{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5MNGSH45PHYD6Z7ULFEWXOXIE2","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":"249806ab5aa8984310257493e0cabcd3f2c7ab0f439e2c899c8ba3c3f5c332d3","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-28T12:59:30Z","title_canon_sha256":"1dc9a71416801111ce7061f016be95956de0bbcc301a295a0bfa6249d51461a4"},"schema_version":"1.0","source":{"id":"1411.7849","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7849","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7849v5","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7849","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"5MNGSH45PHYD","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5MNGSH45PHYD6Z7U","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5MNGSH45","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:e73c0d0d1a8de10ad25ca32aa3af2c4c7344e10a2a8e14d66474380d2f27e671","target":"graph","created_at":"2026-05-18T01:03:31Z","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":"For a field k, let G be a reductive k-group and V an affine k-variety on which G acts. Using the notion of cocharacter-closed G(k)-orbits in V, we prove a rational version of the celebrated Hilbert-Mumford Theorem from geometric invariant theory. We initiate a study of applications stemming from this rationality tool. A number of examples are discussed to illustrate the concept of cocharacter-closure and to highlight how it differs from the usual Zariski-closure. When k is perfect, we give a criterion in terms of closed orbits for G to be k-anisotropic, answering a question of Borel.","authors_text":"Benjamin Martin, Gerhard Roehrle, Michael Bate, Sebastian Herpel","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-28T12:59:30Z","title":"Cocharacter-closure and the rational Hilbert-Mumford Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7849","kind":"arxiv","version":5},"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:e54c526be69ad7d8774ff4d7543f4493c44e9047c121a589c0acf6a962709b1f","target":"record","created_at":"2026-05-18T01:03:31Z","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":"249806ab5aa8984310257493e0cabcd3f2c7ab0f439e2c899c8ba3c3f5c332d3","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-28T12:59:30Z","title_canon_sha256":"1dc9a71416801111ce7061f016be95956de0bbcc301a295a0bfa6249d51461a4"},"schema_version":"1.0","source":{"id":"1411.7849","kind":"arxiv","version":5}},"canonical_sha256":"eb1a691f9d79f03f67f459496bbae826932f6a65cae7281ebd0ca5611aac3b07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb1a691f9d79f03f67f459496bbae826932f6a65cae7281ebd0ca5611aac3b07","first_computed_at":"2026-05-18T01:03:31.194009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:31.194009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wYMt6vVlkSjOmPhYXsHnScn1l4Wy/TT6zzaAdZzcWvjuDylgnTkQjC2eYItPq8kXPXyD4gUvqaA6403ihpzRDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:31.194651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7849","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e54c526be69ad7d8774ff4d7543f4493c44e9047c121a589c0acf6a962709b1f","sha256:e73c0d0d1a8de10ad25ca32aa3af2c4c7344e10a2a8e14d66474380d2f27e671"],"state_sha256":"55121a31ae98926a73c668b0941f31d0f2da924795ade5290d8df0ccfbd9d7a7"}