{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6VEMRTEUWHKOLFHN5ENFZAYBOQ","short_pith_number":"pith:6VEMRTEU","canonical_record":{"source":{"id":"1810.12628","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2018-10-30T10:21:24Z","cross_cats_sorted":["math.AC","math.AG","math.RT"],"title_canon_sha256":"280b8164b69bf12ea6252781580d24f10e55c50e4219cb5db2ab5c9f5336df08","abstract_canon_sha256":"e6102c887150f27f0483e8c54243741a9123a1ea5730a88e2bfe709960842dbc"},"schema_version":"1.0"},"canonical_sha256":"f548c8cc94b1d4e594ede91a5c83017404c971e727105137595a766c0fb433c0","source":{"kind":"arxiv","id":"1810.12628","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12628","created_at":"2026-05-27T14:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12628v2","created_at":"2026-05-27T14:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12628","created_at":"2026-05-27T14:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"6VEMRTEUWHKO","created_at":"2026-05-27T14:06:32Z"},{"alias_kind":"pith_short_16","alias_value":"6VEMRTEUWHKOLFHN","created_at":"2026-05-27T14:06:32Z"},{"alias_kind":"pith_short_8","alias_value":"6VEMRTEU","created_at":"2026-05-27T14:06:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6VEMRTEUWHKOLFHN5ENFZAYBOQ","target":"record","payload":{"canonical_record":{"source":{"id":"1810.12628","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2018-10-30T10:21:24Z","cross_cats_sorted":["math.AC","math.AG","math.RT"],"title_canon_sha256":"280b8164b69bf12ea6252781580d24f10e55c50e4219cb5db2ab5c9f5336df08","abstract_canon_sha256":"e6102c887150f27f0483e8c54243741a9123a1ea5730a88e2bfe709960842dbc"},"schema_version":"1.0"},"canonical_sha256":"f548c8cc94b1d4e594ede91a5c83017404c971e727105137595a766c0fb433c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T14:06:32.192401Z","signature_b64":"oDiNDOpIlpsFY/opgd9Kbx0wf8yVj85i0QpUBfcRzXshQ+4SR4CAqf9z3Fli9SuS+sN+trEynsUhbFAMGf/aCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f548c8cc94b1d4e594ede91a5c83017404c971e727105137595a766c0fb433c0","last_reissued_at":"2026-05-27T14:06:32.189738Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T14:06:32.189738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.12628","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":"2026-05-27T14:06:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWaRVzVxS0jwVlg5tsM9YtV8/cebTaoO/SMVRHDZvgE+hR/T6cxuTrSCeXoYbtJCEA4fq/h9NakQ4WqBN1r7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:30:19.034080Z"},"content_sha256":"f4b0613efeed2f6ab9dabee8f1024113cec94dd23da2449d28ff2b8d2f949dd7","schema_version":"1.0","event_id":"sha256:f4b0613efeed2f6ab9dabee8f1024113cec94dd23da2449d28ff2b8d2f949dd7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6VEMRTEUWHKOLFHN5ENFZAYBOQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smoothness of stabilisers in generic characteristic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC","math.AG","math.RT"],"primary_cat":"math.GR","authors_text":"Benjamin Martin, David I. Stewart, Lewis Topley","submitted_at":"2018-10-30T10:21:24Z","abstract_excerpt":"Let $R$ be a commutative unital ring. Given a finitely presented affine $R$-group scheme $G$ acting on a separated scheme $X$ of finite type over $R$, we show that there is a prime $p_0$ such that for any $R$-algebra $k$ which is an algebraically closed field of characteristic $p\\geq p_0$, the centraliser in $G_k$ of any closed subscheme of $X_k$ is smooth. When $X$ is not necessarily separated we show similarly that for any closed subscheme $Y \\subseteq X$ there is a $p_1$ depending on $Y$ such that when $k$ has characteristic $p \\geq p_1$ the normaliser of $Y$ in $G_k$ is smooth. We prove