{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:42WAWE4PHNUTSCUCGU43VTDAXC","short_pith_number":"pith:42WAWE4P","canonical_record":{"source":{"id":"1010.1606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-10-08T06:42:25Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"68bb52e3f05f5fd168448dd177e05fa8d48d4fe6b6fc1943248fd0f7c981ce3b","abstract_canon_sha256":"50f8880ef2e07cdb016018a3760ff10e44c1b515d84971746009dd7c017fe77e"},"schema_version":"1.0"},"canonical_sha256":"e6ac0b138f3b69390a823539bacc60b8beb191d60664f798c752fd8f096ee806","source":{"kind":"arxiv","id":"1010.1606","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1606","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1606v1","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1606","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"42WAWE4PHNUT","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"42WAWE4PHNUTSCUC","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"42WAWE4P","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:42WAWE4PHNUTSCUCGU43VTDAXC","target":"record","payload":{"canonical_record":{"source":{"id":"1010.1606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-10-08T06:42:25Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"68bb52e3f05f5fd168448dd177e05fa8d48d4fe6b6fc1943248fd0f7c981ce3b","abstract_canon_sha256":"50f8880ef2e07cdb016018a3760ff10e44c1b515d84971746009dd7c017fe77e"},"schema_version":"1.0"},"canonical_sha256":"e6ac0b138f3b69390a823539bacc60b8beb191d60664f798c752fd8f096ee806","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:40.117000Z","signature_b64":"7Yp4XcFJbWpQGiZD8z0EThtDgFjKP5KcKf9xYJM2/DJEk0L+BZt+9N4PQGT1dzmcQ2bbtFXS/mPJJAcpdqYfBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6ac0b138f3b69390a823539bacc60b8beb191d60664f798c752fd8f096ee806","last_reissued_at":"2026-05-18T04:39:40.116203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:40.116203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.1606","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":"2026-05-18T04:39:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pCJh/lUIWqVN/xLEZDUFGU0Y1CPP1lNK85ZmpRk0pHTd6uMgqEEDhZfgHz+bF+L+ECkmAG/N0c8fr9gzSI29Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T19:04:59.170584Z"},"content_sha256":"9ee1a24edc91d46c372a4ebcce9394a448301c4a2bf46f75b9a75a0333fedb3d","schema_version":"1.0","event_id":"sha256:9ee1a24edc91d46c372a4ebcce9394a448301c4a2bf46f75b9a75a0333fedb3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:42WAWE4PHNUTSCUCGU43VTDAXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Good filtrations and strong $F$-regularity of the ring of $U_P$-invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Mitsuyasu Hashimoto","submitted_at":"2010-10-08T06:42:25Z","abstract_excerpt":"Let $k$ be an algebraically closed field of positive characteristic, $G$ a reductive group over $k$, and $V$ a finite dimensional $G$-module. Let $P$ be a parabolic subgroup of $G$, and $U_P$ its unipotent radical. We prove that if $S$=\\textyen $Sym V$ has a good filtration, then the ring of invariants $S^{U_P}$ is strongly $F$-regular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1606","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":"2026-05-18T04:39:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uxQBm++zERa47xp4W67ouumgovwf0N4prOKgRqTTV6M01Pddx1WfFmYHw98HlD2pN/RveNNVE2piysI3bk5VAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T19:04:59.171002Z"},"content_sha256":"ee89e634c7ac3b7bacc0328f96dc7f62ee22033f4defb65b3c19d35c25de94c4","schema_version":"1.0","event_id":"sha256:ee89e634c7ac3b7bacc0328f96dc7f62ee22033f4defb65b3c19d35c25de94c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42WAWE4PHNUTSCUCGU43VTDAXC/bundle.json","state_url":"https://pith.science/pith/42WAWE4PHNUTSCUCGU43VTDAXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42WAWE4PHNUTSCUCGU43VTDAXC/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":"2026-06-26T19:04:59Z","links":{"resolver":"https://pith.science/pith/42WAWE4PHNUTSCUCGU43VTDAXC","bundle":"https://pith.science/pith/42WAWE4PHNUTSCUCGU43VTDAXC/bundle.json","state":"https://pith.science/pith/42WAWE4PHNUTSCUCGU43VTDAXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42WAWE4PHNUTSCUCGU43VTDAXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:42WAWE4PHNUTSCUCGU43VTDAXC","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":"50f8880ef2e07cdb016018a3760ff10e44c1b515d84971746009dd7c017fe77e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-10-08T06:42:25Z","title_canon_sha256":"68bb52e3f05f5fd168448dd177e05fa8d48d4fe6b6fc1943248fd0f7c981ce3b"},"schema_version":"1.0","source":{"id":"1010.1606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1606","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1606v1","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1606","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"42WAWE4PHNUT","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"42WAWE4PHNUTSCUC","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"42WAWE4P","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:ee89e634c7ac3b7bacc0328f96dc7f62ee22033f4defb65b3c19d35c25de94c4","target":"graph","created_at":"2026-05-18T04:39:40Z","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 $k$ be an algebraically closed field of positive characteristic, $G$ a reductive group over $k$, and $V$ a finite dimensional $G$-module. Let $P$ be a parabolic subgroup of $G$, and $U_P$ its unipotent radical. We prove that if $S$=\\textyen $Sym V$ has a good filtration, then the ring of invariants $S^{U_P}$ is strongly $F$-regular.","authors_text":"Mitsuyasu Hashimoto","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-10-08T06:42:25Z","title":"Good filtrations and strong $F$-regularity of the ring of $U_P$-invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1606","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":"sha256:9ee1a24edc91d46c372a4ebcce9394a448301c4a2bf46f75b9a75a0333fedb3d","target":"record","created_at":"2026-05-18T04:39:40Z","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":"50f8880ef2e07cdb016018a3760ff10e44c1b515d84971746009dd7c017fe77e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-10-08T06:42:25Z","title_canon_sha256":"68bb52e3f05f5fd168448dd177e05fa8d48d4fe6b6fc1943248fd0f7c981ce3b"},"schema_version":"1.0","source":{"id":"1010.1606","kind":"arxiv","version":1}},"canonical_sha256":"e6ac0b138f3b69390a823539bacc60b8beb191d60664f798c752fd8f096ee806","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6ac0b138f3b69390a823539bacc60b8beb191d60664f798c752fd8f096ee806","first_computed_at":"2026-05-18T04:39:40.116203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:40.116203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Yp4XcFJbWpQGiZD8z0EThtDgFjKP5KcKf9xYJM2/DJEk0L+BZt+9N4PQGT1dzmcQ2bbtFXS/mPJJAcpdqYfBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:40.117000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ee1a24edc91d46c372a4ebcce9394a448301c4a2bf46f75b9a75a0333fedb3d","sha256:ee89e634c7ac3b7bacc0328f96dc7f62ee22033f4defb65b3c19d35c25de94c4"],"state_sha256":"dd5d0397e74a8c569ef1a84d6f08f6a5c02c5e4a594ea6bbd6e9d83ebb142271"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KtDYszeRaRYVqqzqRnLtBuPjbQEv1nvNYe69qTTB8N0fE3bxaOWWc0hjXMAJE9wOZpbdT56c4yuCqUeCx8X5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T19:04:59.173095Z","bundle_sha256":"d5b74b624a402bd755ca6e8307e25d0b72872926e3fa8a6c1e57442f2582f0b2"}}