{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Z2KOOUO4XUA4IZYD2FDTB7DEXC","short_pith_number":"pith:Z2KOOUO4","schema_version":"1.0","canonical_sha256":"ce94e751dcbd01c46703d14730fc64b8968577dcbc047cf538731544be734ad1","source":{"kind":"arxiv","id":"1501.06526","version":1},"attestation_state":"computed","paper":{"title":"$\\mathrm{Spin}(9)$-invariant valuations on the octonionic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andreas Bernig, Floriane Voide","submitted_at":"2015-01-26T19:05:55Z","abstract_excerpt":"The dimensions of the spaces of $k$-homogeneous $\\mathrm{Spin}(9)$-invariant valuations on the octonionic plane are computed using results from the theory of differential forms on contact manifolds as well as octonionic geometry and representation theory. Moreover, a valuation on Riemannian manifolds of particular interest is constructed which yields, as a special case, an element of $\\mathrm{Val}_2^{\\mathrm{Spin}(9)}$."},"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":"1501.06526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-01-26T19:05:55Z","cross_cats_sorted":[],"title_canon_sha256":"ccc6edab2fab6cb1a50f9b09829edc77f8056d1653f6805217e8fa973ae3bcaa","abstract_canon_sha256":"2b594999644d586fb7a399aaa69239ac588864fa7041c557c022e44a3a4c9a27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:58.637178Z","signature_b64":"MyVbiQf8tUzTW+TZa8UrfqhgceEm0RoIxd79UG4B8rjYcIlFrRZD+VBNg7/45y2/6Ct9jABRtWNrx4x82q48CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce94e751dcbd01c46703d14730fc64b8968577dcbc047cf538731544be734ad1","last_reissued_at":"2026-05-18T00:41:58.636726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:58.636726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\mathrm{Spin}(9)$-invariant valuations on the octonionic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andreas Bernig, Floriane Voide","submitted_at":"2015-01-26T19:05:55Z","abstract_excerpt":"The dimensions of the spaces of $k$-homogeneous $\\mathrm{Spin}(9)$-invariant valuations on the octonionic plane are computed using results from the theory of differential forms on contact manifolds as well as octonionic geometry and representation theory. Moreover, a valuation on Riemannian manifolds of particular interest is constructed which yields, as a special case, an element of $\\mathrm{Val}_2^{\\mathrm{Spin}(9)}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06526","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":"1501.06526","created_at":"2026-05-18T00:41:58.636790+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.06526v1","created_at":"2026-05-18T00:41:58.636790+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06526","created_at":"2026-05-18T00:41:58.636790+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2KOOUO4XUA4","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2KOOUO4XUA4IZYD","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2KOOUO4","created_at":"2026-05-18T12:29:52.810259+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/Z2KOOUO4XUA4IZYD2FDTB7DEXC","json":"https://pith.science/pith/Z2KOOUO4XUA4IZYD2FDTB7DEXC.json","graph_json":"https://pith.science/api/pith-number/Z2KOOUO4XUA4IZYD2FDTB7DEXC/graph.json","events_json":"https://pith.science/api/pith-number/Z2KOOUO4XUA4IZYD2FDTB7DEXC/events.json","paper":"https://pith.science/paper/Z2KOOUO4"},"agent_actions":{"view_html":"https://pith.science/pith/Z2KOOUO4XUA4IZYD2FDTB7DEXC","download_json":"https://pith.science/pith/Z2KOOUO4XUA4IZYD2FDTB7DEXC.json","view_paper":"https://pith.science/paper/Z2KOOUO4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.06526&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2KOOUO4XUA4IZYD2FDTB7DEXC/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2KOOUO4XUA4IZYD2FDTB7DEXC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2KOOUO4XUA4IZYD2FDTB7DEXC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2KOOUO4XUA4IZYD2FDTB7DEXC/action/storage_attestation","attest_author":"https://pith.science/pith/Z2KOOUO4XUA4IZYD2FDTB7DEXC/action/author_attestation","sign_citation":"https://pith.science/pith/Z2KOOUO4XUA4IZYD2FDTB7DEXC/action/citation_signature","submit_replication":"https://pith.science/pith/Z2KOOUO4XUA4IZYD2FDTB7DEXC/action/replication_record"}},"created_at":"2026-05-18T00:41:58.636790+00:00","updated_at":"2026-05-18T00:41:58.636790+00:00"}