{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1996:QUTFDN5J7GUEJR56JB5G7FN3LI","short_pith_number":"pith:QUTFDN5J","schema_version":"1.0","canonical_sha256":"852651b7a9f9a844c7be487a6f95bb5a14a848260dd49797ef287c3c9c130618","source":{"kind":"arxiv","id":"hep-th/9605060","version":1},"attestation_state":"computed","paper":{"title":"The Geometry of Self-dual 2-forms","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. H. Bilge, \\c{S}. Ko\\c{c}ak, T. Dereli","submitted_at":"1996-05-09T06:16:59Z","abstract_excerpt":"We show that self-dual 2-forms in 2n dimensional spaces determine a $n^2-n+1$ dimensional manifold ${\\cal S}_{2n}$ and the dimension of the maximal linear subspaces of ${\\cal S}_{2n}$ is equal to the (Radon-Hurwitz) number of linearly independent vector fields on the sphere $S^{2n-1}$. We provide a direct proof that for $n$ odd ${\\cal S}_{2n}$ has only one-dimensional linear submanifolds. We exhibit $2^c-1$ dimensional subspaces in dimensions which are multiples of $2^c$, for $c=1,2,3$. In particular, we demonstrate that the seven dimensional linear subspaces of ${\\cal S}_{8}$ also include amo"},"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":"hep-th/9605060","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1996-05-09T06:16:59Z","cross_cats_sorted":[],"title_canon_sha256":"7db22806b6885fd6413b4c409562a5af7356ab39a5d0542231edd826ec94afb2","abstract_canon_sha256":"c59b34873af8ae08d0b3c7c7f9a0a27603364409f92011b09681c0fa77c92287"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:38.095081Z","signature_b64":"/aNt94zPq6Wr4xHv3vWx0MMlU9YwJqUswe174GlJ3IQJaHIHGXSBpYSTkXqlzZmgqRxgx8kI0awtKPZh44b1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"852651b7a9f9a844c7be487a6f95bb5a14a848260dd49797ef287c3c9c130618","last_reissued_at":"2026-05-18T01:38:38.094375Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:38.094375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Geometry of Self-dual 2-forms","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. H. Bilge, \\c{S}. Ko\\c{c}ak, T. Dereli","submitted_at":"1996-05-09T06:16:59Z","abstract_excerpt":"We show that self-dual 2-forms in 2n dimensional spaces determine a $n^2-n+1$ dimensional manifold ${\\cal S}_{2n}$ and the dimension of the maximal linear subspaces of ${\\cal S}_{2n}$ is equal to the (Radon-Hurwitz) number of linearly independent vector fields on the sphere $S^{2n-1}$. We provide a direct proof that for $n$ odd ${\\cal S}_{2n}$ has only one-dimensional linear submanifolds. We exhibit $2^c-1$ dimensional subspaces in dimensions which are multiples of $2^c$, for $c=1,2,3$. In particular, we demonstrate that the seven dimensional linear subspaces of ${\\cal S}_{8}$ also include amo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9605060","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":"hep-th/9605060","created_at":"2026-05-18T01:38:38.094483+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9605060v1","created_at":"2026-05-18T01:38:38.094483+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9605060","created_at":"2026-05-18T01:38:38.094483+00:00"},{"alias_kind":"pith_short_12","alias_value":"QUTFDN5J7GUE","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_16","alias_value":"QUTFDN5J7GUEJR56","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_8","alias_value":"QUTFDN5J","created_at":"2026-05-18T12:25:48.327863+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/QUTFDN5J7GUEJR56JB5G7FN3LI","json":"https://pith.science/pith/QUTFDN5J7GUEJR56JB5G7FN3LI.json","graph_json":"https://pith.science/api/pith-number/QUTFDN5J7GUEJR56JB5G7FN3LI/graph.json","events_json":"https://pith.science/api/pith-number/QUTFDN5J7GUEJR56JB5G7FN3LI/events.json","paper":"https://pith.science/paper/QUTFDN5J"},"agent_actions":{"view_html":"https://pith.science/pith/QUTFDN5J7GUEJR56JB5G7FN3LI","download_json":"https://pith.science/pith/QUTFDN5J7GUEJR56JB5G7FN3LI.json","view_paper":"https://pith.science/paper/QUTFDN5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9605060&json=true","fetch_graph":"https://pith.science/api/pith-number/QUTFDN5J7GUEJR56JB5G7FN3LI/graph.json","fetch_events":"https://pith.science/api/pith-number/QUTFDN5J7GUEJR56JB5G7FN3LI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QUTFDN5J7GUEJR56JB5G7FN3LI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QUTFDN5J7GUEJR56JB5G7FN3LI/action/storage_attestation","attest_author":"https://pith.science/pith/QUTFDN5J7GUEJR56JB5G7FN3LI/action/author_attestation","sign_citation":"https://pith.science/pith/QUTFDN5J7GUEJR56JB5G7FN3LI/action/citation_signature","submit_replication":"https://pith.science/pith/QUTFDN5J7GUEJR56JB5G7FN3LI/action/replication_record"}},"created_at":"2026-05-18T01:38:38.094483+00:00","updated_at":"2026-05-18T01:38:38.094483+00:00"}