{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6NGVW3WV6BHUMMHRNCQTL76RPQ","short_pith_number":"pith:6NGVW3WV","canonical_record":{"source":{"id":"1210.3268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-11T15:21:45Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5ee1c2c57212108c184149516eb423328bd495b6fd3612df7a200e8b44ebc3e6","abstract_canon_sha256":"9073188388f6460639918ba39d468730e1a11ed69044dcf8e3bb7324d708342f"},"schema_version":"1.0"},"canonical_sha256":"f34d5b6ed5f04f4630f168a135ffd17c0ac8b923946b57af85a65cd30e26b0b0","source":{"kind":"arxiv","id":"1210.3268","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3268","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3268v1","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3268","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"pith_short_12","alias_value":"6NGVW3WV6BHU","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6NGVW3WV6BHUMMHR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6NGVW3WV","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6NGVW3WV6BHUMMHRNCQTL76RPQ","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-11T15:21:45Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5ee1c2c57212108c184149516eb423328bd495b6fd3612df7a200e8b44ebc3e6","abstract_canon_sha256":"9073188388f6460639918ba39d468730e1a11ed69044dcf8e3bb7324d708342f"},"schema_version":"1.0"},"canonical_sha256":"f34d5b6ed5f04f4630f168a135ffd17c0ac8b923946b57af85a65cd30e26b0b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:27.839227Z","signature_b64":"q6M7snuBhzFbFxjbk016uNL2mPKDB3y/9wZcCyJ8W1kf21jdqTMZCjCJIyGDC4FB9h19Awk0DCoF3vrL4RHWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f34d5b6ed5f04f4630f168a135ffd17c0ac8b923946b57af85a65cd30e26b0b0","last_reissued_at":"2026-05-18T03:43:27.838554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:27.838554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3268","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":"2026-05-18T03:43:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jJT2K/KjqTw1nEZgvPcrX+PpRuKNOqj7Fc6gM8Uw5jazeo13OoKbDZZ92UOX6AMShkl62mLr2LbOVqVpmacCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:13:44.192345Z"},"content_sha256":"e6bc07f79d25be09374130d36bd14702346bd998b4e5e18a330fc65abe7b86df","schema_version":"1.0","event_id":"sha256:e6bc07f79d25be09374130d36bd14702346bd998b4e5e18a330fc65abe7b86df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6NGVW3WV6BHUMMHRNCQTL76RPQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new realization of the Langlands correspondence for PGL(2,F)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Moshe Adrian","submitted_at":"2012-10-11T15:21:45Z","abstract_excerpt":"In this paper, we give a new realization of the local Langlands correspondence for PGL(2,F), where F is a p-adic field of odd residual characteristic. In this case, supercuspidal representations of PGL(2,F) are parameterized by characters of elliptic tori. Taking a cue from real groups, we propose that supercuspidal representations are naturally parameterized by characters of covers of tori. Over the reals, Harish-Chandra defined the discrete series representations by specifying their characters restricted to an elliptic torus, and these characters may naturally be expressed in terms of charac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3268","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":"2026-05-18T03:43:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KAujgmFD0xMl875Quc4hwQkoO+RTkhAFa5B1tT/eUsLC846qlz7YOKQEuQFKlYhqKsWqSVml8qjB3FVoFjCmAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:13:44.192936Z"},"content_sha256":"9364c517cb1e073a0cb90583aa5f2b11b28a3192cc08c746cfd7aaa7c7f6b2d2","schema_version":"1.0","event_id":"sha256:9364c517cb1e073a0cb90583aa5f2b11b28a3192cc08c746cfd7aaa7c7f6b2d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NGVW3WV6BHUMMHRNCQTL76RPQ/bundle.json","state_url":"https://pith.science/pith/6NGVW3WV6BHUMMHRNCQTL76RPQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NGVW3WV6BHUMMHRNCQTL76RPQ/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":"2026-06-07T22:13:44Z","links":{"resolver":"https://pith.science/pith/6NGVW3WV6BHUMMHRNCQTL76RPQ","bundle":"https://pith.science/pith/6NGVW3WV6BHUMMHRNCQTL76RPQ/bundle.json","state":"https://pith.science/pith/6NGVW3WV6BHUMMHRNCQTL76RPQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NGVW3WV6BHUMMHRNCQTL76RPQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6NGVW3WV6BHUMMHRNCQTL76RPQ","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":"9073188388f6460639918ba39d468730e1a11ed69044dcf8e3bb7324d708342f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-11T15:21:45Z","title_canon_sha256":"5ee1c2c57212108c184149516eb423328bd495b6fd3612df7a200e8b44ebc3e6"},"schema_version":"1.0","source":{"id":"1210.3268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3268","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3268v1","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3268","created_at":"2026-05-18T03:43:27Z"},{"alias_kind":"pith_short_12","alias_value":"6NGVW3WV6BHU","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6NGVW3WV6BHUMMHR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6NGVW3WV","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:9364c517cb1e073a0cb90583aa5f2b11b28a3192cc08c746cfd7aaa7c7f6b2d2","target":"graph","created_at":"2026-05-18T03:43:27Z","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":"In this paper, we give a new realization of the local Langlands correspondence for PGL(2,F), where F is a p-adic field of odd residual characteristic. In this case, supercuspidal representations of PGL(2,F) are parameterized by characters of elliptic tori. Taking a cue from real groups, we propose that supercuspidal representations are naturally parameterized by characters of covers of tori. Over the reals, Harish-Chandra defined the discrete series representations by specifying their characters restricted to an elliptic torus, and these characters may naturally be expressed in terms of charac","authors_text":"Moshe Adrian","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-11T15:21:45Z","title":"A new realization of the Langlands correspondence for PGL(2,F)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3268","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:e6bc07f79d25be09374130d36bd14702346bd998b4e5e18a330fc65abe7b86df","target":"record","created_at":"2026-05-18T03:43:27Z","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":"9073188388f6460639918ba39d468730e1a11ed69044dcf8e3bb7324d708342f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-11T15:21:45Z","title_canon_sha256":"5ee1c2c57212108c184149516eb423328bd495b6fd3612df7a200e8b44ebc3e6"},"schema_version":"1.0","source":{"id":"1210.3268","kind":"arxiv","version":1}},"canonical_sha256":"f34d5b6ed5f04f4630f168a135ffd17c0ac8b923946b57af85a65cd30e26b0b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f34d5b6ed5f04f4630f168a135ffd17c0ac8b923946b57af85a65cd30e26b0b0","first_computed_at":"2026-05-18T03:43:27.838554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:27.838554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q6M7snuBhzFbFxjbk016uNL2mPKDB3y/9wZcCyJ8W1kf21jdqTMZCjCJIyGDC4FB9h19Awk0DCoF3vrL4RHWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:27.839227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6bc07f79d25be09374130d36bd14702346bd998b4e5e18a330fc65abe7b86df","sha256:9364c517cb1e073a0cb90583aa5f2b11b28a3192cc08c746cfd7aaa7c7f6b2d2"],"state_sha256":"683e8908dbdf03622b1cceb3971b1b81849eab167572ee97fdee09c0048e5cc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BLfJkPDUy3ykFZ+6rEDFp2XjB8KEcPklEjygwQoU4fsiXyFHTDfRzsKmEy+e4k8z80c5ofXehI3qfTfz4QqmAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:13:44.196229Z","bundle_sha256":"30ab66c3f5b22ef38a044da2d1d9f0eef168b98f806014acfa7096a32164b878"}}