{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:Q6SDTYH757IYXBN2K7D4JA7MWZ","short_pith_number":"pith:Q6SDTYH7","canonical_record":{"source":{"id":"math/9905006","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1999-05-03T01:37:40Z","cross_cats_sorted":[],"title_canon_sha256":"daa97206d3d9b264e966f0b3d3b6c4653cf2de02796df7b7b13031e655bcb56c","abstract_canon_sha256":"6955481f7ce4841b32b65185f0f3a8a08e3c8490ed07473bbc8eee5938091c9e"},"schema_version":"1.0"},"canonical_sha256":"87a439e0ffefd18b85ba57c7c483ecb6534f12ee32f40dd796e8ea53bc51ce26","source":{"kind":"arxiv","id":"math/9905006","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9905006","created_at":"2026-07-04T14:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"math/9905006v1","created_at":"2026-07-04T14:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9905006","created_at":"2026-07-04T14:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"Q6SDTYH757IY","created_at":"2026-07-04T14:41:08Z"},{"alias_kind":"pith_short_16","alias_value":"Q6SDTYH757IYXBN2","created_at":"2026-07-04T14:41:08Z"},{"alias_kind":"pith_short_8","alias_value":"Q6SDTYH7","created_at":"2026-07-04T14:41:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:Q6SDTYH757IYXBN2K7D4JA7MWZ","target":"record","payload":{"canonical_record":{"source":{"id":"math/9905006","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1999-05-03T01:37:40Z","cross_cats_sorted":[],"title_canon_sha256":"daa97206d3d9b264e966f0b3d3b6c4653cf2de02796df7b7b13031e655bcb56c","abstract_canon_sha256":"6955481f7ce4841b32b65185f0f3a8a08e3c8490ed07473bbc8eee5938091c9e"},"schema_version":"1.0"},"canonical_sha256":"87a439e0ffefd18b85ba57c7c483ecb6534f12ee32f40dd796e8ea53bc51ce26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:41:08.500784Z","signature_b64":"llouGMh42RppWtjlPFQmY9OMrgVe9kpyWtM9dxmCerbTkpQ0OiuXDXA5Y2aDFd5CJsxTsfoIncqfaTqhp4acBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87a439e0ffefd18b85ba57c7c483ecb6534f12ee32f40dd796e8ea53bc51ce26","last_reissued_at":"2026-07-04T14:41:08.500407Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:41:08.500407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9905006","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:41:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wHIFzknu9stVXh5pIFY2QSGqcwaELsxHlYXDzj6YkC5V07VuewFQU1iaLzkpqBWsyIxh7JQzCcVOeWVy8ZxUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:04:50.429399Z"},"content_sha256":"74766177bb1a32a0198de091fbf52e0a189a9bd8a557b3588ec722487a2db5bf","schema_version":"1.0","event_id":"sha256:74766177bb1a32a0198de091fbf52e0a189a9bd8a557b3588ec722487a2db5bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:Q6SDTYH757IYXBN2K7D4JA7MWZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mirror Principle II","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Bong H. Lian, Kefeng Liu, S.T. Yau","submitted_at":"1999-05-03T01:37:40Z","abstract_excerpt":"We generalize our theorems in \"Mirror Principle I\" to a class of balloon manifolds. Many of the results are proved for convex projective manifolds. In a subsequent paper, Mirror Principle III, we will extend the results to projective manifolds without the convexity assumption."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9905006","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/9905006/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:41:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ra7hRRqSuNOKNygEIJw8mkXlcGrTSZeMEjlMPjCRqdt/FJQGRgP27zcGN2LxulYd9WxqQmwX9YNr3uq4GI/IAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:04:50.429915Z"},"content_sha256":"f4f1fc92772be9ed6542be69d1393cdaec2812e5f00fa3def54fab7c429d2abb","schema_version":"1.0","event_id":"sha256:f4f1fc92772be9ed6542be69d1393cdaec2812e5f00fa3def54fab7c429d2abb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q6SDTYH757IYXBN2K7D4JA7MWZ/bundle.json","state_url":"https://pith.science/pith/Q6SDTYH757IYXBN