{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VZC5DF765XCTEBENVERTAWVG57","short_pith_number":"pith:VZC5DF76","schema_version":"1.0","canonical_sha256":"ae45d197feedc532048da923305aa6efe472bc7a563b17cb61b72e20e4824b34","source":{"kind":"arxiv","id":"1509.03816","version":2},"attestation_state":"computed","paper":{"title":"Nil-Anosov actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Maquera, Thierry Barbot (LANLG)","submitted_at":"2015-09-13T06:29:13Z","abstract_excerpt":"We consider Anosov actions of a Lie group $G$ of dimension $k$ on a closed manifold of dimension $k+n.$We introduce the notion of Nil-Anosov action of $G$ (which includes the case where $G$ is nilpotent) and establishes the invariance by the entire group $G$of the associated stable and unstable foliations. We then prove a spectral decomposition Theoremfor such an action when the group $G$ is nilpotent. Finally, we focus on the case where $G$ is nilpotent andthe unstable bundle has codimension one. We prove that in this case the action is a Nil-extensionover an Anosov action of an abelian Lie g"},"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":"1509.03816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-13T06:29:13Z","cross_cats_sorted":[],"title_canon_sha256":"a402bd0971c9a9736b3e0534e3bb1cd87ea7dd1c7339bdd405a346c22a00d0af","abstract_canon_sha256":"d85ed67f7be7828130b274513b8360e548554af25aa6eff39fae3dade2a13371"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:55.310287Z","signature_b64":"JMkkC/bF9/Pv/vOkfiEuuZ4PPLuUdNtbtutX9eJ342u5IYKfKV6G4HsNPNGQ7UiiPz5w4hbUbs7ANt5R87kfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae45d197feedc532048da923305aa6efe472bc7a563b17cb61b72e20e4824b34","last_reissued_at":"2026-05-18T01:12:55.309936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:55.309936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nil-Anosov actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Maquera, Thierry Barbot (LANLG)","submitted_at":"2015-09-13T06:29:13Z","abstract_excerpt":"We consider Anosov actions of a Lie group $G$ of dimension $k$ on a closed manifold of dimension $k+n.$We introduce the notion of Nil-Anosov action of $G$ (which includes the case where $G$ is nilpotent) and establishes the invariance by the entire group $G$of the associated stable and unstable foliations. We then prove a spectral decomposition Theoremfor such an action when the group $G$ is nilpotent. Finally, we focus on the case where $G$ is nilpotent andthe unstable bundle has codimension one. We prove that in this case the action is a Nil-extensionover an Anosov action of an abelian Lie g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03816","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":"1509.03816","created_at":"2026-05-18T01:12:55.309995+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.03816v2","created_at":"2026-05-18T01:12:55.309995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03816","created_at":"2026-05-18T01:12:55.309995+00:00"},{"alias_kind":"pith_short_12","alias_value":"VZC5DF765XCT","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"VZC5DF765XCTEBEN","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"VZC5DF76","created_at":"2026-05-18T12:29:47.479230+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/VZC5DF765XCTEBENVERTAWVG57","json":"https://pith.science/pith/VZC5DF765XCTEBENVERTAWVG57.json","graph_json":"https://pith.science/api/pith-number/VZC5DF765XCTEBENVERTAWVG57/graph.json","events_json":"https://pith.science/api/pith-number/VZC5DF765XCTEBENVERTAWVG57/events.json","paper":"https://pith.science/paper/VZC5DF76"},"agent_actions":{"view_html":"https://pith.science/pith/VZC5DF765XCTEBENVERTAWVG57","download_json":"https://pith.science/pith/VZC5DF765XCTEBENVERTAWVG57.json","view_paper":"https://pith.science/paper/VZC5DF76","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.03816&json=true","fetch_graph":"https://pith.science/api/pith-number/VZC5DF765XCTEBENVERTAWVG57/graph.json","fetch_events":"https://pith.science/api/pith-number/VZC5DF765XCTEBENVERTAWVG57/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VZC5DF765XCTEBENVERTAWVG57/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VZC5DF765XCTEBENVERTAWVG57/action/storage_attestation","attest_author":"https://pith.science/pith/VZC5DF765XCTEBENVERTAWVG57/action/author_attestation","sign_citation":"https://pith.science/pith/VZC5DF765XCTEBENVERTAWVG57/action/citation_signature","submit_replication":"https://pith.science/pith/VZC5DF765XCTEBENVERTAWVG57/action/replication_record"}},"created_at":"2026-05-18T01:12:55.309995+00:00","updated_at":"2026-05-18T01:12:55.309995+00:00"}