{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ENBBHKYXMUVPSCSOCZCXXZCAN5","short_pith_number":"pith:ENBBHKYX","canonical_record":{"source":{"id":"1812.03157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-07T18:47:32Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"87802eb8bfec6e1521955d4ccc98279feff9c71777ee7bd7a250a8807335c0b6","abstract_canon_sha256":"fb9a311ad56a007ea11352e2d4580651c3ec197d3697ccc140e9edc9a42f26e7"},"schema_version":"1.0"},"canonical_sha256":"234213ab17652af90a4e16457be4406f6156b01c114c14748b3c832e6af663c5","source":{"kind":"arxiv","id":"1812.03157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03157","created_at":"2026-05-17T23:58:50Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03157v1","created_at":"2026-05-17T23:58:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03157","created_at":"2026-05-17T23:58:50Z"},{"alias_kind":"pith_short_12","alias_value":"ENBBHKYXMUVP","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ENBBHKYXMUVPSCSO","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ENBBHKYX","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ENBBHKYXMUVPSCSOCZCXXZCAN5","target":"record","payload":{"canonical_record":{"source":{"id":"1812.03157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-07T18:47:32Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"87802eb8bfec6e1521955d4ccc98279feff9c71777ee7bd7a250a8807335c0b6","abstract_canon_sha256":"fb9a311ad56a007ea11352e2d4580651c3ec197d3697ccc140e9edc9a42f26e7"},"schema_version":"1.0"},"canonical_sha256":"234213ab17652af90a4e16457be4406f6156b01c114c14748b3c832e6af663c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:50.778568Z","signature_b64":"dCwH2hRa21wqJhzW7PaB3YDPVI8thVx2ZLjI74Ge2PaZuo4fN6xClzajogMsI0uzLJGJzF8ZbObFdYKCxLgzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"234213ab17652af90a4e16457be4406f6156b01c114c14748b3c832e6af663c5","last_reissued_at":"2026-05-17T23:58:50.778002Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:50.778002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.03157","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":"2026-05-17T23:58:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hZaJc85uuKqafTSyLRXiIAiA9b5Xsb5PTJlUHWh8QZYryOFOKFVieWngSeDby6k77RHxZjmzbUVSfoamywkDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:54:23.906762Z"},"content_sha256":"7428c81965c8dd3fca8f2cdf6f8df8de444b660af6797e05ae6d8036b0385cf7","schema_version":"1.0","event_id":"sha256:7428c81965c8dd3fca8f2cdf6f8df8de444b660af6797e05ae6d8036b0385cf7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ENBBHKYXMUVPSCSOCZCXXZCAN5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On top Fourier coefficients of certain automorphic representations of GLn","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Baiying Liu, Bin Xu","submitted_at":"2018-12-07T18:47:32Z","abstract_excerpt":"In this paper, we study top Fourier coefficients of certain automorphic representations of $\\mathrm{GL}_n(\\mathbb{A})$. In particular, we prove a conjecture of Jiang on top Fourier coefficients of isobaric automorphic representations of $\\mathrm{GL}_n(\\mathbb{A})$ of form $$ \\Delta(\\tau_1, b_1) \\boxplus \\Delta(\\tau_2, b_2) \\boxplus \\cdots \\boxplus \\Delta(\\tau_r, b_r)\\,, $$ where $\\Delta(\\tau_i,b_i)$'s are Speh representations in the discrete spectrum of $\\mathrm{GL}_{a_ib_i}(\\mathbb{A})$ with $\\tau_i$'s being unitary cuspidal representations of $\\mathrm{GL}_{a_i}(\\mathbb{A})$, and $n = \\sum_{i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03157","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":"2026-05-17T23:58:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X07476qthSZ9tLV3toypWk72fDlOS9T2OUTbcZzUclWGfL0KXLWP4w6UNmYtS3RBkP/jgamFDl/V9nYHSvVGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:54:23.907434Z"},"content_sha256":"21125c63ca3ee3ae3fe9ab40301ca0a9fbb003d26d51d14fccc5ccd80b5c36da","schema_version":"1.0","event_id":"sha256:21125c63ca3ee3ae3fe9ab40301ca0a9fbb003d26d51d14fccc5ccd80b5c36da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ENBBHKYXMUVPSCSOCZCXXZCAN5/bundle.json","state_url":"https://