{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:FLHBDAAFKQYCEJXDSIHDFNBDHD","short_pith_number":"pith:FLHBDAAF","canonical_record":{"source":{"id":"1908.00961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-08-02T17:23:59Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"1b0e8cd312d8052c470ba990bc351fd1eaef1ae4044f149163817caffea602c4","abstract_canon_sha256":"1e38a79ab216ebaa7c9f4f2e83675407a90897d696274d376ef042efc425c02e"},"schema_version":"1.0"},"canonical_sha256":"2ace11800554302226e3920e32b42338e807ad6efffdb2638dcffa4f8de61f36","source":{"kind":"arxiv","id":"1908.00961","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00961","created_at":"2026-07-05T01:00:32Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00961v1","created_at":"2026-07-05T01:00:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00961","created_at":"2026-07-05T01:00:32Z"},{"alias_kind":"pith_short_12","alias_value":"FLHBDAAFKQYC","created_at":"2026-07-05T01:00:32Z"},{"alias_kind":"pith_short_16","alias_value":"FLHBDAAFKQYCEJXD","created_at":"2026-07-05T01:00:32Z"},{"alias_kind":"pith_short_8","alias_value":"FLHBDAAF","created_at":"2026-07-05T01:00:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:FLHBDAAFKQYCEJXDSIHDFNBDHD","target":"record","payload":{"canonical_record":{"source":{"id":"1908.00961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-08-02T17:23:59Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"1b0e8cd312d8052c470ba990bc351fd1eaef1ae4044f149163817caffea602c4","abstract_canon_sha256":"1e38a79ab216ebaa7c9f4f2e83675407a90897d696274d376ef042efc425c02e"},"schema_version":"1.0"},"canonical_sha256":"2ace11800554302226e3920e32b42338e807ad6efffdb2638dcffa4f8de61f36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:00:32.862675Z","signature_b64":"LaqgGIeCdysPqTgc5JuZPxqCj+IFb6qydbXNIJ9hrstFdLuegR1KUExhWSPZ1KOkilts9MSTkE5+jGKslYzNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ace11800554302226e3920e32b42338e807ad6efffdb2638dcffa4f8de61f36","last_reissued_at":"2026-07-05T01:00:32.862269Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:00:32.862269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.00961","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":"2026-07-05T01:00:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qCaF2ErP5Bp9VgdXGoIqSkSC0lf3Z9DqoPHgAXhO8HqzAJPrGaLqk6JRPG3TNRiW4OzXy5mpVGcl2HuVaS9eAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:42:40.233770Z"},"content_sha256":"f78d4a5bb4e9d2a9d1c553b92c2ecd9d4bafe50791773b9cff9266580a10f96a","schema_version":"1.0","event_id":"sha256:f78d4a5bb4e9d2a9d1c553b92c2ecd9d4bafe50791773b9cff9266580a10f96a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:FLHBDAAFKQYCEJXDSIHDFNBDHD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the fine expansion of the unipotent contribution of the Guo-Jacquet trace formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Pierre-Henri Chaudouard","submitted_at":"2019-08-02T17:23:59Z","abstract_excerpt":"For a useful class of functions (containing functions whose one finite component is essentially a matrix coefficient of a supercuspidal representation), we establish three results about the unipotent contribution of the Guo-Jacquet relative trace formula for the pair $(GL_n(D),GL_n(E))$. First we get a fine expansion in terms of global nilpotent integrals. Second we express these nilpotent integrals in terms of zeta integrals. Finally we prove that they satisfy certain homogeneity properties. The proof is based on a new kind of truncation introduced in a previous article."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00961","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.00961/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:00:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q2jh31iLs+X+XpsBOz29osiErKElPHDKOJ8mrNp9rtUkWpcn1iyxqIyv7E+bd6bdlszvIuo8tf9c3xKYd8DyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:42:40.234258Z"},"content_sha256":"60b3554fe9c2ab0b0f415679ef9db3862309da85e7e1b714d16826c57f7b3f8b","schema_version":"1.0","event_id":"sha256:60b3554fe9c2ab0b0f415679ef9db3862309da85e7e1b714d16826c57f7b3f8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FLHBDAAFKQYCEJXDSIHDFNBDHD/bundle.json","state_url":"https://pith.science