{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6MWRHU2VS267LA2EQS4ISRKUYU","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":"de444ded953c5dda830e5fab8f5f1a154e0da1f8655594365be4261a3e6c2cc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-05-10T13:02:10Z","title_canon_sha256":"6f957764681fe1f730316aedd5f89dfa9210c44a8cfafdb65f29d38e56ab5bc8"},"schema_version":"1.0","source":{"id":"2405.06450","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.06450","created_at":"2026-06-19T16:10:28Z"},{"alias_kind":"arxiv_version","alias_value":"2405.06450v2","created_at":"2026-06-19T16:10:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.06450","created_at":"2026-06-19T16:10:28Z"},{"alias_kind":"pith_short_12","alias_value":"6MWRHU2VS267","created_at":"2026-06-19T16:10:28Z"},{"alias_kind":"pith_short_16","alias_value":"6MWRHU2VS267LA2E","created_at":"2026-06-19T16:10:28Z"},{"alias_kind":"pith_short_8","alias_value":"6MWRHU2V","created_at":"2026-06-19T16:10:28Z"}],"graph_snapshots":[{"event_id":"sha256:61581046bc5f1b102f886a3b0c9336ab5212f269d4f6fb61b63471aa8c6aefe9","target":"graph","created_at":"2026-06-19T16:10:28Z","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/2405.06450/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that, for an equivalence class of irreducible smooth representations of the symplectic group Sp(2n,F) over a non-Archimedean local field F, the Jacquet functor with respect to the maximal Levi subgroup GL(l,F)\\times Sp(2n-2l,F) is multiplicity-free. The proof is based on an explicit computation of Jacquet modules for a broader family of Sp(2n,F)-representations induced from segments, yielding a detailed structural description that may be of independent interest.","authors_text":"Mahendra Kumar Verma, Prem Dagar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-05-10T13:02:10Z","title":"On the Jacquet functor of Symplectic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.06450","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":"sha256:89d94be36a31a2f2d0958e7355b710130ffc891372508cdfc92e16a3d1ff10e9","target":"record","created_at":"2026-06-19T16:10:28Z","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":"de444ded953c5dda830e5fab8f5f1a154e0da1f8655594365be4261a3e6c2cc2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-05-10T13:02:10Z","title_canon_sha256":"6f957764681fe1f730316aedd5f89dfa9210c44a8cfafdb65f29d38e56ab5bc8"},"schema_version":"1.0","source":{"id":"2405.06450","kind":"arxiv","version":2}},"canonical_sha256":"f32d13d35596bdf5834484b8894554c52b9c5b0f25d9f7a2fd330915dacddc38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f32d13d35596bdf5834484b8894554c52b9c5b0f25d9f7a2fd330915dacddc38","first_computed_at":"2026-06-19T16:10:28.189490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:28.189490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZOKdIPXvwLQYuNO12ix3a2fItGOPlCcECfburkDNeqxPwFmswr2UXwX3/b0QJeFeXuy0ZQ+Gg3+YmnOCd6hLBQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:28.189976Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.06450","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89d94be36a31a2f2d0958e7355b710130ffc891372508cdfc92e16a3d1ff10e9","sha256:61581046bc5f1b102f886a3b0c9336ab5212f269d4f6fb61b63471aa8c6aefe9"],"state_sha256":"19f3b10ff2fdd383da12c9e6054ba6d24f7de631bdf09fd101b5def5af1e457a"}