{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:2YY6CRTHCG6EF33T7JQD3TD5NL","short_pith_number":"pith:2YY6CRTH","canonical_record":{"source":{"id":"math/0511150","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2005-11-06T17:06:51Z","cross_cats_sorted":[],"title_canon_sha256":"5d6b1b37a4d4c657df528b61753fbcc6cf6fe2b96d71901ac80ea11d7cd7e6b1","abstract_canon_sha256":"52e29c59b44b3e2edcbdd630af9c76f0c6fa29c7289136b00f90d8a8876ba534"},"schema_version":"1.0"},"canonical_sha256":"d631e1466711bc42ef73fa603dcc7d6ac7c9f631d7198561c64c29fab5e3f4a3","source":{"kind":"arxiv","id":"math/0511150","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0511150","created_at":"2026-07-04T16:21:30Z"},{"alias_kind":"arxiv_version","alias_value":"math/0511150v2","created_at":"2026-07-04T16:21:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0511150","created_at":"2026-07-04T16:21:30Z"},{"alias_kind":"pith_short_12","alias_value":"2YY6CRTHCG6E","created_at":"2026-07-04T16:21:30Z"},{"alias_kind":"pith_short_16","alias_value":"2YY6CRTHCG6EF33T","created_at":"2026-07-04T16:21:30Z"},{"alias_kind":"pith_short_8","alias_value":"2YY6CRTH","created_at":"2026-07-04T16:21:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:2YY6CRTHCG6EF33T7JQD3TD5NL","target":"record","payload":{"canonical_record":{"source":{"id":"math/0511150","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2005-11-06T17:06:51Z","cross_cats_sorted":[],"title_canon_sha256":"5d6b1b37a4d4c657df528b61753fbcc6cf6fe2b96d71901ac80ea11d7cd7e6b1","abstract_canon_sha256":"52e29c59b44b3e2edcbdd630af9c76f0c6fa29c7289136b00f90d8a8876ba534"},"schema_version":"1.0"},"canonical_sha256":"d631e1466711bc42ef73fa603dcc7d6ac7c9f631d7198561c64c29fab5e3f4a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:21:30.611183Z","signature_b64":"k4+5+37qY14ZWj3P876Z4v3+t+tUSa9KHmGzJQY0h+UvQd3vWj65TxyKocITbscTqJAxl9f7xzOvY8rpjQyUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d631e1466711bc42ef73fa603dcc7d6ac7c9f631d7198561c64c29fab5e3f4a3","last_reissued_at":"2026-07-04T16:21:30.610818Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:21:30.610818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0511150","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":"2026-07-04T16:21:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BMip3A9MOJkXvWp1Ft/rN+UzGsq+nPIsDwBl5ImBhwV9ys0wtGOo6S3ZMsBYyecbddqnpx3ijSVPtbh5ukK3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:27:59.156189Z"},"content_sha256":"75b0bab73bfceab91f7427b406f33c154bdbcad351d78287ac63e52ed722c3d4","schema_version":"1.0","event_id":"sha256:75b0bab73bfceab91f7427b406f33c154bdbcad351d78287ac63e52ed722c3d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:2YY6CRTHCG6EF33T7JQD3TD5NL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coassociative K3 fibrations of compact G_2-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexei Kovalev","submitted_at":"2005-11-06T17:06:51Z","abstract_excerpt":"A class of examples of Riemannian metrics with holonomy G_2 on compact 7-manifolds was constructed by the author in arXiv:math.DG/0012189 and later in a joint work with N.-H. Lee in arXiv:0810.0957, using a certain `generalized connected sum' of two asymptotically cylindrical manifolds with holonomy SU(3). We consider, on each of the two initial SU(3)-manifolds, a fibration arising from a Lefschetz pencil of K3 surfaces. The gluing of the two K3 fibrations yields a coassociative fibration of the connected sum G_2-manifold over a 3-dimensional sphere. The singular fibres of this fibration are d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511150","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0511150/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":"2026-07-04T16:21:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w3A2jlc6R0KTNiMRQPfLwdUZERW00ppDbnageC5two8BLT7/GJSq/EU7FG/degsmjNFAc6Twe2Gvdc/F7w0hCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:27:59.156740Z"},"content_sha256":"6c384c18d54432fd7c2bf86833edcca7f922e8c683cb50a553f1a190a2f19a70","schema_version":"1.0","event_id":"sha256:6c384c18d54432fd7c2bf86833edcca7f922e8c683cb50a553f1a190a2f19a70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2YY6CRTHCG6EF33T7JQD3TD5NL/bundle.json","state_url":"https://pith.science/pith/2YY6CRTHCG6EF33T7JQD3TD5NL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2YY6CRTHCG6EF33T7JQD3TD5NL/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":"2026-08-09T15:27:59Z","links":{"resolver":"https://pith.science/pith/2YY6CRTHCG6EF33T7JQD3TD5NL","bundle":"https://pith.science/pith/2YY6CRTHCG6EF33T7JQD3TD5NL/bundle.json","state":"https://pith.science/pith/2YY6CRTHCG6EF33T7JQD3TD5NL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2YY6CRTHCG6EF33T7JQD3TD5NL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:2YY6CRTHCG6EF33T7JQD3TD5NL","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":"52e29c59b44b3e2edcbdd630af9c76f0c6fa29c7289136b00f90d8a8876ba534","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2005-11-06T17:06:51Z","title_canon_sha256":"5d6b1b37a4d4c657df528b61753fbcc6cf6fe2b96d71901ac80ea11d7cd7e6b1"},"schema_version":"1.0","source":{"id":"math/0511150","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0511150","created_at":"2026-07-04T16:21:30Z"},{"alias_kind":"arxiv_version","alias_value":"math/0511150v2","created_at":"2026-07-04T16:21:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0511150","created_at":"2026-07-04T16:21:30Z"},{"alias_kind":"pith_short_12","alias_value":"2YY6CRTHCG6E","created_at":"2026-07-04T16:21:30Z"},{"alias_kind":"pith_short_16","alias_value":"2YY6CRTHCG6EF33T","created_at":"2026-07-04T16:21:30Z"},{"alias_kind":"pith_short_8","alias_value":"2YY6CRTH","created_at":"2026-07-04T16:21:30Z"}],"graph_snapshots":[{"event_id":"sha256:6c384c18d54432fd7c2bf86833edcca7f922e8c683cb50a553f1a190a2f19a70","target":"graph","created_at":"2026-07-04T16:21:30Z","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/0511150/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A class of examples of Riemannian metrics with holonomy G_2 on compact 7-manifolds was constructed by the author in arXiv:math.DG/0012189 and later in a joint work with N.-H. Lee in arXiv:0810.0957, using a certain `generalized connected sum' of two asymptotically cylindrical manifolds with holonomy SU(3). We consider, on each of the two initial SU(3)-manifolds, a fibration arising from a Lefschetz pencil of K3 surfaces. The gluing of the two K3 fibrations yields a coassociative fibration of the connected sum G_2-manifold over a 3-dimensional sphere. The singular fibres of this fibration are d","authors_text":"Alexei Kovalev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2005-11-06T17:06:51Z","title":"Coassociative K3 fibrations of compact G_2-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511150","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":"sha256:75b0bab73bfceab91f7427b406f33c154bdbcad351d78287ac63e52ed722c3d4","target":"record","created_at":"2026-07-04T16:21:30Z","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":"52e29c59b44b3e2edcbdd630af9c76f0c6fa29c7289136b00f90d8a8876ba534","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2005-11-06T17:06:51Z","title_canon_sha256":"5d6b1b37a4d4c657df528b61753fbcc6cf6fe2b96d71901ac80ea11d7cd7e6b1"},"schema_version":"1.0","source":{"id":"math/0511150","kind":"arxiv","version":2}},"canonical_sha256":"d631e1466711bc42ef73fa603dcc7d6ac7c9f631d7198561c64c29fab5e3f4a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d631e1466711bc42ef73fa603dcc7d6ac7c9f631d7198561c64c29fab5e3f4a3","first_computed_at":"2026-07-04T16:21:30.610818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:21:30.610818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k4+5+37qY14ZWj3P876Z4v3+t+tUSa9KHmGzJQY0h+UvQd3vWj65TxyKocITbscTqJAxl9f7xzOvY8rpjQyUDg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:21:30.611183Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0511150","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75b0bab73bfceab91f7427b406f33c154bdbcad351d78287ac63e52ed722c3d4","sha256:6c384c18d54432fd7c2bf86833edcca7f922e8c683cb50a553f1a190a2f19a70"],"state_sha256":"7f068d468229fd2c6fc7deddcc5f79332693b1ba47085ca30aca57b8d61424b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ph/O6jXNmOkQ0jrB3GTyNK7CUgxp1m0uwq6rogIXc/DbML6j2BN6Jy93Lal497WR72hwN3Op4ouM3GvU5kgCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T15:27:59.159849Z","bundle_sha256":"80ea8ad7df0a02612816cac3932d50654e37d7bc84795a0476977fbd91fbea98"}}