{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AVU5LO4LJIEAIGS4CFZMIIGYUK","short_pith_number":"pith:AVU5LO4L","canonical_record":{"source":{"id":"1410.3181","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-13T03:33:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b1f3100f1afc9d08f59fd190cb118641a1485e7bd8d48a789513d6573f0bccc9","abstract_canon_sha256":"382cd4d265dccde91afc2bb2a8095a47655c2c6a9dd7e796517b22f898eb05f0"},"schema_version":"1.0"},"canonical_sha256":"0569d5bb8b4a08041a5c1172c420d8a2858320400b2a5d59ff433d2aa0c8c343","source":{"kind":"arxiv","id":"1410.3181","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3181","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3181v1","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3181","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"AVU5LO4LJIEA","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AVU5LO4LJIEAIGS4","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AVU5LO4L","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AVU5LO4LJIEAIGS4CFZMIIGYUK","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3181","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-13T03:33:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b1f3100f1afc9d08f59fd190cb118641a1485e7bd8d48a789513d6573f0bccc9","abstract_canon_sha256":"382cd4d265dccde91afc2bb2a8095a47655c2c6a9dd7e796517b22f898eb05f0"},"schema_version":"1.0"},"canonical_sha256":"0569d5bb8b4a08041a5c1172c420d8a2858320400b2a5d59ff433d2aa0c8c343","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:11.954115Z","signature_b64":"haH2D1q8EcLxCQK4d83sk/d3lAu9NfnsPA3MjoSA3tEESdtO7JFhU8RmyywTWC9zZdYTCjUbWrcqgsSyZvFlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0569d5bb8b4a08041a5c1172c420d8a2858320400b2a5d59ff433d2aa0c8c343","last_reissued_at":"2026-05-18T02:40:11.953548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:11.953548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3181","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TFRISBOqmlzaKuuJvYF3aEGRQQsHB4Q9+jSii1MVk6G3azegOgaAj4NEiZXtdq2EGSvVdDEdr+EnkCU9grzhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:29:01.263434Z"},"content_sha256":"5d33333e4d97b35e05ce8facc4840f52433ce5200db31d49d4cb837f89df4d9c","schema_version":"1.0","event_id":"sha256:5d33333e4d97b35e05ce8facc4840f52433ce5200db31d49d4cb837f89df4d9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AVU5LO4LJIEAIGS4CFZMIIGYUK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subgroups of polynomial automorphisms with diagonalizable fibers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Shigeru Kuroda","submitted_at":"2014-10-13T03:33:30Z","abstract_excerpt":"Let $R$ be an integral domain over a field $k$, and $G$ a subgroup of the automorphism group of the polynomial ring $R[x_1,..., x_n]$ over $R$. In this paper, we discuss when $G$ is diagonalizable under the assumption that $G$ is diagonalizable over the field of fractions of $R$. We are particularly interested in the case where $G$ is a finite abelian group. Kraft-Russell (2014) implies that every finite abelian subgroup of ${\\rm Aut}_R(R[x_1,x_2])$ is diagonalizable if $R$ is an affine PID over $k={\\bf C}$. One of the main results of this paper says that the same holds for a PID $R$ over any "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3181","kind":"arxiv","version":1},"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":"2026-05-18T02:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zfzD2H//23dac95ZbdfC7osdpeDbYQ3/Waw24oGMkWws0pEks8XgixAClARJ+h1Zfgb+rNdTiSQyhAzpOSp9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:29:01.264107Z"},"content_sha256":"d64b155072e9c3805c372d7106ccc03a8240109c1ac23807eb0322fc68e7e0ab","schema_version":"1.0","event_id":"sha256:d64b155072e9c3805c372d7106ccc03a8240109c1ac23807eb0322fc68e7e0ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AVU5LO4LJIEAIGS4CFZMIIGYUK/bundle.json","state_url":"https://pith.science/pith/AVU5LO4LJIEAIGS4CFZMIIGYUK