{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q3XJABLQ74C34SLFU3J6UOJSDU","short_pith_number":"pith:Q3XJABLQ","canonical_record":{"source":{"id":"1408.5836","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-25T17:20:55Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"94c451ac81856ea31e73cbaf8d200bb5c0162b7e54a6554d54691d8f8a186b02","abstract_canon_sha256":"633495cc3711bbd631a4eb5558054e0734e8b40affe68b6f50adfa9d80975aa0"},"schema_version":"1.0"},"canonical_sha256":"86ee900570ff05be4965a6d3ea39321d2ce95fa38575d6d953296f102beba340","source":{"kind":"arxiv","id":"1408.5836","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5836","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5836v2","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5836","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"pith_short_12","alias_value":"Q3XJABLQ74C3","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q3XJABLQ74C34SLF","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q3XJABLQ","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q3XJABLQ74C34SLFU3J6UOJSDU","target":"record","payload":{"canonical_record":{"source":{"id":"1408.5836","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-25T17:20:55Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"94c451ac81856ea31e73cbaf8d200bb5c0162b7e54a6554d54691d8f8a186b02","abstract_canon_sha256":"633495cc3711bbd631a4eb5558054e0734e8b40affe68b6f50adfa9d80975aa0"},"schema_version":"1.0"},"canonical_sha256":"86ee900570ff05be4965a6d3ea39321d2ce95fa38575d6d953296f102beba340","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:49.612222Z","signature_b64":"Pz1L29TpcCrq6wuYq+miQrstgtxD4AEO2HHsnMUthLYJdEunSQetUGwDQNRB9GMTk+t4cdDBRzFowscaDngrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86ee900570ff05be4965a6d3ea39321d2ce95fa38575d6d953296f102beba340","last_reissued_at":"2026-05-18T01:01:49.611562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:49.611562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.5836","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:01:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDqrAuDqxu7pwjLLVKQyBG4AKnM2b1DXOq0sNsfKqcRIuTD1KAAmuSzNf4ZX+KHwHs9q+Q/hHiTUXhS+7jSfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:45:27.383860Z"},"content_sha256":"00728d3c7dc413f7185d9d2a94efe9249f3f079bde6bd5b8fe9377e697e0d8f3","schema_version":"1.0","event_id":"sha256:00728d3c7dc413f7185d9d2a94efe9249f3f079bde6bd5b8fe9377e697e0d8f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q3XJABLQ74C34SLFU3J6UOJSDU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the acceptable elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RT"],"primary_cat":"math.AG","authors_text":"Sian Nie, Xuhua He","submitted_at":"2014-08-25T17:20:55Z","abstract_excerpt":"In this paper, we study the set $B(G, \\{\\mu\\})$ of acceptable elements for any $p$-adic group $G$. We show that $B(G, \\{\\mu\\})$ contains a unique maximal element and the maximal element is represented by an element in the admissible subset of the associated Iwahori-Weyl group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5836","kind":"arxiv","version":2},"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":"2026-05-18T01:01:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"THwV0/j9rMSuOVc/UHVhx8n3A8tx2Eymm4KXSCeJ18tbcv0nGQ7+5wL37yF12ThCLS2Z0fXjdS0Aq49Vph12AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:45:27.384518Z"},"content_sha256":"376862e1d778e82d5e3bf91716d67e0939b5daf7f6e1d43311ff3c5bb2094533","schema_version":"1.0","event_id":"sha256:376862e1d778e82d5e3bf91716d67e0939b5daf7f6e1d43311ff3c5bb2094533"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3XJABLQ74C34SLFU3J6UOJSDU/bundle.json","state_url":"https://pith.science/pith/Q3XJABLQ74C34SLFU3J6UOJSDU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3XJABLQ74C34SLFU3J6UOJSDU/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":"2026-06-08T15:45:27Z","links":{"resolver":"https://pith.science/pith/Q3XJABLQ74C34SLFU3J6UOJSDU","bundle":"https://pith.science/pith/Q3XJABLQ74C34SLFU3J6UOJSDU/bundle.json","state":"https://pith.science/pith/Q3XJABLQ74C34SLFU3J6UOJSDU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3XJABLQ74C34SLFU3J6UOJSDU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q3XJABLQ74C34SLFU3J6UOJSDU","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":"633495cc3711bbd631a4eb5558054e0734e8b40affe68b6f50adfa9d80975aa0","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-25T17:20:55Z","title_canon_sha256":"94c451ac81856ea31e73cbaf8d200bb5c0162b7e54a6554d54691d8f8a186b02"},"schema_version":"1.0","source":{"id":"1408.5836","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5836","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5836v2","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5836","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"pith_short_12","alias_value":"Q3XJABLQ74C3","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q3XJABLQ74C34SLF","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q3XJABLQ","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:376862e1d778e82d5e3bf91716d67e0939b5daf7f6e1d43311ff3c5bb2094533","target":"graph","created_at":"2026-05-18T01:01:49Z","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 the set $B(G, \\{\\mu\\})$ of acceptable elements for any $p$-adic group $G$. We show that $B(G, \\{\\mu\\})$ contains a unique maximal element and the maximal element is represented by an element in the admissible subset of the associated Iwahori-Weyl group.","authors_text":"Sian Nie, Xuhua He","cross_cats":["math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-25T17:20:55Z","title":"On the acceptable elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5836","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":"sha256:00728d3c7dc413f7185d9d2a94efe9249f3f079bde6bd5b8fe9377e697e0d8f3","target":"record","created_at":"2026-05-18T01:01:49Z","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":"633495cc3711bbd631a4eb5558054e0734e8b40affe68b6f50adfa9d80975aa0","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-25T17:20:55Z","title_canon_sha256":"94c451ac81856ea31e73cbaf8d200bb5c0162b7e54a6554d54691d8f8a186b02"},"schema_version":"1.0","source":{"id":"1408.5836","kind":"arxiv","version":2}},"canonical_sha256":"86ee900570ff05be4965a6d3ea39321d2ce95fa38575d6d953296f102beba340","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86ee900570ff05be4965a6d3ea39321d2ce95fa38575d6d953296f102beba340","first_computed_at":"2026-05-18T01:01:49.611562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:49.611562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pz1L29TpcCrq6wuYq+miQrstgtxD4AEO2HHsnMUthLYJdEunSQetUGwDQNRB9GMTk+t4cdDBRzFowscaDngrDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:49.612222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5836","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00728d3c7dc413f7185d9d2a94efe9249f3f079bde6bd5b8fe9377e697e0d8f3","sha256:376862e1d778e82d5e3bf91716d67e0939b5daf7f6e1d43311ff3c5bb2094533"],"state_sha256":"6ac734eae71e52997d2c8347a993c9be394683c4c8d22dc439265479c6c88a04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IBvnAOl/JHb1sR+Ny6eT88jG+q3yrPW5RB0gHrZoH2755d8o5r5A8VU4mCJw7S3BMfPQfBqxLF2XTJ1Tdg74Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T15:45:27.387885Z","bundle_sha256":"66e97f990b16fd992749ffd622c9dc3dac077ce47a3f32c629b4604b67619f65"}}