{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HKKI3KUZ5CBYEJKS53JNDUT6OL","short_pith_number":"pith:HKKI3KUZ","canonical_record":{"source":{"id":"1111.7057","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-11-30T06:22:24Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"cf1e0b28abce4668bd41edff1ffd88327f8cafbdfbba6db26c1edfef7f3bca4e","abstract_canon_sha256":"33520bd6cc22b11d82df0a432ca21f92b4718c7cf423a65865c2d1b83bd02a60"},"schema_version":"1.0"},"canonical_sha256":"3a948daa99e883822552eed2d1d27e72e87560035ff1f7d4aefb7b0762326c37","source":{"kind":"arxiv","id":"1111.7057","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7057","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7057v4","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7057","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"pith_short_12","alias_value":"HKKI3KUZ5CBY","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HKKI3KUZ5CBYEJKS","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HKKI3KUZ","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HKKI3KUZ5CBYEJKS53JNDUT6OL","target":"record","payload":{"canonical_record":{"source":{"id":"1111.7057","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-11-30T06:22:24Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"cf1e0b28abce4668bd41edff1ffd88327f8cafbdfbba6db26c1edfef7f3bca4e","abstract_canon_sha256":"33520bd6cc22b11d82df0a432ca21f92b4718c7cf423a65865c2d1b83bd02a60"},"schema_version":"1.0"},"canonical_sha256":"3a948daa99e883822552eed2d1d27e72e87560035ff1f7d4aefb7b0762326c37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:33.450672Z","signature_b64":"9Ln9PV88uII3W5N2/kiEF7xCrL0Dc3C/r4UJZG6fdUtb7Sle7aXmLk7/HMqyJxC/uQtj0F3yxstzz10Hu+SvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a948daa99e883822552eed2d1d27e72e87560035ff1f7d4aefb7b0762326c37","last_reissued_at":"2026-05-18T03:12:33.449822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:33.449822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.7057","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:12:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M6bWhqUJCx8nylLEqMOZsfwi2AO/gadEhqySz0T2T9e5k219Lndf407lKu5v2tZDMmCjUDhat9C9RGNGit0QDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:41:46.358523Z"},"content_sha256":"b936e05c56dd67124832ab9949d40becd8bd9d2326414dc28c626e7f7df5c385","schema_version":"1.0","event_id":"sha256:b936e05c56dd67124832ab9949d40becd8bd9d2326414dc28c626e7f7df5c385"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HKKI3KUZ5CBYEJKS53JNDUT6OL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local integrability results in harmonic analysis on reductive groups in large positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.RT","authors_text":"Immanuel Halupczok, Julia Gordon, Raf Cluckers","submitted_at":"2011-11-30T06:22:24Z","abstract_excerpt":"Let $G$ be a connected reductive algebraic group over a non-Archimedean local field $K$, and let $g$ be its Lie algebra. By a theorem of Harish-Chandra, if $K$ has characteristic zero, the Fourier transforms of orbital integrals are represented on the set of regular elements in $g(K)$ by locally constant functions, which, extended by zero to all of $g(K)$, are locally integrable. In this paper, we prove that these functions are in fact specializations of constructible motivic exponential functions. Combining this with the Transfer Principle for integrability [R. Cluckers, J. Gordon, I. Halupcz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7057","kind":"arxiv","version":4},"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":"2026-05-18T03:12:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEKRngG3lboQlN1PMHJBxU7e5oebTQSQF9ZAeoPzVat4B8w/XC7KofJT7MwMG7e6fB866BedpFms1TIdzD3/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:41:46.359239Z"},"content_sha256":"2fdc6b5bbf41b1c8c14c6620d43c25b610fd29384c772f7632c3a025b23c5d01","schema_version":"1.0","event_id":"sha256:2fdc6b5bbf41b1c8c14c6620d43c25b610fd29384c772f7632c3a025b23c5d01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKKI3KUZ5CBYEJKS53JNDUT6OL/bundle.json","state_url":"https://pith.