{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6LGNENSND2MYDWG5O26V4BI6HM","short_pith_number":"pith:6LGNENSN","canonical_record":{"source":{"id":"1109.5822","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-27T09:52:09Z","cross_cats_sorted":[],"title_canon_sha256":"b0a96ecb63e6d66fa4c4ca8820da642e349c4098234040d48cbfc517babcfbac","abstract_canon_sha256":"8dbe99e43bf1e1863c906a44f29bfee6f05f23fff4d73b2157eff3d3124b5e94"},"schema_version":"1.0"},"canonical_sha256":"f2ccd2364d1e9981d8dd76bd5e051e3b17d32bab42d4d629c97280075c2ffaf6","source":{"kind":"arxiv","id":"1109.5822","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5822","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5822v3","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5822","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"pith_short_12","alias_value":"6LGNENSND2MY","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6LGNENSND2MYDWG5","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6LGNENSN","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6LGNENSND2MYDWG5O26V4BI6HM","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5822","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-27T09:52:09Z","cross_cats_sorted":[],"title_canon_sha256":"b0a96ecb63e6d66fa4c4ca8820da642e349c4098234040d48cbfc517babcfbac","abstract_canon_sha256":"8dbe99e43bf1e1863c906a44f29bfee6f05f23fff4d73b2157eff3d3124b5e94"},"schema_version":"1.0"},"canonical_sha256":"f2ccd2364d1e9981d8dd76bd5e051e3b17d32bab42d4d629c97280075c2ffaf6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:18.956111Z","signature_b64":"OtD61oN9DMoh2l3YJu8yGYRwv2cdrrACmlOq1at6zX4K2f/mjbk1dWtBkHUKynPdmy0GsXt19hn3gpds2FzpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2ccd2364d1e9981d8dd76bd5e051e3b17d32bab42d4d629c97280075c2ffaf6","last_reissued_at":"2026-05-18T01:19:18.955496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:18.955496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5822","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vO6Q5eubyffmaLFlBpSanAtD9NcaTpz3trVqekDa3cnUr/zFuPhOu1mLsbz5xt6/zY2MfL4gdxY8X+xopAHzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:54:16.464651Z"},"content_sha256":"60132e9890f60276d6a0c842f43b0a6c7ea892c6107eee96ded8be387373cf14","schema_version":"1.0","event_id":"sha256:60132e9890f60276d6a0c842f43b0a6c7ea892c6107eee96ded8be387373cf14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6LGNENSND2MYDWG5O26V4BI6HM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Good Grosshans filtration in a family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Wilberd van der Kallen","submitted_at":"2011-09-27T09:52:09Z","abstract_excerpt":"We reprove the main result of our joint work [arXiv:0706.0604] with Srinivas, concerning finite Schur filtration dimension, but now with the base field replaced by a commutative noetherian ring k. This leads to finiteness results for the cohomology of a reductive group scheme G over k with coefficients in a finitely generated commutative k-algebra with G action."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5822","kind":"arxiv","version":3},"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":"2026-05-18T01:19:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XH97NJxTwjinV6bW1Yosp/xZSVve2ThLUEUILMQUSE4KMd6ATuQK9wM8RF3Xik5fY2pCaMs42dkWYYsRjUUUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:54:16.465009Z"},"content_sha256":"c8f8c49065246e831473dac30c770d272df86301d2b602d28d6a7fa8aabf2a8a","schema_version":"1.0","event_id":"sha256:c8f8c49065246e831473dac30c770d272df86301d2b602d28d6a7fa8aabf2a8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LGNENSND2MYDWG5O26V4BI6HM/bundle.json","state_url":"https://pith.science/pith/6LGNENSND2MYDWG5O26V4BI6HM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LGNENSND2MYDWG5O26V4BI6HM/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":"2026-05-30T08:54:16Z","links":{"resolver":"https://pith.science/pith/6LGNENSND2MYDWG5O26V4BI6HM","bundle":"https://pith.science/pith/6LGNENSND2MYDWG5O26V4BI6HM/bundle.json","state":"https://pith.science/pith/6LGNENSND2MYDWG5O26V4BI6HM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LGNENSND2MYDWG5O26V4BI6HM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6LGNENSND2MYDWG5O26V4BI6HM","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":"8dbe99e43bf1e1863c906a44f29bfee6f05f23fff4d73b2157eff3d3124b5e94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-27T09:52:09Z","title_canon_sha256":"b0a96ecb63e6d66fa4c4ca8820da642e349c4098234040d48cbfc517babcfbac"},"schema_version":"1.0","source":{"id":"1109.5822","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5822","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5822v3","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5822","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"pith_short_12","alias_value":"6LGNENSND2MY","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6LGNENSND2MYDWG5","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6LGNENSN","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:c8f8c49065246e831473dac30c770d272df86301d2b602d28d6a7fa8aabf2a8a","target":"graph","created_at":"2026-05-18T01:19:18Z","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":"We reprove the main result of our joint work [arXiv:0706.0604] with Srinivas, concerning finite Schur filtration dimension, but now with the base field replaced by a commutative noetherian ring k. This leads to finiteness results for the cohomology of a reductive group scheme G over k with coefficients in a finitely generated commutative k-algebra with G action.","authors_text":"Wilberd van der Kallen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-27T09:52:09Z","title":"Good Grosshans filtration in a family"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5822","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":"sha256:60132e9890f60276d6a0c842f43b0a6c7ea892c6107eee96ded8be387373cf14","target":"record","created_at":"2026-05-18T01:19:18Z","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":"8dbe99e43bf1e1863c906a44f29bfee6f05f23fff4d73b2157eff3d3124b5e94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-27T09:52:09Z","title_canon_sha256":"b0a96ecb63e6d66fa4c4ca8820da642e349c4098234040d48cbfc517babcfbac"},"schema_version":"1.0","source":{"id":"1109.5822","kind":"arxiv","version":3}},"canonical_sha256":"f2ccd2364d1e9981d8dd76bd5e051e3b17d32bab42d4d629c97280075c2ffaf6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2ccd2364d1e9981d8dd76bd5e051e3b17d32bab42d4d629c97280075c2ffaf6","first_computed_at":"2026-05-18T01:19:18.955496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:18.955496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OtD61oN9DMoh2l3YJu8yGYRwv2cdrrACmlOq1at6zX4K2f/mjbk1dWtBkHUKynPdmy0GsXt19hn3gpds2FzpDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:18.956111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5822","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60132e9890f60276d6a0c842f43b0a6c7ea892c6107eee96ded8be387373cf14","sha256:c8f8c49065246e831473dac30c770d272df86301d2b602d28d6a7fa8aabf2a8a"],"state_sha256":"3680b8f7f622d1b38459647985f374c21c9add0c3dc2087cfbfadf3544638dec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2qEWakuqw9LS7Gl0naJOUNB3zH34Vw2fXpzyuLVogj/1wMpUMlZJnM1fGCWhDsVMm0FboqwmEX6tDz7wYFQlDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:54:16.468471Z","bundle_sha256":"9bbc54f268ffc3ee801857e30404d669257ad99ca757622ae072f77042a35c82"}}