{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IUXVUZHVIQA7U6PB4DW4W7OTHM","short_pith_number":"pith:IUXVUZHV","canonical_record":{"source":{"id":"1608.08475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-30T14:35:32Z","cross_cats_sorted":[],"title_canon_sha256":"083c8f17f8ac7fbeec7e8d5c2a9fbb872fd2d2f7aa2385430f1d679282426d56","abstract_canon_sha256":"95b6aaea0125ad9cb1a8ffe7de28bfae50e1de685b85e4420e238862ffe61fb2"},"schema_version":"1.0"},"canonical_sha256":"452f5a64f54401fa79e1e0edcb7dd33b2121f7ecb042839afd418a13553e5222","source":{"kind":"arxiv","id":"1608.08475","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08475","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08475v1","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08475","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"IUXVUZHVIQA7","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IUXVUZHVIQA7U6PB","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IUXVUZHV","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IUXVUZHVIQA7U6PB4DW4W7OTHM","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-30T14:35:32Z","cross_cats_sorted":[],"title_canon_sha256":"083c8f17f8ac7fbeec7e8d5c2a9fbb872fd2d2f7aa2385430f1d679282426d56","abstract_canon_sha256":"95b6aaea0125ad9cb1a8ffe7de28bfae50e1de685b85e4420e238862ffe61fb2"},"schema_version":"1.0"},"canonical_sha256":"452f5a64f54401fa79e1e0edcb7dd33b2121f7ecb042839afd418a13553e5222","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:57.271144Z","signature_b64":"N1931DQAFCyXQkkZqZ9w5iAjXzVjQGQXOyC+bJaZaPCcpYv02tlzMTcqXUGTFRasb7taHZwF/tHZDz/fpJRkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"452f5a64f54401fa79e1e0edcb7dd33b2121f7ecb042839afd418a13553e5222","last_reissued_at":"2026-05-18T00:20:57.270116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:57.270116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08475","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":"2026-05-18T00:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+nH7Ks/epTS6UM+oIyF+BUFus3mu8jI5L0eX/9CWGniRpJZk+DEzUlGcWX3G6aHZR6VPzuTM/QeV2MKn+zX8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:44:49.397857Z"},"content_sha256":"15cceeb9d656ac3bb726e4c98f9e5d87d4cfc6fe2394772ac260af5fa97206db","schema_version":"1.0","event_id":"sha256:15cceeb9d656ac3bb726e4c98f9e5d87d4cfc6fe2394772ac260af5fa97206db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IUXVUZHVIQA7U6PB4DW4W7OTHM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A local relative trace formula for PGL(2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Pascale Harinck, Patrick Delorme","submitted_at":"2016-08-30T14:35:32Z","abstract_excerpt":"Following a scheme inspired by B. Feigon, we describe the spectral side of a local relative trace formula for $G:= PGL(2,\\rm E)$ relative to the symmetric subgroup $H:=PGL(2,\\rm F)$ where $\\rm E/\\rm F$ is an unramified quadratic extension of local non archimedean fields of characteristic $0$. This spectral side is given in terms of regularized normalized periods and normalized $C$-functions of Harish-Chandra. Using the geometric side obtained in a more general setting by P. Delorme, P. Harinck and S. Souaifi , we deduce a local relative trace formula for $G$ relative to $H$. We apply our resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08475","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":"2026-05-18T00:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ho2rR8ZcN0aEEA4YLK3hF2c13q87a/J0EMVDoaOuNFqKdVwsz3armzVdUeicev/GUBuAKl3dJiK7inJpmYqnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:44:49.398194Z"},"content_sha256":"ae0af3d938113cccf01157602ada39a1eb1aceafe75945a2342a5c7f31982b22","schema_version":"1.0","event_id":"sha256:ae0af3d938113cccf01157602ada39a1eb1aceafe75945a2342a5c7f31982b22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IUXVUZHVIQA7U6PB4DW4W7OTHM/bundle.json","state_url":"https://pith.science/pith/IUXVUZHVIQA7U6PB4DW4W7OTHM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IUXVUZHVIQA7U6PB4DW4W7OTHM/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":"2026-06-26T14:44:49Z","links":{"resolver":"https://pith.science/pith/IUXVUZHVIQA7U6PB4DW4W7OTHM","bundle":"https://pith.science/pith/IUXVUZHVIQA7U6PB4DW4W7OTHM/bundle.json","state":"https://pith.science/pith/IUXVUZHVIQA7U6PB4DW4W7OTHM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IUXVUZHVIQA7U6PB4DW4W7OTHM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IUXVUZHVIQA7U6PB4DW4W7OTHM","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":"95b6aaea0125ad9cb1a8ffe7de28bfae50e1de685b85e4420e238862ffe61fb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-30T14:35:32Z","title_canon_sha256":"083c8f17f8ac7fbeec7e8d5c2a9fbb872fd2d2f7aa2385430f1d679282426d56"},"schema_version":"1.0","source":{"id":"1608.08475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08475","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08475v1","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08475","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"IUXVUZHVIQA7","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IUXVUZHVIQA7U6PB","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IUXVUZHV","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:ae0af3d938113cccf01157602ada39a1eb1aceafe75945a2342a5c7f31982b22","target":"graph","created_at":"2026-05-18T00:20:57Z","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":"Following a scheme inspired by B. Feigon, we describe the spectral side of a local relative trace formula for $G:= PGL(2,\\rm E)$ relative to the symmetric subgroup $H:=PGL(2,\\rm F)$ where $\\rm E/\\rm F$ is an unramified quadratic extension of local non archimedean fields of characteristic $0$. This spectral side is given in terms of regularized normalized periods and normalized $C$-functions of Harish-Chandra. Using the geometric side obtained in a more general setting by P. Delorme, P. Harinck and S. Souaifi , we deduce a local relative trace formula for $G$ relative to $H$. We apply our resul","authors_text":"Pascale Harinck, Patrick Delorme","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-30T14:35:32Z","title":"A local relative trace formula for PGL(2)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08475","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":"sha256:15cceeb9d656ac3bb726e4c98f9e5d87d4cfc6fe2394772ac260af5fa97206db","target":"record","created_at":"2026-05-18T00:20:57Z","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":"95b6aaea0125ad9cb1a8ffe7de28bfae50e1de685b85e4420e238862ffe61fb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-30T14:35:32Z","title_canon_sha256":"083c8f17f8ac7fbeec7e8d5c2a9fbb872fd2d2f7aa2385430f1d679282426d56"},"schema_version":"1.0","source":{"id":"1608.08475","kind":"arxiv","version":1}},"canonical_sha256":"452f5a64f54401fa79e1e0edcb7dd33b2121f7ecb042839afd418a13553e5222","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"452f5a64f54401fa79e1e0edcb7dd33b2121f7ecb042839afd418a13553e5222","first_computed_at":"2026-05-18T00:20:57.270116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:57.270116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N1931DQAFCyXQkkZqZ9w5iAjXzVjQGQXOyC+bJaZaPCcpYv02tlzMTcqXUGTFRasb7taHZwF/tHZDz/fpJRkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:57.271144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15cceeb9d656ac3bb726e4c98f9e5d87d4cfc6fe2394772ac260af5fa97206db","sha256:ae0af3d938113cccf01157602ada39a1eb1aceafe75945a2342a5c7f31982b22"],"state_sha256":"850c4fca15744bbd6c4500b3fa9f066741010791f1f777c89cfd54d44ad91005"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cl3muixJrNDRLnjRsL9E7f7pjscyWIkDYXgVfFUndH79hhpAkzfvtFbAM4tuxzsOFh3mbH18a6DPaYLTOXZnBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:44:49.400326Z","bundle_sha256":"634fc872c6cabcd29751106d42a632e9bb3493921910b18dc613b1fa88d9b838"}}