{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TT356H5VJ4WN3TPIREXWQU4WY7","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":"1feff7fa37b433bb31aa86a04d896ff9c2cb49c9f8bb4b59b75bc1d60170b88b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-24T02:02:44Z","title_canon_sha256":"99bb7a5723f99576f94f1123db09d97b2e3fcc64788de501dbb3498e099d5867"},"schema_version":"1.0","source":{"id":"1202.5363","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5363","created_at":"2026-05-18T04:01:37Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5363v1","created_at":"2026-05-18T04:01:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5363","created_at":"2026-05-18T04:01:37Z"},{"alias_kind":"pith_short_12","alias_value":"TT356H5VJ4WN","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TT356H5VJ4WN3TPI","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TT356H5V","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:33d72a4ac88f45a84c49fc7a0682bc5e2bfdd6a3e27ca7edd19fbb023ccc866d","target":"graph","created_at":"2026-05-18T04:01:37Z","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":"In this essay we explore the notion of essential dimension using the theory of valuations of fields. Given a field extension K/k and a valuation on K that is trivial on k, we prove that the rank of the valuation cannot exceed the transcendence degree trdeg K. We use this inequality to prove lower bounds on the essential dimension in some interesting situations. We study orbits of a torus action and find a formula for the essential dimension of the functor of these orbits.","authors_text":"Aurel Meyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-24T02:02:44Z","title":"A Valuation Theoretic Approach to Essential Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5363","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":"sha256:27e71ab8702a5b992d925cf26f8d01ac41b469232001f3cab7db158c4acf8a22","target":"record","created_at":"2026-05-18T04:01:37Z","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":"1feff7fa37b433bb31aa86a04d896ff9c2cb49c9f8bb4b59b75bc1d60170b88b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-24T02:02:44Z","title_canon_sha256":"99bb7a5723f99576f94f1123db09d97b2e3fcc64788de501dbb3498e099d5867"},"schema_version":"1.0","source":{"id":"1202.5363","kind":"arxiv","version":1}},"canonical_sha256":"9cf7df1fb54f2cddcde8892f685396c7c995d3cb1ae705a1a321112c16c57499","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cf7df1fb54f2cddcde8892f685396c7c995d3cb1ae705a1a321112c16c57499","first_computed_at":"2026-05-18T04:01:37.408230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:37.408230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Kx1dd2eHiWTbHimkPhRif7YWPR/vAvLFv/ToD9yYo5dGXimYwD/iyYsRCyGKm6yT8A5PPqEDup9vVGL+VIoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:37.409082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5363","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27e71ab8702a5b992d925cf26f8d01ac41b469232001f3cab7db158c4acf8a22","sha256:33d72a4ac88f45a84c49fc7a0682bc5e2bfdd6a3e27ca7edd19fbb023ccc866d"],"state_sha256":"b90ee078c35e2c1bf80cf57bd7cef51c9c305e435ce912af779f7b6f04906b40"}