2K7D4JA7MWZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q6SDTYH757IYXBN2K7D4JA7MWZ/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":"2026-08-09T20:04:50Z","links":{"resolver":"https://pith.science/pith/Q6SDTYH757IYXBN2K7D4JA7MWZ","bundle":"https://pith.science/pith/Q6SDTYH757IYXBN2K7D4JA7MWZ/bundle.json","state":"https://pith.science/pith/Q6SDTYH757IYXBN2K7D4JA7MWZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q6SDTYH757IYXBN2K7D4JA7MWZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:Q6SDTYH757IYXBN2K7D4JA7MWZ","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":"6955481f7ce4841b32b65185f0f3a8a08e3c8490ed07473bbc8eee5938091c9e","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1999-05-03T01:37:40Z","title_canon_sha256":"daa97206d3d9b264e966f0b3d3b6c4653cf2de02796df7b7b13031e655bcb56c"},"schema_version":"1.0","source":{"id":"math/9905006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9905006","created_at":"2026-07-04T14:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"math/9905006v1","created_at":"2026-07-04T14:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9905006","created_at":"2026-07-04T14:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"Q6SDTYH757IY","created_at":"2026-07-04T14:41:08Z"},{"alias_kind":"pith_short_16","alias_value":"Q6SDTYH757IYXBN2","created_at":"2026-07-04T14:41:08Z"},{"alias_kind":"pith_short_8","alias_value":"Q6SDTYH7","created_at":"2026-07-04T14:41:08Z"}],"graph_snapshots":[{"event_id":"sha256:f4f1fc92772be9ed6542be69d1393cdaec2812e5f00fa3def54fab7c429d2abb","target":"graph","created_at":"2026-07-04T14:41:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/9905006/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize our theorems in \"Mirror Principle I\" to a class of balloon manifolds. Many of the results are proved for convex projective manifolds. In a subsequent paper, Mirror Principle III, we will extend the results to projective manifolds without the convexity assumption.","authors_text":"Bong H. Lian, Kefeng Liu, S.T. Yau","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"1999-05-03T01:37:40Z","title":"Mirror Principle II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9905006","kind":"arxiv","version":1},"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":"sha256:74766177bb1a32a0198de091fbf52e0a189a9bd8a557b3588ec722487a2db5bf","target":"record","created_at":"2026-07-04T14:41:08Z","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":"6955481f7ce4841b32b65185f0f3a8a08e3c8490ed07473bbc8eee5938091c9e","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1999-05-03T01:37:40Z","title_canon_sha256":"daa97206d3d9b264e966f0b3d3b6c4653cf2de02796df7b7b13031e655bcb56c"},"schema_version":"1.0","source":{"id":"math/9905006","kind":"arxiv","version":1}},"canonical_sha256":"87a439e0ffefd18b85ba57c7c483ecb6534f12ee32f40dd796e8ea53bc51ce26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87a439e0ffefd18b85ba57c7c483ecb6534f12ee32f40dd796e8ea53bc51ce26","first_computed_at":"2026-07-04T14:41:08.500407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:41:08.500407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"llouGMh42RppWtjlPFQmY9OMrgVe9kpyWtM9dxmCerbTkpQ0OiuXDXA5Y2aDFd5CJsxTsfoIncqfaTqhp4acBw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:41:08.500784Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9905006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74766177bb1a32a0198de091fbf52e0a189a9bd8a557b3588ec722487a2db5bf","sha256:f4f1fc92772be9ed6542be69d1393cdaec2812e5f00fa3def54fab7c429d2abb"],"state_sha256":"5b4ab550bf0904d760e339a7d6d9ac1c5173a2b76bf4f13391340dcb03328890"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HBuSZTlvuFCwtOS7SP0bBNAVu+Y2b73PJmo19PdJsGPFn1L2Op1ljO32EGYcZwH8Vyl7njjmP8xLpXTw2ORlCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T20:04:50.433871Z","bundle_sha256":"eef2a12f4cb9423c2932a4648bce0333f95d0283950ebaed918d6f5a2b7526a8"}}