{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2W7AFMLSHEPQR64763OLLCS5F2","short_pith_number":"pith:2W7AFMLS","schema_version":"1.0","canonical_sha256":"d5be02b172391f08fb9ff6dcb58a5d2eb4ea9133ccb5f5a0b76a2697123a1d4d","source":{"kind":"arxiv","id":"1001.4773","version":1},"attestation_state":"computed","paper":{"title":"On integrable codimension one Anosov actions of IR^k","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":"2010-01-26T18:58:05Z","abstract_excerpt":"In this paper, we consider codimension one Anosov actions of IR^k, k ? 1, on closed connected orientable manifolds of dimension n+k with n? 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of IR^k admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k=1, we show that, under some assumptions abou"},"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":"1001.4773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-01-26T18:58:05Z","cross_cats_sorted":[],"title_canon_sha256":"4db4c03698faa27c163b5c3446fba7dfaf590661045c2e5f3ed5b3120a1b9c71","abstract_canon_sha256":"c4b57a7607f26d0b842624225c6cb52ece0a16d64cce7ac2612d9ba6d9935b14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:16.440732Z","signature_b64":"fI9irReetqjuW6JklKP68cj9Zu/00PLsfVLLqjLr5w8gyoK/GQqKKPiBfNs0RE80pmjEzFbVw8V5rNTNbpxZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5be02b172391f08fb9ff6dcb58a5d2eb4ea9133ccb5f5a0b76a2697123a1d4d","last_reissued_at":"2026-05-18T03:36:16.440051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:16.440051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On integrable codimension one Anosov actions of IR^k","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":"2010-01-26T18:58:05Z","abstract_excerpt":"In this paper, we consider codimension one Anosov actions of IR^k, k ? 1, on closed connected orientable manifolds of dimension n+k with n? 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of IR^k admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k=1, we show that, under some assumptions abou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4773","kind":"arxiv","version":1},"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":"1001.4773","created_at":"2026-05-18T03:36:16.440163+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.4773v1","created_at":"2026-05-18T03:36:16.440163+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4773","created_at":"2026-05-18T03:36:16.440163+00:00"},{"alias_kind":"pith_short_12","alias_value":"2W7AFMLSHEPQ","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2W7AFMLSHEPQR647","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2W7AFMLS","created_at":"2026-05-18T12:26:03.138858+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/2W7AFMLSHEPQR64763OLLCS5F2","json":"https://pith.science/pith/2W7AFMLSHEPQR64763OLLCS5F2.json","graph_json":"https://pith.science/api/pith-number/2W7AFMLSHEPQR64763OLLCS5F2/graph.json","events_json":"https://pith.science/api/pith-number/2W7AFMLSHEPQR64763OLLCS5F2/events.json","paper":"https://pith.science/paper/2W7AFMLS"},"agent_actions":{"view_html":"https://pith.science/pith/2W7AFMLSHEPQR64763OLLCS5F2","download_json":"https://pith.science/pith/2W7AFMLSHEPQR64763OLLCS5F2.json","view_paper":"https://pith.science/paper/2W7AFMLS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.4773&json=true","fetch_graph":"https://pith.science/api/pith-number/2W7AFMLSHEPQR64763OLLCS5F2/graph.json","fetch_events":"https://pith.science/api/pith-number/2W7AFMLSHEPQR64763OLLCS5F2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2W7AFMLSHEPQR64763OLLCS5F2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2W7AFMLSHEPQR64763OLLCS5F2/action/storage_attestation","attest_author":"https://pith.science/pith/2W7AFMLSHEPQR64763OLLCS5F2/action/author_attestation","sign_citation":"https://pith.science/pith/2W7AFMLSHEPQR64763OLLCS5F2/action/citation_signature","submit_replication":"https://pith.science/pith/2W7AFMLSHEPQR64763OLLCS5F2/action/replication_record"}},"created_at":"2026-05-18T03:36:16.440163+00:00","updated_at":"2026-05-18T03:36:16.440163+00:00"}