{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VDPVIJANG4B6M5XG47EPRQZY5F","short_pith_number":"pith:VDPVIJAN","canonical_record":{"source":{"id":"1007.2633","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-15T18:59:32Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6289dba12cc1d44ae78563e2685c1bb1e6142158b9813c3c0ab1525f5462c7a0","abstract_canon_sha256":"bf67e7cd4851dd6ec1fad956639c5a7d073c4413d7864fb9d6f403ff7b5fd0ee"},"schema_version":"1.0"},"canonical_sha256":"a8df54240d3703e676e6e7c8f8c338e94b4e496b20d92c2653c2078a69e0294d","source":{"kind":"arxiv","id":"1007.2633","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2633","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2633v4","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2633","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"VDPVIJANG4B6","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VDPVIJANG4B6M5XG","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VDPVIJAN","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VDPVIJANG4B6M5XG47EPRQZY5F","target":"record","payload":{"canonical_record":{"source":{"id":"1007.2633","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-15T18:59:32Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6289dba12cc1d44ae78563e2685c1bb1e6142158b9813c3c0ab1525f5462c7a0","abstract_canon_sha256":"bf67e7cd4851dd6ec1fad956639c5a7d073c4413d7864fb9d6f403ff7b5fd0ee"},"schema_version":"1.0"},"canonical_sha256":"a8df54240d3703e676e6e7c8f8c338e94b4e496b20d92c2653c2078a69e0294d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:53.782752Z","signature_b64":"noyFtIdZPELbaomNPephJgZ9yUfAWc0wYSzUfdTvSGUsAyg3tANIOpmFhA92zVIMB/6rPEWApti1blNSWfXhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8df54240d3703e676e6e7c8f8c338e94b4e496b20d92c2653c2078a69e0294d","last_reissued_at":"2026-05-18T04:09:53.782285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:53.782285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.2633","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"74aiB1+KUBoabETMoKAHEPDT6eiJrsM+cu8ia/jUMxH9JH6lZFRBN0d2M/FY/9TkR5nGa2zvaQaw0HLYK+euAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:42:34.984709Z"},"content_sha256":"5426e50bbd2cc7efcb6d2adddd7160bd2d79568a9170922e2f1867d8132dcbee","schema_version":"1.0","event_id":"sha256:5426e50bbd2cc7efcb6d2adddd7160bd2d79568a9170922e2f1867d8132dcbee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VDPVIJANG4B6M5XG47EPRQZY5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Berglund-H\\\"ubsch mirror symmetry via vertex algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Lev A. Borisov","submitted_at":"2010-07-15T18:59:32Z","abstract_excerpt":"We give a vertex algebra proof of the Berglund-H\\\"ubsch duality of nondegenerate invertible potentials. We suggest a way to unify it with the Batyrev-Borisov duality of reflexive Gorenstein cones."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2633","kind":"arxiv","version":4},"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":"2026-05-18T04:09:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H9bw77e10qz5scE5ZGNTBa90IjYxWqaYBOvzniyKE2PWN2jUZYSRijBToiZ49S2R5aldhm/3WIQ1Vtq/6kkaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:42:34.985407Z"},"content_sha256":"792bf9efbcd95c44106c9b1b9e15f65d94c135f32ae02da8ab4d152b272a7d3f","schema_version":"1.0","event_id":"sha256:792bf9efbcd95c44106c9b1b9e15f65d94c135f32ae02da8ab4d152b272a7d3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VDPVIJANG4B6M5XG47EPRQZY5F/bundle.json","state_url":"https://pith.science/pith/VDPVIJANG4B6M5XG47EPRQZY5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VDPVIJANG4B6M5XG47EPRQZY5F/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":"2026-06-10T08:42:34Z","links":{"resolver":"https://pith.science/pith/VDPVIJANG4B6M5XG47EPRQZY5F","bundle":"https://pith.science/pith/VDPVIJANG4B6M5XG47EPRQZY5F/bundle.json","state":"https://pith.science/pith/VDPVIJANG4B6M5XG47EPRQZY5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VDPVIJANG4B6M5XG47EPRQZY5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VDPVIJANG4B6M5XG47EPRQZY5F","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":"bf67e7cd4851dd6ec1fad956639c5a7d073c4413d7864fb9d6f403ff7b5fd0ee","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-15T18:59:32Z","title_canon_sha256":"6289dba12cc1d44ae78563e2685c1bb1e6142158b9813c3c0ab1525f5462c7a0"},"schema_version":"1.0","source":{"id":"1007.2633","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2633","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2633v4","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2633","created_at":"2026-05-18T04:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"VDPVIJANG4B6","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VDPVIJANG4B6M5XG","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VDPVIJAN","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:792bf9efbcd95c44106c9b1b9e15f65d94c135f32ae02da8ab4d152b272a7d3f","target":"graph","created_at":"2026-05-18T04:09:53Z","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 give a vertex algebra proof of the Berglund-H\\\"ubsch duality of nondegenerate invertible potentials. We suggest a way to unify it with the Batyrev-Borisov duality of reflexive Gorenstein cones.","authors_text":"Lev A. Borisov","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-15T18:59:32Z","title":"Berglund-H\\\"ubsch mirror symmetry via vertex algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2633","kind":"arxiv","version":4},"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":"sha256:5426e50bbd2cc7efcb6d2adddd7160bd2d79568a9170922e2f1867d8132dcbee","target":"record","created_at":"2026-05-18T04:09:53Z","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":"bf67e7cd4851dd6ec1fad956639c5a7d073c4413d7864fb9d6f403ff7b5fd0ee","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-15T18:59:32Z","title_canon_sha256":"6289dba12cc1d44ae78563e2685c1bb1e6142158b9813c3c0ab1525f5462c7a0"},"schema_version":"1.0","source":{"id":"1007.2633","kind":"arxiv","version":4}},"canonical_sha256":"a8df54240d3703e676e6e7c8f8c338e94b4e496b20d92c2653c2078a69e0294d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8df54240d3703e676e6e7c8f8c338e94b4e496b20d92c2653c2078a69e0294d","first_computed_at":"2026-05-18T04:09:53.782285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:53.782285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"noyFtIdZPELbaomNPephJgZ9yUfAWc0wYSzUfdTvSGUsAyg3tANIOpmFhA92zVIMB/6rPEWApti1blNSWfXhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:53.782752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.2633","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5426e50bbd2cc7efcb6d2adddd7160bd2d79568a9170922e2f1867d8132dcbee","sha256:792bf9efbcd95c44106c9b1b9e15f65d94c135f32ae02da8ab4d152b272a7d3f"],"state_sha256":"d96411cf7c13681b772963db9a732bd226c92e7bfcae335a5137bda75642b68d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"33BX9bdGhUHeogXOriEYhT2KjtzDUH98sAxmF6wZvM4G/37MxRXBt/HrnKfm9aYzHan4HmBiwNkOKRvpmX1hBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T08:42:34.989725Z","bundle_sha256":"b1978d15467217c5accd6daec7a2a90bb686fd9495dec90a4ac0c68cd10d4c91"}}