{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:2ZABYWVSSEQVDSAMQYEICU52O2","short_pith_number":"pith:2ZABYWVS","canonical_record":{"source":{"id":"math/0703527","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2007-03-18T20:25:07Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"61f11e8708c1df5e2b1c74deba2e6d40191db94c4f40f5e61302e6120dac760c","abstract_canon_sha256":"0a78f70817998c2c907bbe41d490c37d2713202c39eded948f27940e058d5e4d"},"schema_version":"1.0"},"canonical_sha256":"d6401c5ab2912151c80c86088153ba76a5bfd909e1ce2daea004b053f1c11a52","source":{"kind":"arxiv","id":"math/0703527","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703527","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703527v4","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703527","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"2ZABYWVSSEQV","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"2ZABYWVSSEQVDSAM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"2ZABYWVS","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:2ZABYWVSSEQVDSAMQYEICU52O2","target":"record","payload":{"canonical_record":{"source":{"id":"math/0703527","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2007-03-18T20:25:07Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"61f11e8708c1df5e2b1c74deba2e6d40191db94c4f40f5e61302e6120dac760c","abstract_canon_sha256":"0a78f70817998c2c907bbe41d490c37d2713202c39eded948f27940e058d5e4d"},"schema_version":"1.0"},"canonical_sha256":"d6401c5ab2912151c80c86088153ba76a5bfd909e1ce2daea004b053f1c11a52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:45.464176Z","signature_b64":"/fYyUFPBhIskV/eVOcSnTvrqEYZMi8txJEZzbg55NM6uqW7rhU4S7mkDuc+ySTnjaAoU8xB97yqCHDVax2NQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6401c5ab2912151c80c86088153ba76a5bfd909e1ce2daea004b053f1c11a52","last_reissued_at":"2026-05-18T03:56:45.463566Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:45.463566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0703527","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dIYKwddG7zMqt67C+7tPJamdYHRVy0s6g7cwEUd/XPs5F4IGGU7o9u4H+MiR8nKxDoFHQozGCVMkngYZ3KkuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:42:29.030348Z"},"content_sha256":"933fc73dfc06e8e9e8fc6b72fb136ecbfdeed64936256ac8684b3fdf1a1635e1","schema_version":"1.0","event_id":"sha256:933fc73dfc06e8e9e8fc6b72fb136ecbfdeed64936256ac8684b3fdf1a1635e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:2ZABYWVSSEQVDSAMQYEICU52O2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On $\\bbf_q$-rational structure of nilpotent orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Bin Shu, Brian Parshall, Semra Kaptanoglu","submitted_at":"2007-03-18T20:25:07Z","abstract_excerpt":"Let $G$ be a simple algebraic group and $\\ggg=\\Lie(G)$ over $k=\\bar\\bbf_q$ where $q$ is a power of the prime characteristic of $k$, and $F$ a Frobenius morphism on $G$ which can be defined naturally on $\\ggg$. In this paper, we investigate the relation between $F$-stable restricted modules of $\\ggg$ and closed conical subvarieties defined over $\\bbf_q$ in the null cone $\\cn(\\ggg)$ of $\\ggg$. Furthermore, we clearly investigate the $\\bbf_q$-rational structure for all nilpotent orbits in $\\ggg$ under the adjoint action of $G$ when the characteristic of $k$ is good for $G$ and bigger than 3. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703527","kind":"arxiv","version":4},"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":"2026-05-18T03:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jwyuuK8LofoDirIumrjBAgx8zQ5ZXEyPTnORbsjG6/Ye2s7fumHa4gVU427Luro6xw7vc17UeoFj/4QKA48yCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:42:29.030993Z"},"content_sha256":"314ace02e104b3f775eb78958dfd1af5fc8905c66412857f8a5fad9475ea9e6d","schema_version":"1.0","event_id":"sha256:314ace02e104b3f775eb78958dfd1af5fc8905c66412857f8a5fad9475ea9e6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZABYWVSSEQVDSAMQYEICU52O2/bundle.json","state_url":"https://pith.science/pith/2ZABYWVSSEQVDSAMQYEICU52O2