{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SMQ4QJXEVPB2GKZOY75JTGAHAG","short_pith_number":"pith:SMQ4QJXE","canonical_record":{"source":{"id":"1302.0034","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-31T23:03:57Z","cross_cats_sorted":[],"title_canon_sha256":"a99b62b1a15b8a5877184e3120abb595e03129f43a2becbf3e02ca7f57b26ad2","abstract_canon_sha256":"caffef617887ded34dd2903f7266895f32188d68127f2d75a23bbb864ee7d503"},"schema_version":"1.0"},"canonical_sha256":"9321c826e4abc3a32b2ec7fa999807019db8fcc8ffe9934e199d9f6ffce6c55b","source":{"kind":"arxiv","id":"1302.0034","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0034","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0034v1","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0034","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"SMQ4QJXEVPB2","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SMQ4QJXEVPB2GKZO","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SMQ4QJXE","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SMQ4QJXEVPB2GKZOY75JTGAHAG","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0034","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-31T23:03:57Z","cross_cats_sorted":[],"title_canon_sha256":"a99b62b1a15b8a5877184e3120abb595e03129f43a2becbf3e02ca7f57b26ad2","abstract_canon_sha256":"caffef617887ded34dd2903f7266895f32188d68127f2d75a23bbb864ee7d503"},"schema_version":"1.0"},"canonical_sha256":"9321c826e4abc3a32b2ec7fa999807019db8fcc8ffe9934e199d9f6ffce6c55b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:47.687853Z","signature_b64":"USOfTrup5cpNjjOJX3KBt1TBIqKtqn/g/gYNSUCjBH8VZEgox8KNhHHmQyn06kCkijZHRjoDBM5OL4k/3vowBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9321c826e4abc3a32b2ec7fa999807019db8fcc8ffe9934e199d9f6ffce6c55b","last_reissued_at":"2026-05-18T03:34:47.687103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:47.687103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0034","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":"2026-05-18T03:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xY38H7TyQFW0h69uzUTWikE6T71jnrjW4mv+ThdGXSI5BIoRkblANx7UyQzOX44INWZJVzrjqKsyC5Kd0MNSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:54:01.904051Z"},"content_sha256":"7149f4373afc2467ba56a768e69bf70152903b2dccae5d00676b7fa2f6fabe08","schema_version":"1.0","event_id":"sha256:7149f4373afc2467ba56a768e69bf70152903b2dccae5d00676b7fa2f6fabe08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SMQ4QJXEVPB2GKZOY75JTGAHAG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on the Fundamental Lemma for stable twisted Endoscopy of Classical Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Joachim Ballmann, Rainer Weissauer, Uwe Weselmann","submitted_at":"2013-01-31T23:03:57Z","abstract_excerpt":"The twisted fundamental lemmas for three series of stable twisted endoscopy (Sp_{2n} to PGL_{2n+1}, GSpin_{2n+1} to GL_{2n}\\times GL_1, Sp_{2n} to SO_{2n+2}) will be reduced to a fundamental-lemma-like statement for ordinary (i.e. untwisted) stable orbital integrals on the groups $\\SO_{2n+1}$ of type $B_n$ resp. $\\SP_{2n}$ of type $C_n$. This manusript, written around 2001, anticipates similar results of Waldspurger (2008), and may be used to reduce the twisted fundamental lemma to the work of Ngo. The original aim was to reduce the fundumantal lemma for the lift from Sp_4 to PGL_5 to the twis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0034","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":"2026-05-18T03:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5qDFqD1g0jqF+cLd//7Spy/rfHvCkhy3uyattSmTidDD0+DqybfjCYnReCf/ldV2jhvjIbqUnefkGF8BGbTCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:54:01.904413Z"},"content_sha256":"2d0dc73625fa3ce87df3ba2238751712beaf3494a76dec88d161d5e644a85e26","schema_version":"1.0","event_id":"sha256:2d0dc73625fa3ce87df3ba2238751712beaf3494a76dec88d161d5e644a85e26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SMQ4QJXEVPB2GKZOY75JTGAHAG/bundle.json","state_url":"https