{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2HRSBI25PFNVJEBKRPTGXHT4DC","short_pith_number":"pith:2HRSBI25","canonical_record":{"source":{"id":"1102.2132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-02-10T14:47:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1af413fd71e17361cbba10558e087eb08af56f38474d87d4fc5943fb30a6fe3b","abstract_canon_sha256":"af91237ac10688a8339c7216ab374f940d669ae646bf904a2795b3dbe5aec4f1"},"schema_version":"1.0"},"canonical_sha256":"d1e320a35d795b54902a8be66b9e7c18877a72997e0587a9c2dd9ccd9e104d2c","source":{"kind":"arxiv","id":"1102.2132","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2132","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2132v2","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2132","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"2HRSBI25PFNV","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2HRSBI25PFNVJEBK","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2HRSBI25","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2HRSBI25PFNVJEBKRPTGXHT4DC","target":"record","payload":{"canonical_record":{"source":{"id":"1102.2132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-02-10T14:47:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1af413fd71e17361cbba10558e087eb08af56f38474d87d4fc5943fb30a6fe3b","abstract_canon_sha256":"af91237ac10688a8339c7216ab374f940d669ae646bf904a2795b3dbe5aec4f1"},"schema_version":"1.0"},"canonical_sha256":"d1e320a35d795b54902a8be66b9e7c18877a72997e0587a9c2dd9ccd9e104d2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:42.021205Z","signature_b64":"18XKyjowl8OeiqREN19RBqc0Ssf/wnekbx1mAygtm0dsSg9+1EV1BqR13E5l8MIgnwrwRrZ0TLHKquxFJg3qDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1e320a35d795b54902a8be66b9e7c18877a72997e0587a9c2dd9ccd9e104d2c","last_reissued_at":"2026-05-18T01:21:42.020727Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:42.020727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.2132","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7rkkm70a4bPYDFgTtmEwyk9KweAFUn3dw/C5B46Jgbljax2uPc4urky3j9/BIbirlMAgnE3PlC3J4zlOIkvYCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:56:30.052067Z"},"content_sha256":"379d2dfbe4eeae86b527583567514a4af15cedcc70890a8198ac6d273d5b43ca","schema_version":"1.0","event_id":"sha256:379d2dfbe4eeae86b527583567514a4af15cedcc70890a8198ac6d273d5b43ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2HRSBI25PFNVJEBKRPTGXHT4DC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite separating sets and quasi-affine quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Emilie Dufresne","submitted_at":"2011-02-10T14:47:26Z","abstract_excerpt":"Nagata's famous counterexample to Hilbert's fourteenth problem shows that the ring of invariants of an algebraic group action on an affine algebraic variety is not always finitely generated. In some sense, however, invariant rings are not far from affine. Indeed, invariant rings are always quasi-affine, and there always exist finite separating sets. In this paper, we give a new method for finding a quasi-affine variety on which the ring of regular functions is equal to a given invariant ring, and we give a criterion to recognize separating algebras. The method and criterion are used on some kn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2132","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xoloAi//Wg8rEUh2UNI4DuvA2rcEMRVNysJjDpMePoluePi74wJ2iQKr25o/VAvFNkldlj6Q4ZAbUjv5EZXqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:56:30.052749Z"},"content_sha256":"3120c52f87952040a1c45225718bab9d0201b3d44d32dc2d2cddb5b7575c60f2","schema_version":"1.0","event_id":"sha256:3120c52f87952040a1c45225718bab9d0201b3d44d32dc2d2cddb5b7575c60f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2HRSBI25PFNVJEBKRPTGXHT4DC/bundle.json","state_url":"https://pith.science/pith/2HRSBI25PFNVJEBKRPTGXHT4DC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2HRSBI25PFNVJEBKRPTGXHT4DC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T19:56:30Z","links":{"resolver":"https://pith.science/pith/2HRSBI25PFNVJEBKRPTGXHT4DC","bundle":"https://pith.science/pith/2HRSBI25PFNVJEBKRPTGXHT4DC/bundle.json","state":"https://pith.science/pith/2HRSBI25PFNVJEBKRPTGXHT4DC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2HRSBI25PFNVJEBKRPTGXHT4DC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2HRSBI25PFNVJEBKRPTGXHT4DC","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":"af91237ac10688a8339c7216ab374f940d669ae646bf904a2795b3dbe5aec4f1","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-02-10T14:47:26Z","title_canon_sha256":"1af413fd71e17361cbba10558e087eb08af56f38474d87d4fc5943fb30a6fe3b"},"schema_version":"1.0","source":{"id":"1102.2132","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2132","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2132v2","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2132","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"2HRSBI25PFNV","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2HRSBI25PFNVJEBK","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2HRSBI25","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:3120c52f87952040a1c45225718bab9d0201b3d44d32dc2d2cddb5b7575c60f2","target":"graph","created_at":"2026-05-18T01:21:42Z","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":"Nagata's famous counterexample to Hilbert's fourteenth problem shows that the ring of invariants of an algebraic group action on an affine algebraic variety is not always finitely generated. In some sense, however, invariant rings are not far from affine. Indeed, invariant rings are always quasi-affine, and there always exist finite separating sets. In this paper, we give a new method for finding a quasi-affine variety on which the ring of regular functions is equal to a given invariant ring, and we give a criterion to recognize separating algebras. The method and criterion are used on some kn","authors_text":"Emilie Dufresne","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-02-10T14:47:26Z","title":"Finite separating sets and quasi-affine quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2132","kind":"arxiv","version":2},"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":"sha256:379d2dfbe4eeae86b527583567514a4af15cedcc70890a8198ac6d273d5b43ca","target":"record","created_at":"2026-05-18T01:21:42Z","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":"af91237ac10688a8339c7216ab374f940d669ae646bf904a2795b3dbe5aec4f1","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-02-10T14:47:26Z","title_canon_sha256":"1af413fd71e17361cbba10558e087eb08af56f38474d87d4fc5943fb30a6fe3b"},"schema_version":"1.0","source":{"id":"1102.2132","kind":"arxiv","version":2}},"canonical_sha256":"d1e320a35d795b54902a8be66b9e7c18877a72997e0587a9c2dd9ccd9e104d2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1e320a35d795b54902a8be66b9e7c18877a72997e0587a9c2dd9ccd9e104d2c","first_computed_at":"2026-05-18T01:21:42.020727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:42.020727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"18XKyjowl8OeiqREN19RBqc0Ssf/wnekbx1mAygtm0dsSg9+1EV1BqR13E5l8MIgnwrwRrZ0TLHKquxFJg3qDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:42.021205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.2132","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:379d2dfbe4eeae86b527583567514a4af15cedcc70890a8198ac6d273d5b43ca","sha256:3120c52f87952040a1c45225718bab9d0201b3d44d32dc2d2cddb5b7575c60f2"],"state_sha256":"580092ff3ecb1d47494cffdda963ed98709b599ae2f69413c7f9aaebf7da8172"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xd0pZpzSdDiUYyMrqcCqR2CuriWObF0Df6i6ff+6N4pik8TYgD0uaqMosJgVnH4UjjGb5qfCcN+uDL/F8aM/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:56:30.056216Z","bundle_sha256":"077f7e2bad6c623cb19f462bf3d44b995384a61d7f16647a07c7adedc09f7e39"}}