{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TTT2ZLSCR6IHOPUTY6XDSVW5GF","short_pith_number":"pith:TTT2ZLSC","schema_version":"1.0","canonical_sha256":"9ce7acae428f90773e93c7ae3956dd31742a64819e6a8526ad48cee3572c750f","source":{"kind":"arxiv","id":"1701.04999","version":2},"attestation_state":"computed","paper":{"title":"A spectral decomposition of orbital integrals for $PGL(2,F)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David Kazhdan, Stephen DeBacker","submitted_at":"2017-01-18T10:30:27Z","abstract_excerpt":"Let $F$ be a local non-archimedian field, $G$ a semisimple $F$-group, $dg$ a Haar measure on $G$ and $\\mathcal S(G)$ be the space of locally constant complex valued functions $f$ on $G$ with compact support. For any regular elliptic congugacy class $\\Omega =h^G\\subset G$ we denote by $I_\\Omega$ the $G$-invariant functional on $\\mathcal S (G)$ given by $$I_\\Omega (f)=\\int_G f(g^{-1}hg)dg$$ This paper provides the spectral decomposition of functionals $I_\\Omega$ in the case $G=PGL(2,F)$ and in the last section first steps of such an analysis for the general case."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.04999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-18T10:30:27Z","cross_cats_sorted":[],"title_canon_sha256":"3f3226cda3b39903f8aff56f70e13bd28dd7d4852be86d0a4545ed5751b8001b","abstract_canon_sha256":"871b07a6bebffb674a26994895332ccfc5a26f329a6d89e93bc456e5237a18a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:12.741401Z","signature_b64":"vXV9EVfaZxwryvCXSoe5xisNv1Sfcrppf5wiZucuVM/fUUKzqwrpu0XJeja19T+Y8PeBKsmZ9fFrI5bVnjO6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ce7acae428f90773e93c7ae3956dd31742a64819e6a8526ad48cee3572c750f","last_reissued_at":"2026-05-18T00:52:12.740968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:12.740968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A spectral decomposition of orbital integrals for $PGL(2,F)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David Kazhdan, Stephen DeBacker","submitted_at":"2017-01-18T10:30:27Z","abstract_excerpt":"Let $F$ be a local non-archimedian field, $G$ a semisimple $F$-group, $dg$ a Haar measure on $G$ and $\\mathcal S(G)$ be the space of locally constant complex valued functions $f$ on $G$ with compact support. For any regular elliptic congugacy class $\\Omega =h^G\\subset G$ we denote by $I_\\Omega$ the $G$-invariant functional on $\\mathcal S (G)$ given by $$I_\\Omega (f)=\\int_G f(g^{-1}hg)dg$$ This paper provides the spectral decomposition of functionals $I_\\Omega$ in the case $G=PGL(2,F)$ and in the last section first steps of such an analysis for the general case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04999","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.04999","created_at":"2026-05-18T00:52:12.741033+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.04999v2","created_at":"2026-05-18T00:52:12.741033+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04999","created_at":"2026-05-18T00:52:12.741033+00:00"},{"alias_kind":"pith_short_12","alias_value":"TTT2ZLSCR6IH","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TTT2ZLSCR6IHOPUT","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TTT2ZLSC","created_at":"2026-05-18T12:31:46.661854+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TTT2ZLSCR6IHOPUTY6XDSVW5GF","json":"https://pith.science/pith/TTT2ZLSCR6IHOPUTY6XDSVW5GF.json","graph_json":"https://pith.science/api/pith-number/TTT2ZLSCR6IHOPUTY6XDSVW5GF/graph.json","events_json":"https://pith.science/api/pith-number/TTT2ZLSCR6IHOPUTY6XDSVW5GF/events.json","paper":"https://pith.science/paper/TTT2ZLSC"},"agent_actions":{"view_html":"https://pith.science/pith/TTT2ZLSCR6IHOPUTY6XDSVW5GF","download_json":"https://pith.science/pith/TTT2ZLSCR6IHOPUTY6XDSVW5GF.json","view_paper":"https://pith.science/paper/TTT2ZLSC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.04999&json=true","fetch_graph":"https://pith.science/api/pith-number/TTT2ZLSCR6IHOPUTY6XDSVW5GF/graph.json","fetch_events":"https://pith.science/api/pith-number/TTT2ZLSCR6IHOPUTY6XDSVW5GF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TTT2ZLSCR6IHOPUTY6XDSVW5GF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TTT2ZLSCR6IHOPUTY6XDSVW5GF/action/storage_attestation","attest_author":"https://pith.science/pith/TTT2ZLSCR6IHOPUTY6XDSVW5GF/action/author_attestation","sign_citation":"https://pith.science/pith/TTT2ZLSCR6IHOPUTY6XDSVW5GF/action/citation_signature","submit_replication":"https://pith.science/pith/TTT2ZLSCR6IHOPUTY6XDSVW5GF/action/replication_record"}},"created_at":"2026-05-18T00:52:12.741033+00:00","updated_at":"2026-05-18T00:52:12.741033+00:00"}