{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NSCDOD43YDFXXAX7Z4HPWQCB7A","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":"684500562694af1a044cec4d8fbb470dd150b653ba8075fd24b56c4433986abb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-28T12:54:59Z","title_canon_sha256":"0273f182d2d31c53f067ad64add7ea34ae39f2cc2ffc546cd021ef74bbde1fff"},"schema_version":"1.0","source":{"id":"1306.6817","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.6817","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1306.6817v3","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6817","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"NSCDOD43YDFX","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NSCDOD43YDFXXAX7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NSCDOD43","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:d290a86c50770f80887b13085ae5c7032c8332e73f6c23abd863af4261532071","target":"graph","created_at":"2026-05-18T01:08:27Z","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":"Given an $\\widetilde n$-dimensional manifold $\\widetilde M$ equipped with a $\\widetilde G$-structure $\\widetilde\\pi:\\widetilde P\\rightarrow \\widetilde M$, there is a naturally induced $G$-structure $\\pi: P\\rightarrow M$ on any submanifold $M\\subset\\widetilde M$ that satisfies appropriate regularity conditions. We study generalized integrability problems for a given $G$-structure $\\pi: P\\rightarrow M$, namely the questions of whether it is locally equivalent to induced $G$-structures on regular submanifolds of homogeneous $\\widetilde G$-structures $\\widetilde\\pi:\\widetilde P\\to \\widetilde{H}/\\w","authors_text":"Andrea Santi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-28T12:54:59Z","title":"A generalized integrability problem for G-Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6817","kind":"arxiv","version":3},"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":"sha256:7e6c248eab5f919f51fa118e275a7200ae3abf37d0a5a2a3438dce4ea1225d6f","target":"record","created_at":"2026-05-18T01:08:27Z","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":"684500562694af1a044cec4d8fbb470dd150b653ba8075fd24b56c4433986abb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-28T12:54:59Z","title_canon_sha256":"0273f182d2d31c53f067ad64add7ea34ae39f2cc2ffc546cd021ef74bbde1fff"},"schema_version":"1.0","source":{"id":"1306.6817","kind":"arxiv","version":3}},"canonical_sha256":"6c84370f9bc0cb7b82ffcf0efb4041f81d8b102d00abf5eac9871879e7a300c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c84370f9bc0cb7b82ffcf0efb4041f81d8b102d00abf5eac9871879e7a300c3","first_computed_at":"2026-05-18T01:08:27.636904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:27.636904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i1bPz0mqVTLOO7VyVpJLqFwTb+XeebP85K0lUS6m3fU8y1K6ecXLs02mr5vAHXmE0hmwr9yfKtP8hjJW+b7oBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:27.637395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.6817","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e6c248eab5f919f51fa118e275a7200ae3abf37d0a5a2a3438dce4ea1225d6f","sha256:d290a86c50770f80887b13085ae5c7032c8332e73f6c23abd863af4261532071"],"state_sha256":"2bcab2cd8b0f3056a5fa00d79f0f77d9cfeac230c2f5f504f6d1de03c8bf595b"}