{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:P2DDTV5D6GE5M6TQU5DIODNRNH","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":"fbef86afa5c25f2c248689db4a4449e761026c2f929d281ca63f96a38342454c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2025-06-06T00:41:56Z","title_canon_sha256":"8bca857e9efbc82f78b1b7ee0c7c8d685598805c455a967c8530776e2c63dab0"},"schema_version":"1.0","source":{"id":"2506.05650","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05650","created_at":"2026-05-20T00:00:20Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05650v3","created_at":"2026-05-20T00:00:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05650","created_at":"2026-05-20T00:00:20Z"},{"alias_kind":"pith_short_12","alias_value":"P2DDTV5D6GE5","created_at":"2026-05-20T00:00:20Z"},{"alias_kind":"pith_short_16","alias_value":"P2DDTV5D6GE5M6TQ","created_at":"2026-05-20T00:00:20Z"},{"alias_kind":"pith_short_8","alias_value":"P2DDTV5D","created_at":"2026-05-20T00:00:20Z"}],"graph_snapshots":[{"event_id":"sha256:8da6ca920d64e370b28bae0e0e319c48ffed6c9204cd808f4b3e04d4ed7b8fee","target":"graph","created_at":"2026-05-20T00:00:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.05650/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a faithful linear representation $V$ of a finite group $G$ in coprime characteristic, we show that if the field Noether number $\\beta_{\\mathrm{field}}$ is the minimum $d$ such that the invariant polynomials of degree $\\leq d$ generate the field $k(V)^G$ of rational invariants as a field, and the spanning degree $D_\\mathrm{span}$ is the minimum $d$ such that the polynomials of degree $\\leq d$ span the rational function field $k(V)$ as a vector space over $k(V)^G$, then $\\beta_{\\mathrm{field}} \\leq 2D_\\mathrm{span} + 1$, and this is sharp. This generalizes a recent result of Edidin and Katz.","authors_text":"Ben Blum-Smith, Harm Derksen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2025-06-06T00:41:56Z","title":"Generic orbits, normal bases, and generation degree for fields of rational invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05650","kind":"arxiv","version":3},"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":"sha256:9fc3eb33f3c117dbeeac5d002016d1802746d2c8935640ea9d23ec3011d23dde","target":"record","created_at":"2026-05-20T00:00:20Z","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":"fbef86afa5c25f2c248689db4a4449e761026c2f929d281ca63f96a38342454c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2025-06-06T00:41:56Z","title_canon_sha256":"8bca857e9efbc82f78b1b7ee0c7c8d685598805c455a967c8530776e2c63dab0"},"schema_version":"1.0","source":{"id":"2506.05650","kind":"arxiv","version":3}},"canonical_sha256":"7e8639d7a3f189d67a70a746870db169cba1603e3b2d157c5b88cd7ae5ac468a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e8639d7a3f189d67a70a746870db169cba1603e3b2d157c5b88cd7ae5ac468a","first_computed_at":"2026-05-20T00:00:20.819385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:20.819385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DdBfWlLR6cU6AcX7WeGqQEHUxgoAHqoC26bI/GLi5CrfXT+5QO7+VQD56l0xB8vlqGblkXzpJ+9g8UmfkG/sDw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:20.819853Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.05650","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fc3eb33f3c117dbeeac5d002016d1802746d2c8935640ea9d23ec3011d23dde","sha256:8da6ca920d64e370b28bae0e0e319c48ffed6c9204cd808f4b3e04d4ed7b8fee"],"state_sha256":"1beca68aad9a35f5d0180b9be4c94d16fe4e57319f87b26524e91c15f56f8232"}