th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12628","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.12628/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-27T14:06:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"syJV/m7d2KopRPdy1kZIU5qDov7tg+UR8/YQSCMV+ELs5KDXEz0ndtIvBk/6o80Ho0IiNC8ycs/YgSid87V4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:30:19.034936Z"},"content_sha256":"d77dc78a648a33f9de81e60878395c978fe4f4f2596fa923ca23019cc52b257b","schema_version":"1.0","event_id":"sha256:d77dc78a648a33f9de81e60878395c978fe4f4f2596fa923ca23019cc52b257b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ/bundle.json","state_url":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ/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":"2026-06-01T01:30:19Z","links":{"resolver":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ","bundle":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ/bundle.json","state":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6VEMRTEUWHKOLFHN5ENFZAYBOQ","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":"e6102c887150f27f0483e8c54243741a9123a1ea5730a88e2bfe709960842dbc","cross_cats_sorted":["math.AC","math.AG","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2018-10-30T10:21:24Z","title_canon_sha256":"280b8164b69bf12ea6252781580d24f10e55c50e4219cb5db2ab5c9f5336df08"},"schema_version":"1.0","source":{"id":"1810.12628","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12628","created_at":"2026-05-27T14:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12628v2","created_at":"2026-05-27T14:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12628","created_at":"2026-05-27T14:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"6VEMRTEUWHKO","created_at":"2026-05-27T14:06:32Z"},{"alias_kind":"pith_short_16","alias_value":"6VEMRTEUWHKOLFHN","created_at":"2026-05-27T14:06:32Z"},{"alias_kind":"pith_short_8","alias_value":"6VEMRTEU","created_at":"2026-05-27T14:06:32Z"}],"graph_snapshots":[{"event_id":"sha256:d77dc78a648a33f9de81e60878395c978fe4f4f2596fa923ca23019cc52b257b","target":"graph","created_at":"2026-05-27T14:06:32Z","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/1810.12628/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $R$ be a commutative unital ring. Given a finitely presented affine $R$-group scheme $G$ acting on a separated scheme $X$ of finite type over $R$, we show that there is a prime $p_0$ such that for any $R$-algebra $k$ which is an algebraically closed field of characteristic $p\\geq p_0$, the centraliser in $G_k$ of any closed subscheme of $X_k$ is smooth. When $X$ is not necessarily separated we show similarly that for any closed subscheme $Y \\subseteq X$ there is a $p_1$ depending on $Y$ such that when $k$ has characteristic $p \\geq p_1$ the normaliser of $Y$ in $G_k$ is smooth. We prove th","authors_text":"Benjamin Martin, David I. Stewart, Lewis Topley","cross_cats":["math.AC","math.AG","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2018-10-30T10:21:24Z","title":"Smoothness of stabilisers in generic characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12628","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:f4b0613efeed2f6ab9dabee8f1024113cec94dd23da2449d28ff2b8d2f949dd7","target":"record","created_at":"2026-05-27T14:06:32Z","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":"e6102c887150f27f0483e8c54243741a9123a1ea5730a88e2bfe709960842dbc","cross_cats_sorted":["math.AC","math.AG","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2018-10-30T10:21:24Z","title_canon_sha256":"280b8164b69bf12ea6252781580d24f10e55c50e4219cb5db2ab5c9f5336df08"},"schema_version":"1.0","source":{"id":"1810.12628","kind":"arxiv","version":2}},"canonical_sha256":"f548c8cc94b1d4e594ede91a5c83017404c971e727105137595a766c0fb433c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f548c8cc94b1d4e594ede91a5c83017404c971e727105137595a766c0fb433c0","first_computed_at":"2026-05-27T14:06:32.189738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T14:06:32.189738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oDiNDOpIlpsFY/opgd9Kbx0wf8yVj85i0QpUBfcRzXshQ+4SR4CAqf9z3Fli9SuS+sN+trEynsUhbFAMGf/aCA==","signature_status":"signed_v1","signed_at":"2026-05-27T14:06:32.192401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12628","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4b0613efeed2f6ab9dabee8f1024113cec94dd23da2449d28ff2b8d2f949dd7","sha256:d77dc78a648a33f9de81e60878395c978fe4f4f2596fa923ca23019cc52b257b"],"state_sha256":"2f288c9079fa41a2eafed4137b04cc72d4ee4c38a499ab2deab5c56b637b4f89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zeywUoixwrqDCOswqVPENS5jss7dQblOGKJ7BGO9JvPAjFd1+u7Q1SOi77Q6gfSucOAd8eDXl+zqK1xav9ccDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:30:19.038594Z","bundle_sha256":"25cb05ee7dca5cf13cef3c96711ea4501ac37676329200fc963382fffbbde520"}}