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AVU5LO4LJIEAIGS4CFZMIIGYUK/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":"2026-05-31T14:29:01Z","links":{"resolver":"https://pith.science/pith/AVU5LO4LJIEAIGS4CFZMIIGYUK","bundle":"https://pith.science/pith/AVU5LO4LJIEAIGS4CFZMIIGYUK/bundle.json","state":"https://pith.science/pith/AVU5LO4LJIEAIGS4CFZMIIGYUK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AVU5LO4LJIEAIGS4CFZMIIGYUK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AVU5LO4LJIEAIGS4CFZMIIGYUK","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":"382cd4d265dccde91afc2bb2a8095a47655c2c6a9dd7e796517b22f898eb05f0","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-13T03:33:30Z","title_canon_sha256":"b1f3100f1afc9d08f59fd190cb118641a1485e7bd8d48a789513d6573f0bccc9"},"schema_version":"1.0","source":{"id":"1410.3181","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3181","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3181v1","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3181","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"AVU5LO4LJIEA","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AVU5LO4LJIEAIGS4","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AVU5LO4L","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:d64b155072e9c3805c372d7106ccc03a8240109c1ac23807eb0322fc68e7e0ab","target":"graph","created_at":"2026-05-18T02:40:11Z","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":"Let $R$ be an integral domain over a field $k$, and $G$ a subgroup of the automorphism group of the polynomial ring $R[x_1,..., x_n]$ over $R$. In this paper, we discuss when $G$ is diagonalizable under the assumption that $G$ is diagonalizable over the field of fractions of $R$. We are particularly interested in the case where $G$ is a finite abelian group. Kraft-Russell (2014) implies that every finite abelian subgroup of ${\\rm Aut}_R(R[x_1,x_2])$ is diagonalizable if $R$ is an affine PID over $k={\\bf C}$. One of the main results of this paper says that the same holds for a PID $R$ over any ","authors_text":"Shigeru Kuroda","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-13T03:33:30Z","title":"Subgroups of polynomial automorphisms with diagonalizable fibers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3181","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":"sha256:5d33333e4d97b35e05ce8facc4840f52433ce5200db31d49d4cb837f89df4d9c","target":"record","created_at":"2026-05-18T02:40:11Z","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":"382cd4d265dccde91afc2bb2a8095a47655c2c6a9dd7e796517b22f898eb05f0","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-13T03:33:30Z","title_canon_sha256":"b1f3100f1afc9d08f59fd190cb118641a1485e7bd8d48a789513d6573f0bccc9"},"schema_version":"1.0","source":{"id":"1410.3181","kind":"arxiv","version":1}},"canonical_sha256":"0569d5bb8b4a08041a5c1172c420d8a2858320400b2a5d59ff433d2aa0c8c343","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0569d5bb8b4a08041a5c1172c420d8a2858320400b2a5d59ff433d2aa0c8c343","first_computed_at":"2026-05-18T02:40:11.953548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:11.953548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"haH2D1q8EcLxCQK4d83sk/d3lAu9NfnsPA3MjoSA3tEESdtO7JFhU8RmyywTWC9zZdYTCjUbWrcqgsSyZvFlAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:11.954115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3181","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d33333e4d97b35e05ce8facc4840f52433ce5200db31d49d4cb837f89df4d9c","sha256:d64b155072e9c3805c372d7106ccc03a8240109c1ac23807eb0322fc68e7e0ab"],"state_sha256":"228bfda7675a76c97b3bff64428f0ccae9fc7e9a5edb215f36900610cb7bdd4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ghgLqgJaE4GNtHr2Lln3w9Idn0WhslLpKqMY66UbOOkunA52f0mSpi/nGIdqLujljbBqlQiaulHFXQLsUfwuAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:29:01.268369Z","bundle_sha256":"2089a765335fbec2668ed93bb67aaa64e5929edf01a99031cf84c93e4acf8663"}}