{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:V4QVZSCYIYUWIHYWR3ZKSX4BIN","short_pith_number":"pith:V4QVZSCY","schema_version":"1.0","canonical_sha256":"af215cc8584629641f168ef2a95f8143577c5841f776c33b566313ac92376134","source":{"kind":"arxiv","id":"0902.2135","version":2},"attestation_state":"computed","paper":{"title":"Moduli of Coassociative Submanifolds and Semi-Flat Coassociative Fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"David Baraglia","submitted_at":"2009-02-12T15:42:02Z","abstract_excerpt":"We study the natural structure on the moduli space of deformations of compact coassociative submanifolds. We show that a G2-manifold with a T^4-action of isomorphisms such that the orbits are coassociative tori is locally equivalent to a minimal 3-manifold in R^{3,3} = H^2(T^4,R) with positive induced metric. By studying minimal surfaces in quadrics we show how to construct minimal 3-manifold cones in R^{3,3} and hence G2-metrics from equations similar to a set of affine Toda equations. The relation to semi-flat special Lagrangian fibrations and the Monge-Amp\\`ere equation are explained."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0902.2135","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-02-12T15:42:02Z","cross_cats_sorted":[],"title_canon_sha256":"20e1890701afec44aaa8e804c83f3d0c6a9cd2fb8ec209fa66a5087eb78edb5b","abstract_canon_sha256":"ac08187d0ebd754645b88cd1808f68bb8df066ab51d99e38817503df973a0b8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:44.953943Z","signature_b64":"SkIdL4HUIVxv/FSYorlS+c6RhoPbhNYQ3ARGnq2CPYEagKX6XyvHLUsq7MPVBiEznKyQmMQuF2a02nwZXWVmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af215cc8584629641f168ef2a95f8143577c5841f776c33b566313ac92376134","last_reissued_at":"2026-05-18T04:41:44.953500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:44.953500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moduli of Coassociative Submanifolds and Semi-Flat Coassociative Fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"David Baraglia","submitted_at":"2009-02-12T15:42:02Z","abstract_excerpt":"We study the natural structure on the moduli space of deformations of compact coassociative submanifolds. We show that a G2-manifold with a T^4-action of isomorphisms such that the orbits are coassociative tori is locally equivalent to a minimal 3-manifold in R^{3,3} = H^2(T^4,R) with positive induced metric. By studying minimal surfaces in quadrics we show how to construct minimal 3-manifold cones in R^{3,3} and hence G2-metrics from equations similar to a set of affine Toda equations. The relation to semi-flat special Lagrangian fibrations and the Monge-Amp\\`ere equation are explained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2135","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0902.2135","created_at":"2026-05-18T04:41:44.953580+00:00"},{"alias_kind":"arxiv_version","alias_value":"0902.2135v2","created_at":"2026-05-18T04:41:44.953580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2135","created_at":"2026-05-18T04:41:44.953580+00:00"},{"alias_kind":"pith_short_12","alias_value":"V4QVZSCYIYUW","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"V4QVZSCYIYUWIHYW","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"V4QVZSCY","created_at":"2026-05-18T12:26:02.257875+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V4QVZSCYIYUWIHYWR3ZKSX4BIN","json":"https://pith.science/pith/V4QVZSCYIYUWIHYWR3ZKSX4BIN.json","graph_json":"https://pith.science/api/pith-number/V4QVZSCYIYUWIHYWR3ZKSX4BIN/graph.json","events_json":"https://pith.science/api/pith-number/V4QVZSCYIYUWIHYWR3ZKSX4BIN/events.json","paper":"https://pith.science/paper/V4QVZSCY"},"agent_actions":{"view_html":"https://pith.science/pith/V4QVZSCYIYUWIHYWR3ZKSX4BIN","download_json":"https://pith.science/pith/V4QVZSCYIYUWIHYWR3ZKSX4BIN.json","view_paper":"https://pith.science/paper/V4QVZSCY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0902.2135&json=true","fetch_graph":"https://pith.science/api/pith-number/V4QVZSCYIYUWIHYWR3ZKSX4BIN/graph.json","fetch_events":"https://pith.science/api/pith-number/V4QVZSCYIYUWIHYWR3ZKSX4BIN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V4QVZSCYIYUWIHYWR3ZKSX4BIN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V4QVZSCYIYUWIHYWR3ZKSX4BIN/action/storage_attestation","attest_author":"https://pith.science/pith/V4QVZSCYIYUWIHYWR3ZKSX4BIN/action/author_attestation","sign_citation":"https://pith.science/pith/V4QVZSCYIYUWIHYWR3ZKSX4BIN/action/citation_signature","submit_replication":"https://pith.science/pith/V4QVZSCYIYUWIHYWR3ZKSX4BIN/action/replication_record"}},"created_at":"2026-05-18T04:41:44.953580+00:00","updated_at":"2026-05-18T04:41:44.953580+00:00"}