{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SNUBKJA2BIXKUGSMN6MCN3ZEWY","short_pith_number":"pith:SNUBKJA2","canonical_record":{"source":{"id":"2606.22846","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-22T04:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"5cc3994cdaa73a94b8b6001728bc35be6e22a58d45925a0adc585281a0de753d","abstract_canon_sha256":"68840767c3135e3073294f87deb314f19418b8c45cb5a564c429684fc8b280b2"},"schema_version":"1.0"},"canonical_sha256":"936815241a0a2eaa1a4c6f9826ef24b632495dd79df5653712d0106f7221bae6","source":{"kind":"arxiv","id":"2606.22846","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22846","created_at":"2026-06-23T02:14:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22846v1","created_at":"2026-06-23T02:14:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22846","created_at":"2026-06-23T02:14:01Z"},{"alias_kind":"pith_short_12","alias_value":"SNUBKJA2BIXK","created_at":"2026-06-23T02:14:01Z"},{"alias_kind":"pith_short_16","alias_value":"SNUBKJA2BIXKUGSM","created_at":"2026-06-23T02:14:01Z"},{"alias_kind":"pith_short_8","alias_value":"SNUBKJA2","created_at":"2026-06-23T02:14:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SNUBKJA2BIXKUGSMN6MCN3ZEWY","target":"record","payload":{"canonical_record":{"source":{"id":"2606.22846","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-22T04:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"5cc3994cdaa73a94b8b6001728bc35be6e22a58d45925a0adc585281a0de753d","abstract_canon_sha256":"68840767c3135e3073294f87deb314f19418b8c45cb5a564c429684fc8b280b2"},"schema_version":"1.0"},"canonical_sha256":"936815241a0a2eaa1a4c6f9826ef24b632495dd79df5653712d0106f7221bae6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:14:01.012576Z","signature_b64":"9+d1mVMUoKXvUNIClvDATRkitetbvss3w9zYo7VeIxcC+/NGPVP7lZaq9BjgyPY85bf8QTs9/ExMQGEMFtUtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"936815241a0a2eaa1a4c6f9826ef24b632495dd79df5653712d0106f7221bae6","last_reissued_at":"2026-06-23T02:14:01.012146Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:14:01.012146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.22846","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":"2026-06-23T02:14:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"524ayMP9cghgfG7QZ+OGEYwyZTPuIRBIwgJMk/dxoKX1egXsxzKqGA+bBhGsmvcC+UMQ/ffV177bkJVA2N/HBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:45:25.146533Z"},"content_sha256":"559f6565535db556b9b0073c152d821f8201d022d8d3cf96dab9d37f532e0435","schema_version":"1.0","event_id":"sha256:559f6565535db556b9b0073c152d821f8201d022d8d3cf96dab9d37f532e0435"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SNUBKJA2BIXKUGSMN6MCN3ZEWY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted Jacquet modules associated to maximal parabolic subgroups and cuspidal representations of $GL(n, q)$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Himanshi Khurana, Krishna Kaipa, Kumar Balasubramanian","submitted_at":"2026-06-22T04:46:39Z","abstract_excerpt":"Let $\\pi$ be a cuspidal representation $GL(n,F)$ over a finite field $F$. Let $P=MN$ be the Levi decomposition of a maximal parabolic subgroup corresponding to the partition $(k,n-k)$ of $n$. Given a rank $r$ character $\\psi_r$ of the unipotent radical $N$, the twisted Jacquet module $\\pi_{N, \\psi_r}$ is a representation of the subgroup $M_r$ of $M$ which stabilizes $\\psi_r$. The main problem we solve in this work is to determine the structure of $\\pi_{N, \\psi_r}$ as a $M_r$-module. This problem was first studied by D. Prasad, who solved the problem for the case $r=k=n/2$. This and subsequent "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22846","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22846/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":"2026-06-23T02:14:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7DLLbsUYY9sLT6xZE6iU8STqm+XjbA6y3x84ecgXaGosTxiPvKWXv8jqDuk0iEAYr7E/baj4P06mr9LG8wcYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:45:25.146914Z"},"content_sha256":"06822b4a38d783d819916eee4155c872d15e00de201331f07ec280fd5dbb64f7","schema_version":"1.0","event_id":"sha256:06822b4a38d783d819916eee4155c872d15e00de201331f07ec280fd5dbb64f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SNUBKJA2BIXKUGSMN6MCN3ZEWY/bundle.json","state_url":"https://pith.science/