{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:WOUSSBNFP2HRJWM3A4GXWYETHP","short_pith_number":"pith:WOUSSBNF","schema_version":"1.0","canonical_sha256":"b3a92905a57e8f14d99b070d7b60933bda112317fe324b0ff4ff679fbd9567c7","source":{"kind":"arxiv","id":"1011.5340","version":1},"attestation_state":"computed","paper":{"title":"On the Solvability of the Transvection group of Extrinsic Symplectic Symmetric Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Lorenz J. Schwachh\\\"ofer","submitted_at":"2010-11-24T11:22:47Z","abstract_excerpt":"Let $M$ be a symplectic symmetric space, and let $\\imath : M \\to V$ be an extrinsic symplectic symmetric immersion, i.e., $(V, \\Omega)$ is a symplectic vector space and $\\imath$ is an injective symplectic immersion such that for each point $p \\in M$, the geodesic symmetry in $p$ is compatible with the reflection in the affine normal space at $\\imath(p)$. We show that the existence of such an immersion implies that the transvection group of $M$ is solvable."},"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":"1011.5340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-24T11:22:47Z","cross_cats_sorted":[],"title_canon_sha256":"1589c78910a777592b0eb7647b399246a6d800a5482d61234fe70f73d28be1d3","abstract_canon_sha256":"cd52193c5539d54faa79784b6a49a4cb5c827e181dd6e1586c89ea32cd04c6f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:41.501650Z","signature_b64":"2i0yO4mK7Zun1US1HISboPpP5hGEiOpxMm9293haa4GhGR/c7Gq9dsPzy4JCMK2CQv1p/gM/DesKEAN9GlAmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3a92905a57e8f14d99b070d7b60933bda112317fe324b0ff4ff679fbd9567c7","last_reissued_at":"2026-05-18T02:04:41.500865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:41.500865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Solvability of the Transvection group of Extrinsic Symplectic Symmetric Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Lorenz J. Schwachh\\\"ofer","submitted_at":"2010-11-24T11:22:47Z","abstract_excerpt":"Let $M$ be a symplectic symmetric space, and let $\\imath : M \\to V$ be an extrinsic symplectic symmetric immersion, i.e., $(V, \\Omega)$ is a symplectic vector space and $\\imath$ is an injective symplectic immersion such that for each point $p \\in M$, the geodesic symmetry in $p$ is compatible with the reflection in the affine normal space at $\\imath(p)$. We show that the existence of such an immersion implies that the transvection group of $M$ is solvable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5340","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":"1011.5340","created_at":"2026-05-18T02:04:41.500977+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.5340v1","created_at":"2026-05-18T02:04:41.500977+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5340","created_at":"2026-05-18T02:04:41.500977+00:00"},{"alias_kind":"pith_short_12","alias_value":"WOUSSBNFP2HR","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"WOUSSBNFP2HRJWM3","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"WOUSSBNF","created_at":"2026-05-18T12:26:17.028572+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/WOUSSBNFP2HRJWM3A4GXWYETHP","json":"https://pith.science/pith/WOUSSBNFP2HRJWM3A4GXWYETHP.json","graph_json":"https://pith.science/api/pith-number/WOUSSBNFP2HRJWM3A4GXWYETHP/graph.json","events_json":"https://pith.science/api/pith-number/WOUSSBNFP2HRJWM3A4GXWYETHP/events.json","paper":"https://pith.science/paper/WOUSSBNF"},"agent_actions":{"view_html":"https://pith.science/pith/WOUSSBNFP2HRJWM3A4GXWYETHP","download_json":"https://pith.science/pith/WOUSSBNFP2HRJWM3A4GXWYETHP.json","view_paper":"https://pith.science/paper/WOUSSBNF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.5340&json=true","fetch_graph":"https://pith.science/api/pith-number/WOUSSBNFP2HRJWM3A4GXWYETHP/graph.json","fetch_events":"https://pith.science/api/pith-number/WOUSSBNFP2HRJWM3A4GXWYETHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WOUSSBNFP2HRJWM3A4GXWYETHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WOUSSBNFP2HRJWM3A4GXWYETHP/action/storage_attestation","attest_author":"https://pith.science/pith/WOUSSBNFP2HRJWM3A4GXWYETHP/action/author_attestation","sign_citation":"https://pith.science/pith/WOUSSBNFP2HRJWM3A4GXWYETHP/action/citation_signature","submit_replication":"https://pith.science/pith/WOUSSBNFP2HRJWM3A4GXWYETHP/action/replication_record"}},"created_at":"2026-05-18T02:04:41.500977+00:00","updated_at":"2026-05-18T02:04:41.500977+00:00"}