pith.science/pith/ENBBHKYXMUVPSCSOCZCXXZCAN5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ENBBHKYXMUVPSCSOCZCXXZCAN5/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":"2026-06-08T12:54:23Z","links":{"resolver":"https://pith.science/pith/ENBBHKYXMUVPSCSOCZCXXZCAN5","bundle":"https://pith.science/pith/ENBBHKYXMUVPSCSOCZCXXZCAN5/bundle.json","state":"https://pith.science/pith/ENBBHKYXMUVPSCSOCZCXXZCAN5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ENBBHKYXMUVPSCSOCZCXXZCAN5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ENBBHKYXMUVPSCSOCZCXXZCAN5","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":"fb9a311ad56a007ea11352e2d4580651c3ec197d3697ccc140e9edc9a42f26e7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-07T18:47:32Z","title_canon_sha256":"87802eb8bfec6e1521955d4ccc98279feff9c71777ee7bd7a250a8807335c0b6"},"schema_version":"1.0","source":{"id":"1812.03157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03157","created_at":"2026-05-17T23:58:50Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03157v1","created_at":"2026-05-17T23:58:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03157","created_at":"2026-05-17T23:58:50Z"},{"alias_kind":"pith_short_12","alias_value":"ENBBHKYXMUVP","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ENBBHKYXMUVPSCSO","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ENBBHKYX","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:21125c63ca3ee3ae3fe9ab40301ca0a9fbb003d26d51d14fccc5ccd80b5c36da","target":"graph","created_at":"2026-05-17T23:58:50Z","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 study top Fourier coefficients of certain automorphic representations of $\\mathrm{GL}_n(\\mathbb{A})$. In particular, we prove a conjecture of Jiang on top Fourier coefficients of isobaric automorphic representations of $\\mathrm{GL}_n(\\mathbb{A})$ of form $$ \\Delta(\\tau_1, b_1) \\boxplus \\Delta(\\tau_2, b_2) \\boxplus \\cdots \\boxplus \\Delta(\\tau_r, b_r)\\,, $$ where $\\Delta(\\tau_i,b_i)$'s are Speh representations in the discrete spectrum of $\\mathrm{GL}_{a_ib_i}(\\mathbb{A})$ with $\\tau_i$'s being unitary cuspidal representations of $\\mathrm{GL}_{a_i}(\\mathbb{A})$, and $n = \\sum_{i","authors_text":"Baiying Liu, Bin Xu","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-07T18:47:32Z","title":"On top Fourier coefficients of certain automorphic representations of GLn"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03157","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":"sha256:7428c81965c8dd3fca8f2cdf6f8df8de444b660af6797e05ae6d8036b0385cf7","target":"record","created_at":"2026-05-17T23:58:50Z","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":"fb9a311ad56a007ea11352e2d4580651c3ec197d3697ccc140e9edc9a42f26e7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-07T18:47:32Z","title_canon_sha256":"87802eb8bfec6e1521955d4ccc98279feff9c71777ee7bd7a250a8807335c0b6"},"schema_version":"1.0","source":{"id":"1812.03157","kind":"arxiv","version":1}},"canonical_sha256":"234213ab17652af90a4e16457be4406f6156b01c114c14748b3c832e6af663c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"234213ab17652af90a4e16457be4406f6156b01c114c14748b3c832e6af663c5","first_computed_at":"2026-05-17T23:58:50.778002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:50.778002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dCwH2hRa21wqJhzW7PaB3YDPVI8thVx2ZLjI74Ge2PaZuo4fN6xClzajogMsI0uzLJGJzF8ZbObFdYKCxLgzDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:50.778568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.03157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7428c81965c8dd3fca8f2cdf6f8df8de444b660af6797e05ae6d8036b0385cf7","sha256:21125c63ca3ee3ae3fe9ab40301ca0a9fbb003d26d51d14fccc5ccd80b5c36da"],"state_sha256":"6d9ce7e265a27787003fdc8333be4c0a08f7e96c2867f659ca1df50f76e6712c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mPOvOHijcMxxERlj/KKtVZhtm3O2YiOPCTXWZf1HhNPud3fuBz+QqnhADwUEpu/7EwcUFrYb/V1sHY1U1hGsDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:54:23.910383Z","bundle_sha256":"c44ada31444845dd532ca15d2cf8fd153f2e91ce0b20a9a857bab038f4dad800"}}