://pith.science/pith/SMQ4QJXEVPB2GKZOY75JTGAHAG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SMQ4QJXEVPB2GKZOY75JTGAHAG/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":"2026-06-12T06:54:01Z","links":{"resolver":"https://pith.science/pith/SMQ4QJXEVPB2GKZOY75JTGAHAG","bundle":"https://pith.science/pith/SMQ4QJXEVPB2GKZOY75JTGAHAG/bundle.json","state":"https://pith.science/pith/SMQ4QJXEVPB2GKZOY75JTGAHAG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SMQ4QJXEVPB2GKZOY75JTGAHAG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SMQ4QJXEVPB2GKZOY75JTGAHAG","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":"caffef617887ded34dd2903f7266895f32188d68127f2d75a23bbb864ee7d503","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-31T23:03:57Z","title_canon_sha256":"a99b62b1a15b8a5877184e3120abb595e03129f43a2becbf3e02ca7f57b26ad2"},"schema_version":"1.0","source":{"id":"1302.0034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0034","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0034v1","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0034","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"SMQ4QJXEVPB2","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SMQ4QJXEVPB2GKZO","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SMQ4QJXE","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:2d0dc73625fa3ce87df3ba2238751712beaf3494a76dec88d161d5e644a85e26","target":"graph","created_at":"2026-05-18T03:34:47Z","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":"The twisted fundamental lemmas for three series of stable twisted endoscopy (Sp_{2n} to PGL_{2n+1}, GSpin_{2n+1} to GL_{2n}\\times GL_1, Sp_{2n} to SO_{2n+2}) will be reduced to a fundamental-lemma-like statement for ordinary (i.e. untwisted) stable orbital integrals on the groups $\\SO_{2n+1}$ of type $B_n$ resp. $\\SP_{2n}$ of type $C_n$. This manusript, written around 2001, anticipates similar results of Waldspurger (2008), and may be used to reduce the twisted fundamental lemma to the work of Ngo. The original aim was to reduce the fundumantal lemma for the lift from Sp_4 to PGL_5 to the twis","authors_text":"Joachim Ballmann, Rainer Weissauer, Uwe Weselmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-31T23:03:57Z","title":"Remarks on the Fundamental Lemma for stable twisted Endoscopy of Classical Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0034","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":"sha256:7149f4373afc2467ba56a768e69bf70152903b2dccae5d00676b7fa2f6fabe08","target":"record","created_at":"2026-05-18T03:34:47Z","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":"caffef617887ded34dd2903f7266895f32188d68127f2d75a23bbb864ee7d503","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-31T23:03:57Z","title_canon_sha256":"a99b62b1a15b8a5877184e3120abb595e03129f43a2becbf3e02ca7f57b26ad2"},"schema_version":"1.0","source":{"id":"1302.0034","kind":"arxiv","version":1}},"canonical_sha256":"9321c826e4abc3a32b2ec7fa999807019db8fcc8ffe9934e199d9f6ffce6c55b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9321c826e4abc3a32b2ec7fa999807019db8fcc8ffe9934e199d9f6ffce6c55b","first_computed_at":"2026-05-18T03:34:47.687103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:47.687103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"USOfTrup5cpNjjOJX3KBt1TBIqKtqn/g/gYNSUCjBH8VZEgox8KNhHHmQyn06kCkijZHRjoDBM5OL4k/3vowBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:47.687853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7149f4373afc2467ba56a768e69bf70152903b2dccae5d00676b7fa2f6fabe08","sha256:2d0dc73625fa3ce87df3ba2238751712beaf3494a76dec88d161d5e644a85e26"],"state_sha256":"df5dd8937e53472f2c5e3981129eb95deee23b45c921d14d20be18ec7ae194b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q0N0xD6PAyYPJEPzZ/ERU/q4O+zC1r7VpASnLuvpTbHd5QCEIsH2ocIrPQ90W+alitMMb4RU1YZaVSzAko/uDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:54:01.906663Z","bundle_sha256":"0734aef9494a16ae39f230d6703b6321f69cb8eee7c3e2a56978e960c06764c5"}}