{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:C2IF4HHEDMP3FC6NWPH6O6OHKL","short_pith_number":"pith:C2IF4HHE","canonical_record":{"source":{"id":"1209.5116","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-23T21:44:59Z","cross_cats_sorted":[],"title_canon_sha256":"6d05348b76b4306ed1ba99b9d919189a552f604c012474462e51d6843c61b778","abstract_canon_sha256":"99b02cb052c9573663a8d9b24999780a95d3b4230e3edf39886fba7ee123a344"},"schema_version":"1.0"},"canonical_sha256":"16905e1ce41b1fb28bcdb3cfe779c752f4825ad8e52f535bd1deb989ee93a697","source":{"kind":"arxiv","id":"1209.5116","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5116","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5116v2","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5116","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"C2IF4HHEDMP3","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C2IF4HHEDMP3FC6N","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C2IF4HHE","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:C2IF4HHEDMP3FC6NWPH6O6OHKL","target":"record","payload":{"canonical_record":{"source":{"id":"1209.5116","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-23T21:44:59Z","cross_cats_sorted":[],"title_canon_sha256":"6d05348b76b4306ed1ba99b9d919189a552f604c012474462e51d6843c61b778","abstract_canon_sha256":"99b02cb052c9573663a8d9b24999780a95d3b4230e3edf39886fba7ee123a344"},"schema_version":"1.0"},"canonical_sha256":"16905e1ce41b1fb28bcdb3cfe779c752f4825ad8e52f535bd1deb989ee93a697","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:39.560758Z","signature_b64":"uB8bM46StbytLoWhHpujUenjQ/WmazqMVNG8Y4ogegzvUgbeOXvvPtO1RsPX580iviHb2XAjmYI8z5MgHRr3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16905e1ce41b1fb28bcdb3cfe779c752f4825ad8e52f535bd1deb989ee93a697","last_reissued_at":"2026-05-18T02:26:39.560205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:39.560205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.5116","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":"2026-05-18T02:26:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KOJQ2jBll5xNyAenVEQSWFOphqYBgL8Efo/hakpdx+YwN/tarhh+uq7iEMCTHpeOHlieogysGAlnxxsIn+kTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:09:05.338101Z"},"content_sha256":"6496815cc727f9ae9b878df46512424c796a3e276d9883cbcecd91f540871394","schema_version":"1.0","event_id":"sha256:6496815cc727f9ae9b878df46512424c796a3e276d9883cbcecd91f540871394"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:C2IF4HHEDMP3FC6NWPH6O6OHKL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Desingularization of Coassociative 4-folds with Conical Singularities: Obstructions and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jason D. Lotay","submitted_at":"2012-09-23T21:44:59Z","abstract_excerpt":"We study the problem of desingularizing coassociative conical singularities via gluing, allowing for topological and analytic obstructions, and discuss applications. This extends the author's earlier work on the unobstructed case. We interpret the analytic obstructions geometrically via the obstruction theory for deformations of conically singular coassociative 4-folds, and thus relate them to the stability of the singularities. We use our results to describe the relationship between moduli spaces of coassociative 4-folds with conical singularities and those of their desingularizations. We als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5116","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":"2026-05-18T02:26:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Jr7FOLK8WpDcGkcQ+5GnuzNMzTfqVOZbbG4EcM+NMb1IKxzIYqtGwIoM5zTLzcKTt9Y1PYr66fSgQ3bxpJhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:09:05.338467Z"},"content_sha256":"34e8f5b575ede9d48eaaf32ff089bde7d7e870ab3a4cc84b896a5287308d160d","schema_version":"1.0","event_id":"sha256:34e8f5b575ede9d48eaaf32ff089bde7d7e870ab3a4cc84b896a5287308d160d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C2IF4HHEDMP3FC6NWPH6O6OHKL/bundle.json","state_url":"https://pith.science/pith/C2IF4HHEDMP3FC6NWPH6O6OHKL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C2IF4HHEDMP3FC6NWPH6O6OHKL/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":"2026-06-29T14:09:05Z","links":{"resolver":"https://pith.science/pith/C2IF4HHEDMP3FC6NWPH6O6OHKL","bundle":"https://pith.science/pith/C2IF4HHEDMP3FC6NWPH6O6OHKL/bundle.json","state":"https://pith.science/pith/C2IF4HHEDMP3FC6NWPH6O6OHKL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C2IF4HHEDMP3FC6NWPH6O6OHKL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C2IF4HHEDMP3FC6NWPH6O6OHKL","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":"99b02cb052c9573663a8d9b24999780a95d3b4230e3edf39886fba7ee123a344","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-23T21:44:59Z","title_canon_sha256":"6d05348b76b4306ed1ba99b9d919189a552f604c012474462e51d6843c61b778"},"schema_version":"1.0","source":{"id":"1209.5116","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5116","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5116v2","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5116","created_at":"2026-05-18T02:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"C2IF4HHEDMP3","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C2IF4HHEDMP3FC6N","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C2IF4HHE","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:34e8f5b575ede9d48eaaf32ff089bde7d7e870ab3a4cc84b896a5287308d160d","target":"graph","created_at":"2026-05-18T02:26:39Z","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 study the problem of desingularizing coassociative conical singularities via gluing, allowing for topological and analytic obstructions, and discuss applications. This extends the author's earlier work on the unobstructed case. We interpret the analytic obstructions geometrically via the obstruction theory for deformations of conically singular coassociative 4-folds, and thus relate them to the stability of the singularities. We use our results to describe the relationship between moduli spaces of coassociative 4-folds with conical singularities and those of their desingularizations. We als","authors_text":"Jason D. Lotay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-23T21:44:59Z","title":"Desingularization of Coassociative 4-folds with Conical Singularities: Obstructions and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5116","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":"sha256:6496815cc727f9ae9b878df46512424c796a3e276d9883cbcecd91f540871394","target":"record","created_at":"2026-05-18T02:26:39Z","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":"99b02cb052c9573663a8d9b24999780a95d3b4230e3edf39886fba7ee123a344","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-23T21:44:59Z","title_canon_sha256":"6d05348b76b4306ed1ba99b9d919189a552f604c012474462e51d6843c61b778"},"schema_version":"1.0","source":{"id":"1209.5116","kind":"arxiv","version":2}},"canonical_sha256":"16905e1ce41b1fb28bcdb3cfe779c752f4825ad8e52f535bd1deb989ee93a697","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16905e1ce41b1fb28bcdb3cfe779c752f4825ad8e52f535bd1deb989ee93a697","first_computed_at":"2026-05-18T02:26:39.560205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:39.560205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uB8bM46StbytLoWhHpujUenjQ/WmazqMVNG8Y4ogegzvUgbeOXvvPtO1RsPX580iviHb2XAjmYI8z5MgHRr3DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:39.560758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5116","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6496815cc727f9ae9b878df46512424c796a3e276d9883cbcecd91f540871394","sha256:34e8f5b575ede9d48eaaf32ff089bde7d7e870ab3a4cc84b896a5287308d160d"],"state_sha256":"4d34b750d1413213b24443157108c5163328e55346f1ff2c44367c3455b9dff5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dpApH/Rl8GYmZyYzzfwSRTtYi4eHQmEEVKvrxgtXccTxY/6p/5ybgedcPwopfaaRuMuiCjQ688CfK/rEXHcQBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T14:09:05.340393Z","bundle_sha256":"074c4e91a904a3b7530e14de76f1293452dab1dab67d943218087b9e11319cc9"}}