science/pith/HKKI3KUZ5CBYEJKS53JNDUT6OL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKKI3KUZ5CBYEJKS53JNDUT6OL/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":"2026-05-27T09:41:46Z","links":{"resolver":"https://pith.science/pith/HKKI3KUZ5CBYEJKS53JNDUT6OL","bundle":"https://pith.science/pith/HKKI3KUZ5CBYEJKS53JNDUT6OL/bundle.json","state":"https://pith.science/pith/HKKI3KUZ5CBYEJKS53JNDUT6OL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKKI3KUZ5CBYEJKS53JNDUT6OL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HKKI3KUZ5CBYEJKS53JNDUT6OL","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":"33520bd6cc22b11d82df0a432ca21f92b4718c7cf423a65865c2d1b83bd02a60","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-11-30T06:22:24Z","title_canon_sha256":"cf1e0b28abce4668bd41edff1ffd88327f8cafbdfbba6db26c1edfef7f3bca4e"},"schema_version":"1.0","source":{"id":"1111.7057","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7057","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7057v4","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7057","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"pith_short_12","alias_value":"HKKI3KUZ5CBY","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HKKI3KUZ5CBYEJKS","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HKKI3KUZ","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:2fdc6b5bbf41b1c8c14c6620d43c25b610fd29384c772f7632c3a025b23c5d01","target":"graph","created_at":"2026-05-18T03:12:33Z","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":"Let $G$ be a connected reductive algebraic group over a non-Archimedean local field $K$, and let $g$ be its Lie algebra. By a theorem of Harish-Chandra, if $K$ has characteristic zero, the Fourier transforms of orbital integrals are represented on the set of regular elements in $g(K)$ by locally constant functions, which, extended by zero to all of $g(K)$, are locally integrable. In this paper, we prove that these functions are in fact specializations of constructible motivic exponential functions. Combining this with the Transfer Principle for integrability [R. Cluckers, J. Gordon, I. Halupcz","authors_text":"Immanuel Halupczok, Julia Gordon, Raf Cluckers","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-11-30T06:22:24Z","title":"Local integrability results in harmonic analysis on reductive groups in large positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7057","kind":"arxiv","version":4},"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:b936e05c56dd67124832ab9949d40becd8bd9d2326414dc28c626e7f7df5c385","target":"record","created_at":"2026-05-18T03:12:33Z","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":"33520bd6cc22b11d82df0a432ca21f92b4718c7cf423a65865c2d1b83bd02a60","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-11-30T06:22:24Z","title_canon_sha256":"cf1e0b28abce4668bd41edff1ffd88327f8cafbdfbba6db26c1edfef7f3bca4e"},"schema_version":"1.0","source":{"id":"1111.7057","kind":"arxiv","version":4}},"canonical_sha256":"3a948daa99e883822552eed2d1d27e72e87560035ff1f7d4aefb7b0762326c37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a948daa99e883822552eed2d1d27e72e87560035ff1f7d4aefb7b0762326c37","first_computed_at":"2026-05-18T03:12:33.449822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:33.449822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Ln9PV88uII3W5N2/kiEF7xCrL0Dc3C/r4UJZG6fdUtb7Sle7aXmLk7/HMqyJxC/uQtj0F3yxstzz10Hu+SvBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:33.450672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.7057","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b936e05c56dd67124832ab9949d40becd8bd9d2326414dc28c626e7f7df5c385","sha256:2fdc6b5bbf41b1c8c14c6620d43c25b610fd29384c772f7632c3a025b23c5d01"],"state_sha256":"14130c97b0515ec64b64ccf027c892973f8995937f87f456f8b7da03c4865599"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F6OC6h/fg1vcpDjDw+pA4xqNOVRpM06pY70sISOZo45M0LN2DsFfJtN2qLvrgf287pcxoC7dAR83SS3UABBTAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:41:46.363024Z","bundle_sha256":"e19cb9d2e810b413d7281e0dbfb1f9dfef3e8dacf9ff9926e379ce14aa2d5c9e"}}