{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:HA7BWT7VKDBAFQMTIIEXMR7J77","short_pith_number":"pith:HA7BWT7V","schema_version":"1.0","canonical_sha256":"383e1b4ff550c202c19342097647e9ffd2b1ad01623097ec52cb9f7780276f7c","source":{"kind":"arxiv","id":"0706.3223","version":1},"attestation_state":"computed","paper":{"title":"Smooth maps of a foliated manifold in a symplectic manifold","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Mahuya Datta, Md. Rabiul Islam","submitted_at":"2007-06-21T21:05:14Z","abstract_excerpt":"The immersions of a smooth manifold $M$ in a symplectic manifold $(N,\\sigma)$ inducing a given closed form $\\omega$ on $M$ satisfy the $C^0$-dense $h$-principle in the space of all continuous maps which pull back the deRham cohomology class of $\\sigma$ onto that of $\\omega$. In this paper we prove a foliated version of this result due to Gromov."},"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":"0706.3223","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-06-21T21:05:14Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"08ccd5c864ecb55b13c02a46ed02025c8a5849574b87ad9e0b2ef27c0c73b3ae","abstract_canon_sha256":"678e832332fee93f19427cf4f14119c883576f9241bf626e62a98c36fe8444af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:20.897343Z","signature_b64":"T3YMWURxIDxM2f6Jy6G6jAkooFUx80EKdXKTM9dVwD3+u2/C4qkGGWVj0B8IBfwQQeKyc8+Q5cF/GiVOs+ayCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"383e1b4ff550c202c19342097647e9ffd2b1ad01623097ec52cb9f7780276f7c","last_reissued_at":"2026-05-18T04:40:20.896837Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:20.896837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smooth maps of a foliated manifold in a symplectic manifold","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Mahuya Datta, Md. Rabiul Islam","submitted_at":"2007-06-21T21:05:14Z","abstract_excerpt":"The immersions of a smooth manifold $M$ in a symplectic manifold $(N,\\sigma)$ inducing a given closed form $\\omega$ on $M$ satisfy the $C^0$-dense $h$-principle in the space of all continuous maps which pull back the deRham cohomology class of $\\sigma$ onto that of $\\omega$. In this paper we prove a foliated version of this result due to Gromov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3223","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":"0706.3223","created_at":"2026-05-18T04:40:20.896912+00:00"},{"alias_kind":"arxiv_version","alias_value":"0706.3223v1","created_at":"2026-05-18T04:40:20.896912+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3223","created_at":"2026-05-18T04:40:20.896912+00:00"},{"alias_kind":"pith_short_12","alias_value":"HA7BWT7VKDBA","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"HA7BWT7VKDBAFQMT","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"HA7BWT7V","created_at":"2026-05-18T12:25:55.427421+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/HA7BWT7VKDBAFQMTIIEXMR7J77","json":"https://pith.science/pith/HA7BWT7VKDBAFQMTIIEXMR7J77.json","graph_json":"https://pith.science/api/pith-number/HA7BWT7VKDBAFQMTIIEXMR7J77/graph.json","events_json":"https://pith.science/api/pith-number/HA7BWT7VKDBAFQMTIIEXMR7J77/events.json","paper":"https://pith.science/paper/HA7BWT7V"},"agent_actions":{"view_html":"https://pith.science/pith/HA7BWT7VKDBAFQMTIIEXMR7J77","download_json":"https://pith.science/pith/HA7BWT7VKDBAFQMTIIEXMR7J77.json","view_paper":"https://pith.science/paper/HA7BWT7V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0706.3223&json=true","fetch_graph":"https://pith.science/api/pith-number/HA7BWT7VKDBAFQMTIIEXMR7J77/graph.json","fetch_events":"https://pith.science/api/pith-number/HA7BWT7VKDBAFQMTIIEXMR7J77/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HA7BWT7VKDBAFQMTIIEXMR7J77/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HA7BWT7VKDBAFQMTIIEXMR7J77/action/storage_attestation","attest_author":"https://pith.science/pith/HA7BWT7VKDBAFQMTIIEXMR7J77/action/author_attestation","sign_citation":"https://pith.science/pith/HA7BWT7VKDBAFQMTIIEXMR7J77/action/citation_signature","submit_replication":"https://pith.science/pith/HA7BWT7VKDBAFQMTIIEXMR7J77/action/replication_record"}},"created_at":"2026-05-18T04:40:20.896912+00:00","updated_at":"2026-05-18T04:40:20.896912+00:00"}