{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:X52NSPSZWZFKO7JP7JF3FIOD6W","short_pith_number":"pith:X52NSPSZ","canonical_record":{"source":{"id":"1703.03709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-10T15:15:58Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"0fc9c4b86579326d5d99fa291e359f78dd34ef7109c1c9b676bce6089795b3a2","abstract_canon_sha256":"93fa086b181bbff181da6bd31dfad52334253b95d89e40a7b4c52fb7bc2745c9"},"schema_version":"1.0"},"canonical_sha256":"bf74d93e59b64aa77d2ffa4bb2a1c3f5ab78faa63055e49e687b029f9b2bda02","source":{"kind":"arxiv","id":"1703.03709","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03709","created_at":"2026-05-17T23:57:32Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03709v2","created_at":"2026-05-17T23:57:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03709","created_at":"2026-05-17T23:57:32Z"},{"alias_kind":"pith_short_12","alias_value":"X52NSPSZWZFK","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X52NSPSZWZFKO7JP","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X52NSPSZ","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:X52NSPSZWZFKO7JP7JF3FIOD6W","target":"record","payload":{"canonical_record":{"source":{"id":"1703.03709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-10T15:15:58Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"0fc9c4b86579326d5d99fa291e359f78dd34ef7109c1c9b676bce6089795b3a2","abstract_canon_sha256":"93fa086b181bbff181da6bd31dfad52334253b95d89e40a7b4c52fb7bc2745c9"},"schema_version":"1.0"},"canonical_sha256":"bf74d93e59b64aa77d2ffa4bb2a1c3f5ab78faa63055e49e687b029f9b2bda02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:32.995253Z","signature_b64":"afqWGwoWS19ppDRtfDp2GiRBJ+6eDXrUSYIfjcOy0IDUJGbdCbKzvxjCnygGZ/7aPFzu9mEegEu6eFY/nzjBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf74d93e59b64aa77d2ffa4bb2a1c3f5ab78faa63055e49e687b029f9b2bda02","last_reissued_at":"2026-05-17T23:57:32.994556Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:32.994556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.03709","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jLlt8kNdQKGM57DtX8E155b/nqNLlpGHU34AuAzEfRZtrmB6+if4v5p81RgoZaAyZ+L12xWqeS8VR3PWtSazBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T02:21:27.464513Z"},"content_sha256":"2ba3f48d82c77bcc871c0413576af22cad8ed9511aa4058b529df3420a09cafc","schema_version":"1.0","event_id":"sha256:2ba3f48d82c77bcc871c0413576af22cad8ed9511aa4058b529df3420a09cafc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:X52NSPSZWZFKO7JP7JF3FIOD6W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral theory for non-unitary twists","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.FA","authors_text":"Anton Deitmar","submitted_at":"2017-03-10T15:15:58Z","abstract_excerpt":"Let $G$ be a Lie-group and $\\Ga\\subset G$ a cocompact lattice. For a finite-dimensional, not necessarily unitary representation $\\om$ of $\\Ga$ we show that the $G$-representation on $L^2(\\Ga\\bs G,\\om)$ admits a complete filtration with irreducible quotients. As a consequence, we show the trace formula for non-unitary twists and arbitrary locally compact groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03709","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nI8L7S64O98djAWZZjQXutXMY9+AT9VIPN/eo4fIc69dwrPGC/gxUDqhH14KFsITWHgFlVz06GpoDhts0mkbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T02:21:27.464860Z"},"content_sha256":"8f91b98ff517924ebd6810673b93ebf41435ddac4f627c8fd12fe036bfadb103","schema_version":"1.0","event_id":"sha256:8f91b98ff517924ebd6810673b93ebf41435ddac4f627c8fd12fe036bfadb103"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X52NSPSZWZFKO7JP7JF3FIOD6W/bundle.json","state_url":"https://pith.science/pith/X52NSPSZWZFKO7JP7JF3FIOD6W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X52NSPSZWZFKO7JP7JF3FIOD6W/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":"2026-07-03T02:21:27Z","links":{"resolver":"https://pith.science/pith/X52NSPSZWZFKO7JP7JF3FIOD6W","bundle":"https://pith.science/pith/X52NSPSZWZFKO7JP7JF3FIOD6W/bundle.json","state":"https://pith.science/pith/X52NSPSZWZFKO7JP7JF3FIOD6W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X52NSPSZWZFKO7JP7JF3FIOD6W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:X52NSPSZWZFKO7JP7JF3FIOD6W","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":"93fa086b181bbff181da6bd31dfad52334253b95d89e40a7b4c52fb7bc2745c9","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-10T15:15:58Z","title_canon_sha256":"0fc9c4b86579326d5d99fa291e359f78dd34ef7109c1c9b676bce6089795b3a2"},"schema_version":"1.0","source":{"id":"1703.03709","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03709","created_at":"2026-05-17T23:57:32Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03709v2","created_at":"2026-05-17T23:57:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03709","created_at":"2026-05-17T23:57:32Z"},{"alias_kind":"pith_short_12","alias_value":"X52NSPSZWZFK","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X52NSPSZWZFKO7JP","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X52NSPSZ","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:8f91b98ff517924ebd6810673b93ebf41435ddac4f627c8fd12fe036bfadb103","target":"graph","created_at":"2026-05-17T23:57:32Z","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"},"paper":{"abstract_excerpt":"Let $G$ be a Lie-group and $\\Ga\\subset G$ a cocompact lattice. For a finite-dimensional, not necessarily unitary representation $\\om$ of $\\Ga$ we show that the $G$-representation on $L^2(\\Ga\\bs G,\\om)$ admits a complete filtration with irreducible quotients. As a consequence, we show the trace formula for non-unitary twists and arbitrary locally compact groups.","authors_text":"Anton Deitmar","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-10T15:15:58Z","title":"Spectral theory for non-unitary twists"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03709","kind":"arxiv","version":2},"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":"sha256:2ba3f48d82c77bcc871c0413576af22cad8ed9511aa4058b529df3420a09cafc","target":"record","created_at":"2026-05-17T23:57:32Z","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":"93fa086b181bbff181da6bd31dfad52334253b95d89e40a7b4c52fb7bc2745c9","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-10T15:15:58Z","title_canon_sha256":"0fc9c4b86579326d5d99fa291e359f78dd34ef7109c1c9b676bce6089795b3a2"},"schema_version":"1.0","source":{"id":"1703.03709","kind":"arxiv","version":2}},"canonical_sha256":"bf74d93e59b64aa77d2ffa4bb2a1c3f5ab78faa63055e49e687b029f9b2bda02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf74d93e59b64aa77d2ffa4bb2a1c3f5ab78faa63055e49e687b029f9b2bda02","first_computed_at":"2026-05-17T23:57:32.994556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:32.994556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"afqWGwoWS19ppDRtfDp2GiRBJ+6eDXrUSYIfjcOy0IDUJGbdCbKzvxjCnygGZ/7aPFzu9mEegEu6eFY/nzjBDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:32.995253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.03709","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ba3f48d82c77bcc871c0413576af22cad8ed9511aa4058b529df3420a09cafc","sha256:8f91b98ff517924ebd6810673b93ebf41435ddac4f627c8fd12fe036bfadb103"],"state_sha256":"78b8cfad97fea1ffd91771eb223b0c566b4614d070107fb663062fd853775438"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pyOEbuTQlcrpAIq+j3R8iHSC1PKpdoOOEQO8NUrtaZ68e2U0A3WbNsJeHNOtfCfxhzAuLmMKoAfOoJDg5gxzAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T02:21:27.466768Z","bundle_sha256":"cbd2205a590c39543a220e8def7683a3d571d839683bb33907a9cc3527766cee"}}