{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B7ZGLPO7YJPZLSCGXUNQAK3XHL","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":"6e839065a5ca99a0d0ad8dffd2fe47811a7e65e5369b8be32eaca29b3dc95041","cross_cats_sorted":["math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-13T11:07:36Z","title_canon_sha256":"06492666d17553a911b81529a6d1022d670b47d72f56d654e68674f5e55d0ee5"},"schema_version":"1.0","source":{"id":"1203.2765","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2765","created_at":"2026-05-18T03:30:42Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2765v3","created_at":"2026-05-18T03:30:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2765","created_at":"2026-05-18T03:30:42Z"},{"alias_kind":"pith_short_12","alias_value":"B7ZGLPO7YJPZ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B7ZGLPO7YJPZLSCG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B7ZGLPO7","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:f4251784a27cdb577e1ed8e940a5d99081a79f728bb6124aaebac469544d6d69","target":"graph","created_at":"2026-05-18T03:30:42Z","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":"This paper is devoted to a systematic study of the geometry of nondegenerate $\\bbR^n$-actions on $n$-manifolds. The motivations for this study come from both dynamics, where these actions form a special class of integrable dynamical systems and the understanding of their nature is important for the study of other Hamiltonian and non-Hamiltonian integrable systems, and geometry, where these actions are related to a lot of other geometric objects, including reflection groups, singular affine structures, toric and quasi-toric manifolds, monodromy phenomena, topological invariants, etc. We constru","authors_text":"Nguyen Tien Zung, Nguyen Van Minh","cross_cats":["math.DG","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-13T11:07:36Z","title":"Geometry of nondegenerate $\\mathbb{R}^n$-actions on $n$-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2765","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:d6177aa1e6f8dfa9bcf62ab654bf7751180beb5821197ca23513de304e1cc948","target":"record","created_at":"2026-05-18T03:30:42Z","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":"6e839065a5ca99a0d0ad8dffd2fe47811a7e65e5369b8be32eaca29b3dc95041","cross_cats_sorted":["math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-13T11:07:36Z","title_canon_sha256":"06492666d17553a911b81529a6d1022d670b47d72f56d654e68674f5e55d0ee5"},"schema_version":"1.0","source":{"id":"1203.2765","kind":"arxiv","version":3}},"canonical_sha256":"0ff265bddfc25f95c846bd1b002b773ae77361af57703f4b2f7817e24c504904","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ff265bddfc25f95c846bd1b002b773ae77361af57703f4b2f7817e24c504904","first_computed_at":"2026-05-18T03:30:42.279279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:42.279279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h88fe6JEDzNV12qT5uekEvDmTCooFXtLGHqr9811Sz3nNYLowK7gUoJcldb85GGzmrlYo3eoxvxNImvR7fG5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:42.280190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2765","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6177aa1e6f8dfa9bcf62ab654bf7751180beb5821197ca23513de304e1cc948","sha256:f4251784a27cdb577e1ed8e940a5d99081a79f728bb6124aaebac469544d6d69"],"state_sha256":"340e18447fac185d50f6faaefa60e5dfbdf14a460550ac75d437ac27f790b6d8"}