pith/SNUBKJA2BIXKUGSMN6MCN3ZEWY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SNUBKJA2BIXKUGSMN6MCN3ZEWY/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":"2026-06-28T15:45:25Z","links":{"resolver":"https://pith.science/pith/SNUBKJA2BIXKUGSMN6MCN3ZEWY","bundle":"https://pith.science/pith/SNUBKJA2BIXKUGSMN6MCN3ZEWY/bundle.json","state":"https://pith.science/pith/SNUBKJA2BIXKUGSMN6MCN3ZEWY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SNUBKJA2BIXKUGSMN6MCN3ZEWY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SNUBKJA2BIXKUGSMN6MCN3ZEWY","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":"68840767c3135e3073294f87deb314f19418b8c45cb5a564c429684fc8b280b2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-22T04:46:39Z","title_canon_sha256":"5cc3994cdaa73a94b8b6001728bc35be6e22a58d45925a0adc585281a0de753d"},"schema_version":"1.0","source":{"id":"2606.22846","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22846","created_at":"2026-06-23T02:14:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22846v1","created_at":"2026-06-23T02:14:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22846","created_at":"2026-06-23T02:14:01Z"},{"alias_kind":"pith_short_12","alias_value":"SNUBKJA2BIXK","created_at":"2026-06-23T02:14:01Z"},{"alias_kind":"pith_short_16","alias_value":"SNUBKJA2BIXKUGSM","created_at":"2026-06-23T02:14:01Z"},{"alias_kind":"pith_short_8","alias_value":"SNUBKJA2","created_at":"2026-06-23T02:14:01Z"}],"graph_snapshots":[{"event_id":"sha256:06822b4a38d783d819916eee4155c872d15e00de201331f07ec280fd5dbb64f7","target":"graph","created_at":"2026-06-23T02:14:01Z","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/2606.22846/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\pi$ be a cuspidal representation $GL(n,F)$ over a finite field $F$. Let $P=MN$ be the Levi decomposition of a maximal parabolic subgroup corresponding to the partition $(k,n-k)$ of $n$. Given a rank $r$ character $\\psi_r$ of the unipotent radical $N$, the twisted Jacquet module $\\pi_{N, \\psi_r}$ is a representation of the subgroup $M_r$ of $M$ which stabilizes $\\psi_r$. The main problem we solve in this work is to determine the structure of $\\pi_{N, \\psi_r}$ as a $M_r$-module. This problem was first studied by D. Prasad, who solved the problem for the case $r=k=n/2$. This and subsequent ","authors_text":"Himanshi Khurana, Krishna Kaipa, Kumar Balasubramanian","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-22T04:46:39Z","title":"Twisted Jacquet modules associated to maximal parabolic subgroups and cuspidal representations of $GL(n, q)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22846","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":"sha256:559f6565535db556b9b0073c152d821f8201d022d8d3cf96dab9d37f532e0435","target":"record","created_at":"2026-06-23T02:14:01Z","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":"68840767c3135e3073294f87deb314f19418b8c45cb5a564c429684fc8b280b2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-22T04:46:39Z","title_canon_sha256":"5cc3994cdaa73a94b8b6001728bc35be6e22a58d45925a0adc585281a0de753d"},"schema_version":"1.0","source":{"id":"2606.22846","kind":"arxiv","version":1}},"canonical_sha256":"936815241a0a2eaa1a4c6f9826ef24b632495dd79df5653712d0106f7221bae6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"936815241a0a2eaa1a4c6f9826ef24b632495dd79df5653712d0106f7221bae6","first_computed_at":"2026-06-23T02:14:01.012146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:14:01.012146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9+d1mVMUoKXvUNIClvDATRkitetbvss3w9zYo7VeIxcC+/NGPVP7lZaq9BjgyPY85bf8QTs9/ExMQGEMFtUtAQ==","signature_status":"signed_v1","signed_at":"2026-06-23T02:14:01.012576Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22846","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:559f6565535db556b9b0073c152d821f8201d022d8d3cf96dab9d37f532e0435","sha256:06822b4a38d783d819916eee4155c872d15e00de201331f07ec280fd5dbb64f7"],"state_sha256":"a4bbb9e246594c52008749665737ee46300bd09215ae6812c108e23fd44e86a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HIRbEuk5+scmtVqtd2pm45O/jt6O7/IZvY32zYWqYsXpjS/V/Kr4L92/G5fttUCouxTzraP6ODwviq6GiZpsCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T15:45:25.148848Z","bundle_sha256":"aec8c9847dda50e35d226baf83aaae789a25e493e3a7122422df49f0096e0d4f"}}