{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:237Y3X7AUA766NJ3D4BHD73O7S","short_pith_number":"pith:237Y3X7A","canonical_record":{"source":{"id":"1205.4207","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-18T17:51:21Z","cross_cats_sorted":[],"title_canon_sha256":"8340cb34928ce469a4216effc7aa020dd8db9f1a722a51d375f2db41692a7311","abstract_canon_sha256":"25be0ac425328cf6668de058f6724dc12af3d2b2532dcebe441d8fd239488329"},"schema_version":"1.0"},"canonical_sha256":"d6ff8ddfe0a03fef353b1f0271ff6efca1c0d3f0d9edc36b3e6aaee28be70eee","source":{"kind":"arxiv","id":"1205.4207","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4207","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4207v7","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4207","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"237Y3X7AUA76","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"237Y3X7AUA766NJ3","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"237Y3X7A","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:237Y3X7AUA766NJ3D4BHD73O7S","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4207","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-18T17:51:21Z","cross_cats_sorted":[],"title_canon_sha256":"8340cb34928ce469a4216effc7aa020dd8db9f1a722a51d375f2db41692a7311","abstract_canon_sha256":"25be0ac425328cf6668de058f6724dc12af3d2b2532dcebe441d8fd239488329"},"schema_version":"1.0"},"canonical_sha256":"d6ff8ddfe0a03fef353b1f0271ff6efca1c0d3f0d9edc36b3e6aaee28be70eee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:23.336265Z","signature_b64":"li8zAeu8HiB3yJT0fuaB3+BMGjhBGp93ezTI7erGFlK6mqCzOtUlQz6oM4Jzx+wS6BHEoxsPeXK98CzX1weoAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6ff8ddfe0a03fef353b1f0271ff6efca1c0d3f0d9edc36b3e6aaee28be70eee","last_reissued_at":"2026-05-18T01:06:23.335604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:23.335604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4207","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6s5OLjDwkOJu/GoZ2Q2DIzdeUAZuKKGnsCw+D7iFop11SERM3LCHweOFxaYz2S2beOmDMjpaQPSM6QOxXDljCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:23:57.497197Z"},"content_sha256":"8919c87a2b220e2da5be7b0d2265b67682be22e7655b7193b6d23a569a5e23df","schema_version":"1.0","event_id":"sha256:8919c87a2b220e2da5be7b0d2265b67682be22e7655b7193b6d23a569a5e23df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:237Y3X7AUA766NJ3D4BHD73O7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global Torelli Theorem for Projective Manifolds of Calabi-Yau Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kefeng Liu, Yang Shen","submitted_at":"2012-05-18T17:51:21Z","abstract_excerpt":"We prove that the period maps from the Torelli space and the moduli space with level $m$ structure of Calabi-Yau type manifolds to the corresponding period domain of polarized Hodge structures are injective. The proof is based on the construction of holomorphic affine structure on the Teichm\\\"uller space and the construction of the completion space of the Torelli space with respect to the Hodge metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4207","kind":"arxiv","version":7},"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":"2026-05-18T01:06:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cnkMHtgE60+w5Jy/iTKUPVxl5HjaMIv1fQjWwg18aQxfxQQUnVyRyopElFoyG+ggpWOAbFkk8i12FCbkVVJdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:23:57.497594Z"},"content_sha256":"4632cea1a40094966ff6fd5899335f4dffaf0a07e9b055e29fd7e7f4394c6d12","schema_version":"1.0","event_id":"sha256:4632cea1a40094966ff6fd5899335f4dffaf0a07e9b055e29fd7e7f4394c6d12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/237Y3X7AUA766NJ3D4BHD73O7S/bundle.json","state_url":"https://pith.science/pith/237Y3X7AUA766NJ3D4BHD73O7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/237Y3X7AUA766NJ3D4BHD73O7S/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":"2026-05-30T18:23:57Z","links":{"resolver":"https://pith.science/pith/237Y3X7AUA766NJ3D4BHD73O7S","bundle":"https://pith.science/pith/237Y3X7AUA766NJ3D4BHD73O7S/bundle.json","state":"https://pith.science/pith/237Y3X7AUA766NJ3D4BHD73O7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/237Y3X7AUA766NJ3D4BHD73O7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:237Y3X7AUA766NJ3D4BHD73O7S","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":"25be0ac425328cf6668de058f6724dc12af3d2b2532dcebe441d8fd239488329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-18T17:51:21Z","title_canon_sha256":"8340cb34928ce469a4216effc7aa020dd8db9f1a722a51d375f2db41692a7311"},"schema_version":"1.0","source":{"id":"1205.4207","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4207","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4207v7","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4207","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"237Y3X7AUA76","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"237Y3X7AUA766NJ3","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"237Y3X7A","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:4632cea1a40094966ff6fd5899335f4dffaf0a07e9b055e29fd7e7f4394c6d12","target":"graph","created_at":"2026-05-18T01:06:23Z","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":"We prove that the period maps from the Torelli space and the moduli space with level $m$ structure of Calabi-Yau type manifolds to the corresponding period domain of polarized Hodge structures are injective. The proof is based on the construction of holomorphic affine structure on the Teichm\\\"uller space and the construction of the completion space of the Torelli space with respect to the Hodge metric.","authors_text":"Kefeng Liu, Yang Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-18T17:51:21Z","title":"Global Torelli Theorem for Projective Manifolds of Calabi-Yau Type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4207","kind":"arxiv","version":7},"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":"sha256:8919c87a2b220e2da5be7b0d2265b67682be22e7655b7193b6d23a569a5e23df","target":"record","created_at":"2026-05-18T01:06:23Z","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":"25be0ac425328cf6668de058f6724dc12af3d2b2532dcebe441d8fd239488329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-18T17:51:21Z","title_canon_sha256":"8340cb34928ce469a4216effc7aa020dd8db9f1a722a51d375f2db41692a7311"},"schema_version":"1.0","source":{"id":"1205.4207","kind":"arxiv","version":7}},"canonical_sha256":"d6ff8ddfe0a03fef353b1f0271ff6efca1c0d3f0d9edc36b3e6aaee28be70eee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6ff8ddfe0a03fef353b1f0271ff6efca1c0d3f0d9edc36b3e6aaee28be70eee","first_computed_at":"2026-05-18T01:06:23.335604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:23.335604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"li8zAeu8HiB3yJT0fuaB3+BMGjhBGp93ezTI7erGFlK6mqCzOtUlQz6oM4Jzx+wS6BHEoxsPeXK98CzX1weoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:23.336265Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4207","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8919c87a2b220e2da5be7b0d2265b67682be22e7655b7193b6d23a569a5e23df","sha256:4632cea1a40094966ff6fd5899335f4dffaf0a07e9b055e29fd7e7f4394c6d12"],"state_sha256":"328ccff11228524d470fbd0d3e0989a80cd2826a60798dd60c38d0241a914eda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wPX0LgX+eXWea7Pywm8imiXpQBJiR57IBOS29qzBJENuowli/BIGL0JFLcM+1OfhvU81IJvXwXJAL6KIu9xdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:23:57.500896Z","bundle_sha256":"8aa3f653de1e7fe8964b9af50a9c9888d05620364be2b0a8bf4ae94b9a572d92"}}