{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IV33A6RY2MLF7MBO4HJQOVFFSZ","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":"f3c6fdaa6f5e58b703dfdecbcff6fc833acf01a852e8af863e8167bf5cca04f5","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-31T09:14:18Z","title_canon_sha256":"0a211a1ffee7adb94920dd0d69e00bba22ac20fa5274222691f4ba1ef9371afd"},"schema_version":"1.0","source":{"id":"1610.09836","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09836","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09836v2","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09836","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"IV33A6RY2MLF","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IV33A6RY2MLF7MBO","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IV33A6RY","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:f0c9ce69747e4b49c5ed810bd3f87e041a450bfe21e3655dd43175873fceb2c3","target":"graph","created_at":"2026-05-18T00:09:53Z","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":"There is a strong analogy between compact, torsion-free $G_2$-manifolds $(X,\\varphi,*\\varphi)$ and Calabi-Yau 3-folds $(Y,J,g,\\omega)$. We can also generalize $(X,\\varphi,*\\varphi)$ to 'tamed almost $G_2$-manifolds' $(X,\\varphi,\\psi)$, where we compare $\\varphi$ with $\\omega$ and $\\psi$ with $J$. Associative 3-folds in $X$, a special kind of minimal submanifold, are analogous to $J$-holomorphic curves in $Y$.\n  Several areas of Symplectic Geometry -- Gromov-Witten theory, Quantum Cohomology, Lagrangian Floer cohomology, Fukaya categories -- are built using 'counts' of moduli spaces of $J$-holo","authors_text":"Dominic Joyce","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-31T09:14:18Z","title":"Conjectures on counting associative 3-folds in $G_2$-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09836","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":"sha256:2e5be921280318fd140c881819c68fb2fe71cf97deb7932539a2703f92087f5b","target":"record","created_at":"2026-05-18T00:09:53Z","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":"f3c6fdaa6f5e58b703dfdecbcff6fc833acf01a852e8af863e8167bf5cca04f5","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-31T09:14:18Z","title_canon_sha256":"0a211a1ffee7adb94920dd0d69e00bba22ac20fa5274222691f4ba1ef9371afd"},"schema_version":"1.0","source":{"id":"1610.09836","kind":"arxiv","version":2}},"canonical_sha256":"4577b07a38d3165fb02ee1d30754a59641c727b7d239c1223cd3f252a8b8ae51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4577b07a38d3165fb02ee1d30754a59641c727b7d239c1223cd3f252a8b8ae51","first_computed_at":"2026-05-18T00:09:53.260575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:53.260575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"370x+u9z4pnXKJ4oklj4Rh6NbY7aVyUtrEfzVvBD8ckvTnAPHoZACuDhI92T45A5acwkniBdqBWS/9bLuapVCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:53.261215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09836","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e5be921280318fd140c881819c68fb2fe71cf97deb7932539a2703f92087f5b","sha256:f0c9ce69747e4b49c5ed810bd3f87e041a450bfe21e3655dd43175873fceb2c3"],"state_sha256":"4c038cf4bb7e491777000b2f95a50ffe35835eb0f6c10e555423069c283765d4"}