{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QBIDAL4P77KHUSPVY5A6R3F3SB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1cb81d764ae53b43c77565bf12935439f5c43305968c4cf910e580f14a812c76","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-06T06:53:26Z","title_canon_sha256":"83f0f2aaef8cf8a7fbd7299eb2053e04f27559937b4db163e9d34470731a3929"},"schema_version":"1.0","source":{"id":"0907.0922","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0922","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0922v1","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0922","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"QBIDAL4P77KH","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QBIDAL4P77KHUSPV","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QBIDAL4P","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:7d9840b1e5f1377ad29241c25bbd88903734f3663428bd033d8fb282ae4b1639","target":"graph","created_at":"2026-05-18T00:50:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that the essential dimension of the spinor group Spin_n grows exponentially with n; in particular, we give a precise formula for this essential dimension when n is not divisible by 4. We use this result to show that the number of 3-fold Pfister forms needed to represent the Witt class of a general quadratic form of rank n with trivial discriminant and Hasse-Witt invariant grows exponentially with n.\n  This paper overlaps with our earlier preprint arXiv:math/0701903 . That preprint has splintered into several parts, which have since acquired a life of their own. In particular, see \"Ess","authors_text":"Angelo Vistoli, Patrick Brosnan, Zinovy Reichstein","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-06T06:53:26Z","title":"Essential dimension, spinor groups and quadratic forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0922","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:db656e14a9776b8dc4875ea8de4b977ccea69f224ddba69b3634aafb632ee44c","target":"record","created_at":"2026-05-18T00:50:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1cb81d764ae53b43c77565bf12935439f5c43305968c4cf910e580f14a812c76","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-06T06:53:26Z","title_canon_sha256":"83f0f2aaef8cf8a7fbd7299eb2053e04f27559937b4db163e9d34470731a3929"},"schema_version":"1.0","source":{"id":"0907.0922","kind":"arxiv","version":1}},"canonical_sha256":"8050302f8fffd47a49f5c741e8ecbb90468fad02b5b5b632a3bd535f851f1101","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8050302f8fffd47a49f5c741e8ecbb90468fad02b5b5b632a3bd535f851f1101","first_computed_at":"2026-05-18T00:50:24.216509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:24.216509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lSR8dJ+eMToAKRXmEe28shwfDhrgThAOGcRpW+fwJUAfCN7sJ2q2WwpYyMo5O9XQYQncz06zKybhsc3p2tKRAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:24.217147Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0922","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db656e14a9776b8dc4875ea8de4b977ccea69f224ddba69b3634aafb632ee44c","sha256:7d9840b1e5f1377ad29241c25bbd88903734f3663428bd033d8fb282ae4b1639"],"state_sha256":"1a97ab8e97da1cc7987a3889bf15649e28b802cfcc8da0f917da657c50b6c4d8"}