/pith/FLHBDAAFKQYCEJXDSIHDFNBDHD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FLHBDAAFKQYCEJXDSIHDFNBDHD/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":"2026-08-16T08:42:40Z","links":{"resolver":"https://pith.science/pith/FLHBDAAFKQYCEJXDSIHDFNBDHD","bundle":"https://pith.science/pith/FLHBDAAFKQYCEJXDSIHDFNBDHD/bundle.json","state":"https://pith.science/pith/FLHBDAAFKQYCEJXDSIHDFNBDHD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FLHBDAAFKQYCEJXDSIHDFNBDHD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FLHBDAAFKQYCEJXDSIHDFNBDHD","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":"1e38a79ab216ebaa7c9f4f2e83675407a90897d696274d376ef042efc425c02e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-08-02T17:23:59Z","title_canon_sha256":"1b0e8cd312d8052c470ba990bc351fd1eaef1ae4044f149163817caffea602c4"},"schema_version":"1.0","source":{"id":"1908.00961","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00961","created_at":"2026-07-05T01:00:32Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00961v1","created_at":"2026-07-05T01:00:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00961","created_at":"2026-07-05T01:00:32Z"},{"alias_kind":"pith_short_12","alias_value":"FLHBDAAFKQYC","created_at":"2026-07-05T01:00:32Z"},{"alias_kind":"pith_short_16","alias_value":"FLHBDAAFKQYCEJXD","created_at":"2026-07-05T01:00:32Z"},{"alias_kind":"pith_short_8","alias_value":"FLHBDAAF","created_at":"2026-07-05T01:00:32Z"}],"graph_snapshots":[{"event_id":"sha256:60b3554fe9c2ab0b0f415679ef9db3862309da85e7e1b714d16826c57f7b3f8b","target":"graph","created_at":"2026-07-05T01:00:32Z","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/1908.00961/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a useful class of functions (containing functions whose one finite component is essentially a matrix coefficient of a supercuspidal representation), we establish three results about the unipotent contribution of the Guo-Jacquet relative trace formula for the pair $(GL_n(D),GL_n(E))$. First we get a fine expansion in terms of global nilpotent integrals. Second we express these nilpotent integrals in terms of zeta integrals. Finally we prove that they satisfy certain homogeneity properties. The proof is based on a new kind of truncation introduced in a previous article.","authors_text":"Pierre-Henri Chaudouard","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-08-02T17:23:59Z","title":"On the fine expansion of the unipotent contribution of the Guo-Jacquet trace formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00961","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:f78d4a5bb4e9d2a9d1c553b92c2ecd9d4bafe50791773b9cff9266580a10f96a","target":"record","created_at":"2026-07-05T01:00:32Z","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":"1e38a79ab216ebaa7c9f4f2e83675407a90897d696274d376ef042efc425c02e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-08-02T17:23:59Z","title_canon_sha256":"1b0e8cd312d8052c470ba990bc351fd1eaef1ae4044f149163817caffea602c4"},"schema_version":"1.0","source":{"id":"1908.00961","kind":"arxiv","version":1}},"canonical_sha256":"2ace11800554302226e3920e32b42338e807ad6efffdb2638dcffa4f8de61f36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ace11800554302226e3920e32b42338e807ad6efffdb2638dcffa4f8de61f36","first_computed_at":"2026-07-05T01:00:32.862269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:00:32.862269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LaqgGIeCdysPqTgc5JuZPxqCj+IFb6qydbXNIJ9hrstFdLuegR1KUExhWSPZ1KOkilts9MSTkE5+jGKslYzNDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:00:32.862675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00961","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f78d4a5bb4e9d2a9d1c553b92c2ecd9d4bafe50791773b9cff9266580a10f96a","sha256:60b3554fe9c2ab0b0f415679ef9db3862309da85e7e1b714d16826c57f7b3f8b"],"state_sha256":"d136be6bfaa312d0cdad91c1286280e0f1433e4b36981d26accb5ea720517fe1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QGdGmJo+PPN6SgRXRQor44oqaxBRULYt+Qru5G8pHLTX08Odatfr/n9+sR//1iR/m5I/4xEdqwbIs1ZS1dd1BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T08:42:40.238926Z","bundle_sha256":"b6fd0315618917b7f31418c167c61e6c2211ba4a3987e00b25c316dec0292961"}}