{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KGEY63DVYQEQLQUVGCCZQNUHUD","short_pith_number":"pith:KGEY63DV","schema_version":"1.0","canonical_sha256":"51898f6c75c40905c2953085983687a0da234007e4f0ecfb23d62f969866fb73","source":{"kind":"arxiv","id":"1011.1744","version":3},"attestation_state":"computed","paper":{"title":"Smooth moduli spaces of associative submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Damien Gayet (ICJ)","submitted_at":"2010-11-08T09:57:29Z","abstract_excerpt":"Let $M^7$ be a smooth manifold equipped with a $G_2$-structure $\\phi$, and $Y^3$ be an closed compact $\\phi$-associative submanifold. In \\cite{McL}, R. McLean proved that the moduli space $\\bm_{Y,\\phi}$ of the $\\phi$-associative deformations of $Y$ has vanishing virtual dimension. In this paper, we perturb $\\phi$ into a $G_2$-structure $\\psi$ in order to ensure the smoothness of $\\bm_{Y,\\psi}$ near $Y$. If $Y$ is allowed to have a boundary moving in a fixed coassociative submanifold $X$, it was proved in \\cite{GaWi} that the moduli space $\\bm_{Y,X}$ of the associative deformations of $Y$ with "},"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":"1011.1744","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-08T09:57:29Z","cross_cats_sorted":[],"title_canon_sha256":"be61d9041a739422954de0bdf57dc725918b4baa123ef0bd7964aaed871efc37","abstract_canon_sha256":"e9a3e215a3d54d0f799fc44790fba97be0bf1a2f8d67a9aa2ded0b3765633b95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:06.696981Z","signature_b64":"ogWJts++V++fe0zvxybSkqnK9y21LNRSUupxmVh+cHmPgSLtr15hPfQyua2OiFfyCfOgJ+Vg1IhFNU7JOOktCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51898f6c75c40905c2953085983687a0da234007e4f0ecfb23d62f969866fb73","last_reissued_at":"2026-05-18T03:16:06.696254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:06.696254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smooth moduli spaces of associative submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Damien Gayet (ICJ)","submitted_at":"2010-11-08T09:57:29Z","abstract_excerpt":"Let $M^7$ be a smooth manifold equipped with a $G_2$-structure $\\phi$, and $Y^3$ be an closed compact $\\phi$-associative submanifold. In \\cite{McL}, R. McLean proved that the moduli space $\\bm_{Y,\\phi}$ of the $\\phi$-associative deformations of $Y$ has vanishing virtual dimension. In this paper, we perturb $\\phi$ into a $G_2$-structure $\\psi$ in order to ensure the smoothness of $\\bm_{Y,\\psi}$ near $Y$. If $Y$ is allowed to have a boundary moving in a fixed coassociative submanifold $X$, it was proved in \\cite{GaWi} that the moduli space $\\bm_{Y,X}$ of the associative deformations of $Y$ with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1744","kind":"arxiv","version":3},"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":"1011.1744","created_at":"2026-05-18T03:16:06.696370+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.1744v3","created_at":"2026-05-18T03:16:06.696370+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1744","created_at":"2026-05-18T03:16:06.696370+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGEY63DVYQEQ","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGEY63DVYQEQLQUV","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGEY63DV","created_at":"2026-05-18T12:26:09.077623+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/KGEY63DVYQEQLQUVGCCZQNUHUD","json":"https://pith.science/pith/KGEY63DVYQEQLQUVGCCZQNUHUD.json","graph_json":"https://pith.science/api/pith-number/KGEY63DVYQEQLQUVGCCZQNUHUD/graph.json","events_json":"https://pith.science/api/pith-number/KGEY63DVYQEQLQUVGCCZQNUHUD/events.json","paper":"https://pith.science/paper/KGEY63DV"},"agent_actions":{"view_html":"https://pith.science/pith/KGEY63DVYQEQLQUVGCCZQNUHUD","download_json":"https://pith.science/pith/KGEY63DVYQEQLQUVGCCZQNUHUD.json","view_paper":"https://pith.science/paper/KGEY63DV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.1744&json=true","fetch_graph":"https://pith.science/api/pith-number/KGEY63DVYQEQLQUVGCCZQNUHUD/graph.json","fetch_events":"https://pith.science/api/pith-number/KGEY63DVYQEQLQUVGCCZQNUHUD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGEY63DVYQEQLQUVGCCZQNUHUD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGEY63DVYQEQLQUVGCCZQNUHUD/action/storage_attestation","attest_author":"https://pith.science/pith/KGEY63DVYQEQLQUVGCCZQNUHUD/action/author_attestation","sign_citation":"https://pith.science/pith/KGEY63DVYQEQLQUVGCCZQNUHUD/action/citation_signature","submit_replication":"https://pith.science/pith/KGEY63DVYQEQLQUVGCCZQNUHUD/action/replication_record"}},"created_at":"2026-05-18T03:16:06.696370+00:00","updated_at":"2026-05-18T03:16:06.696370+00:00"}