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We show that every 4-form $\\omega$ on a smooth manifold $M$ can be induced from $\\sigma$ by a smooth immersion $f:M\\to Gr_k(\\H^n)$ (for sufficiently large $k$ and $n$) provided there exists a continuous map $f_0:M\\to Gr_k(\\H^n)$ which pulls back the cohomology class of $\\sigma$ onto that of $\\omega$."},"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":"1212.5885","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-24T09:59:13Z","cross_cats_sorted":[],"title_canon_sha256":"49c6107d76a6a5afccb12818f664c85f1ba13cf4154defe9a10d74908b7d86a8","abstract_canon_sha256":"014a390cc79136df76ceb6848f3498068a58148b2e017c2c0ecba5f18cc22c97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:51.073403Z","signature_b64":"v8xD27MsRoanQQFc53QuRrNshIIPHbH2hPid03L6a4UGgaVIMGL/NzXwWCcl/jB5MnaWpKyHljNBthBFpAfvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a63110f2f84f692b9d993ed7a3123f3981be35851fc02a2eeb4ea3af77a9f42","last_reissued_at":"2026-05-18T03:37:51.072585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:51.072585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Immersions in a Quaternionic Grassmannian inducing a given 4-form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mahuya Datta","submitted_at":"2012-12-24T09:59:13Z","abstract_excerpt":"Let $Gr_k(\\H^n)$ be the Grassmannian manifold of Quaternionic $k$-planes in $\\H^n$ and let $\\gamma^n_k\\to Gr_k(\\H^n)$ denote the Stiefel bundle of quaternionic $k$-frames in $\\H^n$. Let $\\sigma$ denote the first symplectic Pontrjagin form associated with the universal connection on $\\gamma^n_k$. We show that every 4-form $\\omega$ on a smooth manifold $M$ can be induced from $\\sigma$ by a smooth immersion $f:M\\to Gr_k(\\H^n)$ (for sufficiently large $k$ and $n$) provided there exists a continuous map $f_0:M\\to Gr_k(\\H^n)$ which pulls back the cohomology class of $\\sigma$ onto that of $\\omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5885","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":"1212.5885","created_at":"2026-05-18T03:37:51.072731+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.5885v1","created_at":"2026-05-18T03:37:51.072731+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5885","created_at":"2026-05-18T03:37:51.072731+00:00"},{"alias_kind":"pith_short_12","alias_value":"RJRRCDZPQT3J","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"RJRRCDZPQT3JFOOZ","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"RJRRCDZP","created_at":"2026-05-18T12:27:20.899486+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/RJRRCDZPQT3JFOOZSPWXUMJD6O","json":"https://pith.science/pith/RJRRCDZPQT3JFOOZSPWXUMJD6O.json","graph_json":"https://pith.science/api/pith-number/RJRRCDZPQT3JFOOZSPWXUMJD6O/graph.json","events_json":"https://pith.science/api/pith-number/RJRRCDZPQT3JFOOZSPWXUMJD6O/events.json","paper":"https://pith.science/paper/RJRRCDZP"},"agent_actions":{"view_html":"https://pith.science/pith/RJRRCDZPQT3JFOOZSPWXUMJD6O","download_json":"https://pith.science/pith/RJRRCDZPQT3JFOOZSPWXUMJD6O.json","view_paper":"https://pith.science/paper/RJRRCDZP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.5885&json=true","fetch_graph":"https://pith.science/api/pith-number/RJRRCDZPQT3JFOOZSPWXUMJD6O/graph.json","fetch_events":"https://pith.science/api/pith-number/RJRRCDZPQT3JFOOZSPWXUMJD6O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RJRRCDZPQT3JFOOZSPWXUMJD6O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RJRRCDZPQT3JFOOZSPWXUMJD6O/action/storage_attestation","attest_author":"https://pith.science/pith/RJRRCDZPQT3JFOOZSPWXUMJD6O/action/author_attestation","sign_citation":"https://pith.science/pith/RJRRCDZPQT3JFOOZSPWXUMJD6O/action/citation_signature","submit_replication":"https://pith.science/pith/RJRRCDZPQT3JFOOZSPWXUMJD6O/action/replication_record"}},"created_at":"2026-05-18T03:37:51.072731+00:00","updated_at":"2026-05-18T03:37:51.072731+00:00"}