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZABYWVSSEQVDSAMQYEICU52O2/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":"2026-05-31T13:42:29Z","links":{"resolver":"https://pith.science/pith/2ZABYWVSSEQVDSAMQYEICU52O2","bundle":"https://pith.science/pith/2ZABYWVSSEQVDSAMQYEICU52O2/bundle.json","state":"https://pith.science/pith/2ZABYWVSSEQVDSAMQYEICU52O2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZABYWVSSEQVDSAMQYEICU52O2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:2ZABYWVSSEQVDSAMQYEICU52O2","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":"0a78f70817998c2c907bbe41d490c37d2713202c39eded948f27940e058d5e4d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2007-03-18T20:25:07Z","title_canon_sha256":"61f11e8708c1df5e2b1c74deba2e6d40191db94c4f40f5e61302e6120dac760c"},"schema_version":"1.0","source":{"id":"math/0703527","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703527","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703527v4","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703527","created_at":"2026-05-18T03:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"2ZABYWVSSEQV","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"2ZABYWVSSEQVDSAM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"2ZABYWVS","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:314ace02e104b3f775eb78958dfd1af5fc8905c66412857f8a5fad9475ea9e6d","target":"graph","created_at":"2026-05-18T03:56:45Z","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 $G$ be a simple algebraic group and $\\ggg=\\Lie(G)$ over $k=\\bar\\bbf_q$ where $q$ is a power of the prime characteristic of $k$, and $F$ a Frobenius morphism on $G$ which can be defined naturally on $\\ggg$. In this paper, we investigate the relation between $F$-stable restricted modules of $\\ggg$ and closed conical subvarieties defined over $\\bbf_q$ in the null cone $\\cn(\\ggg)$ of $\\ggg$. Furthermore, we clearly investigate the $\\bbf_q$-rational structure for all nilpotent orbits in $\\ggg$ under the adjoint action of $G$ when the characteristic of $k$ is good for $G$ and bigger than 3. The ","authors_text":"Bin Shu, Brian Parshall, Semra Kaptanoglu","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2007-03-18T20:25:07Z","title":"On $\\bbf_q$-rational structure of nilpotent orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703527","kind":"arxiv","version":4},"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":"sha256:933fc73dfc06e8e9e8fc6b72fb136ecbfdeed64936256ac8684b3fdf1a1635e1","target":"record","created_at":"2026-05-18T03:56:45Z","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":"0a78f70817998c2c907bbe41d490c37d2713202c39eded948f27940e058d5e4d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2007-03-18T20:25:07Z","title_canon_sha256":"61f11e8708c1df5e2b1c74deba2e6d40191db94c4f40f5e61302e6120dac760c"},"schema_version":"1.0","source":{"id":"math/0703527","kind":"arxiv","version":4}},"canonical_sha256":"d6401c5ab2912151c80c86088153ba76a5bfd909e1ce2daea004b053f1c11a52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6401c5ab2912151c80c86088153ba76a5bfd909e1ce2daea004b053f1c11a52","first_computed_at":"2026-05-18T03:56:45.463566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:45.463566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/fYyUFPBhIskV/eVOcSnTvrqEYZMi8txJEZzbg55NM6uqW7rhU4S7mkDuc+ySTnjaAoU8xB97yqCHDVax2NQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:45.464176Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0703527","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:933fc73dfc06e8e9e8fc6b72fb136ecbfdeed64936256ac8684b3fdf1a1635e1","sha256:314ace02e104b3f775eb78958dfd1af5fc8905c66412857f8a5fad9475ea9e6d"],"state_sha256":"31f76eb7e1877ac4b4c2773dd2e857ffbb15bd1ad31e239bc0482d4d9e890d6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8f3KZwHvduuDWHEfIScGXiIsTn5FTq+rkzv1gq0rQL2m6lQCIR16npcsAFZRMkiz8HAA9zswZfEcdpF0EaC1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T13:42:29.035092Z","bundle_sha256":"422d46bad0e51b14ca2228c5a3a371566a2315a952ce4f30c4fa716b30bb00c8"}}