{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AP5HRFSJETZJFU762XGGABPCPP","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":"f1614df20974b5bc99a35f2848716d8d3171a804434c6ebc530f7815368da8c4","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-07-09T15:49:47Z","title_canon_sha256":"c6ca286464b68a0d784f25568b188de0135e4b478e8e71b0ee56a02d1ce2deec"},"schema_version":"1.0","source":{"id":"2507.06963","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.06963","created_at":"2026-07-05T11:34:25Z"},{"alias_kind":"arxiv_version","alias_value":"2507.06963v1","created_at":"2026-07-05T11:34:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06963","created_at":"2026-07-05T11:34:25Z"},{"alias_kind":"pith_short_12","alias_value":"AP5HRFSJETZJ","created_at":"2026-07-05T11:34:25Z"},{"alias_kind":"pith_short_16","alias_value":"AP5HRFSJETZJFU76","created_at":"2026-07-05T11:34:25Z"},{"alias_kind":"pith_short_8","alias_value":"AP5HRFSJ","created_at":"2026-07-05T11:34:25Z"}],"graph_snapshots":[{"event_id":"sha256:882ce979a1c75ee548616426408382d6b31550aea90d6737ba9a6c5cccd5cf72","target":"graph","created_at":"2026-07-05T11:34:25Z","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/2507.06963/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we establish a new Fundamental Lemma for Hecke correspondences. Let $F$ be a local field containing the cube roots of unity. We exhibit an algebra isomorphism of the spherical Hecke algebra of $PGL_3(F)$ and the spherical Hecke algebra of anti-genuine functions on the cubic cover $G'$ of $SL_3(F)$. Then we show that there is a matching (up to a specific transfer factor) of distributions on the two groups for all functions that correspond under this isomorphism. On $PGL_3(F)$ the distributions are relative distributions attached to a period involving the minimal representation on ","authors_text":"Omer Offen, Solomon Friedberg","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-07-09T15:49:47Z","title":"On the cubic Shimura lift to $PGL(3)$: Hecke correspondences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06963","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:e1515ee893d81f9c902743123e0ae0ecab267f716496fc7313804cf5b2af7753","target":"record","created_at":"2026-07-05T11:34:25Z","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":"f1614df20974b5bc99a35f2848716d8d3171a804434c6ebc530f7815368da8c4","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-07-09T15:49:47Z","title_canon_sha256":"c6ca286464b68a0d784f25568b188de0135e4b478e8e71b0ee56a02d1ce2deec"},"schema_version":"1.0","source":{"id":"2507.06963","kind":"arxiv","version":1}},"canonical_sha256":"03fa78964924f292d3fed5cc6005e27bc0ca7239bf0325fb6dcda3cb284d1e12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03fa78964924f292d3fed5cc6005e27bc0ca7239bf0325fb6dcda3cb284d1e12","first_computed_at":"2026-07-05T11:34:25.735155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:34:25.735155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xH13/7rAYQleyYjZlQZPXGhZS6k8/QdgzjtMhsawGTzcC8fC1yWgCOQ/O+R/r3VhRr6Jf6wxBHDajK2la7M4CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:34:25.735665Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.06963","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1515ee893d81f9c902743123e0ae0ecab267f716496fc7313804cf5b2af7753","sha256:882ce979a1c75ee548616426408382d6b31550aea90d6737ba9a6c5cccd5cf72"],"state_sha256":"dc1d603715ec4d203c5be2113874c7b0e9f46b80ef56c814d7afdefe4e2d373a"}