVICELROTYUDDLWR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z4IQVHKASVEVICELROTYUDDLWR","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":"4035f575cbb72afc4a01bdd697f4d33936a05044cda6df7fa0ab60b27db131b1","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2015-03-10T13:41:37Z","title_canon_sha256":"22dd47651fc6f250472615013ceabb80b5532d7c1c811213ce62e25b6bdabfe1"},"schema_version":"1.0","source":{"id":"1503.02899","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02899","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02899v2","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02899","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"pith_short_12","alias_value":"Z4IQVHKASVEV","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z4IQVHKASVEVICEL","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z4IQVHKA","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:e7616246f7da266dd8f1f11d3a0e1c79e8b51deb7e8acfa34fb6b4fcb4552229","target":"graph","created_at":"2026-05-18T01:25:01Z","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":"Yau proved an existence theorem for Ricci-flat K\\\"ahler metrics in the 1970's, but we still have no closed form expressions for them. Nevertheless there are several ways to get approximate expressions, both numerical and analytical. We survey some of this work and explain how it can be used to obtain physical predictions from superstring theory.","authors_text":"Michael R. Douglas","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2015-03-10T13:41:37Z","title":"Calabi-Yau metrics and string compactification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02899","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":"sha256:9d9b3a3d8b1d38eaae3f09780bc6ef8d24e3974891f5a3383809af195bac21f7","target":"record","created_at":"2026-05-18T01:25:01Z","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":"4035f575cbb72afc4a01bdd697f4d33936a05044cda6df7fa0ab60b27db131b1","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2015-03-10T13:41:37Z","title_canon_sha256":"22dd47651fc6f250472615013ceabb80b5532d7c1c811213ce62e25b6bdabfe1"},"schema_version":"1.0","source":{"id":"1503.02899","kind":"arxiv","version":2}},"canonical_sha256":"cf110a9d40954954088b8ba78a0c6bb473d4ab3a97ce0cf4527590aad5278a1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf110a9d40954954088b8ba78a0c6bb473d4ab3a97ce0cf4527590aad5278a1c","first_computed_at":"2026-05-18T01:25:01.569753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:01.569753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bCNcMhveVkNspcehWQni9jkks6rBhf+MeQTU0Pa/Y/btdFtlx/URTZ1tMTgCIOqB+U59p4KYzm5d5anPwftcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:01.570499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02899","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d9b3a3d8b1d38eaae3f09780bc6ef8d24e3974891f5a3383809af195bac21f7","sha256:e7616246f7da266dd8f1f11d3a0e1c79e8b51deb7e8acfa34fb6b4fcb4552229"],"state_sha256":"0f9c5a13e48fd5cb43e78dd9f46a9f9fee7f02ab3b29facf00b0c378bb2671bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HPWKMgQz16x6CrEt6fxSZ6ut4tuW8eABLQ0yRScfTAHyDooYpM+k0BH6lKXF8okIbkeW3PPDGVPU9gpotssNAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T09:17:23.493414Z","bundle_sha256":"d2999a11a700e69ac23225a293a49e06fd097107016e832ad6f4b66815206f1a"}}