{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PVHR6THG6E627UVQAIJ6URQQYO","short_pith_number":"pith:PVHR6THG","canonical_record":{"source":{"id":"1209.4122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-09-18T23:53:56Z","cross_cats_sorted":[],"title_canon_sha256":"5a4eae181f58a732e1164ed1321ccd5e6260b04ccb35bb768d2cbcafdb455ef2","abstract_canon_sha256":"f1ce663f61e5d2168d8992cbf619a3aa1b69ef4c1f95b3749cb147e3ff4973c2"},"schema_version":"1.0"},"canonical_sha256":"7d4f1f4ce6f13dafd2b00213ea4610c381824a1b9ba21fb8993278def2b9a704","source":{"kind":"arxiv","id":"1209.4122","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4122","created_at":"2026-05-18T03:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4122v1","created_at":"2026-05-18T03:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4122","created_at":"2026-05-18T03:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"PVHR6THG6E62","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PVHR6THG6E627UVQ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PVHR6THG","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PVHR6THG6E627UVQAIJ6URQQYO","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-09-18T23:53:56Z","cross_cats_sorted":[],"title_canon_sha256":"5a4eae181f58a732e1164ed1321ccd5e6260b04ccb35bb768d2cbcafdb455ef2","abstract_canon_sha256":"f1ce663f61e5d2168d8992cbf619a3aa1b69ef4c1f95b3749cb147e3ff4973c2"},"schema_version":"1.0"},"canonical_sha256":"7d4f1f4ce6f13dafd2b00213ea4610c381824a1b9ba21fb8993278def2b9a704","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:47.971127Z","signature_b64":"ULsYf87t/osIGxg8WtOXBb49So6QAXFx/etOYI5X0hGHf5X3kP4LoXeovPdqlxJAmO1MTQWzvKhHuu1bK1UpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d4f1f4ce6f13dafd2b00213ea4610c381824a1b9ba21fb8993278def2b9a704","last_reissued_at":"2026-05-18T03:33:47.970373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:47.970373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4122","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":"2026-05-18T03:33:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"deM6fP1Nm9fR3KtXDVX9YX9NY5brK1LCEWAptytPZPiXEvdXpys2+lB/pTinBDOxJ1Nj5k+hKoSJ0gtLdzcGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:42:50.707258Z"},"content_sha256":"5b142c051c8120d5adc0cb08b1bdb2deb122a08ce6a92a595889cadd779e5de1","schema_version":"1.0","event_id":"sha256:5b142c051c8120d5adc0cb08b1bdb2deb122a08ce6a92a595889cadd779e5de1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PVHR6THG6E627UVQAIJ6URQQYO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fourier Transforms of Nilpotent, Coadjoint Orbits for GL(n,R)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Benjamin Harris","submitted_at":"2012-09-18T23:53:56Z","abstract_excerpt":"The main result of this paper is an explicit formula for the Fourier transform of the canonical measure on a nilpotent coadjoint orbit for GL(n,R). This paper also includes some results on limit formulas for reductive Lie groups including new proofs of classical limit formulas of Rao and Harish-Chandra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4122","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":"2026-05-18T03:33:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DF0Dlv1TvK2zVf1WDZW/xQz/Ts3/19C1QsIi4z6drBdqmlS9ApfVU3FIJnV8oYu0H7+coCY0pNjoYmVfWVYCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:42:50.707995Z"},"content_sha256":"e31edf0105a99fce2156e7db486a73c35f45db792b4103dee82e9a1178387d9d","schema_version":"1.0","event_id":"sha256:e31edf0105a99fce2156e7db486a73c35f45db792b4103dee82e9a1178387d9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PVHR6THG6E627UVQAIJ6URQQYO/bundle.json","state_url":"https://pith.science/pith/PVHR6THG6E627UVQAIJ6URQQYO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PVHR6THG6E627UVQAIJ6URQQYO/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":"2026-06-09T05:42:50Z","links":{"resolver":"https://pith.science/pith/PVHR6THG6E627UVQAIJ6URQQYO","bundle":"https://pith.science/pith/PVHR6THG6E627UVQAIJ6URQQYO/bundle.json","state":"https://pith.science/pith/PVHR6THG6E627UVQAIJ6URQQYO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PVHR6THG6E627UVQAIJ6URQQYO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PVHR6THG6E627UVQAIJ6URQQYO","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":"f1ce663f61e5d2168d8992cbf619a3aa1b69ef4c1f95b3749cb147e3ff4973c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-09-18T23:53:56Z","title_canon_sha256":"5a4eae181f58a732e1164ed1321ccd5e6260b04ccb35bb768d2cbcafdb455ef2"},"schema_version":"1.0","source":{"id":"1209.4122","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4122","created_at":"2026-05-18T03:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4122v1","created_at":"2026-05-18T03:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4122","created_at":"2026-05-18T03:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"PVHR6THG6E62","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PVHR6THG6E627UVQ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PVHR6THG","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:e31edf0105a99fce2156e7db486a73c35f45db792b4103dee82e9a1178387d9d","target":"graph","created_at":"2026-05-18T03:33:47Z","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":"The main result of this paper is an explicit formula for the Fourier transform of the canonical measure on a nilpotent coadjoint orbit for GL(n,R). This paper also includes some results on limit formulas for reductive Lie groups including new proofs of classical limit formulas of Rao and Harish-Chandra.","authors_text":"Benjamin Harris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-09-18T23:53:56Z","title":"Fourier Transforms of Nilpotent, Coadjoint Orbits for GL(n,R)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4122","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":"sha256:5b142c051c8120d5adc0cb08b1bdb2deb122a08ce6a92a595889cadd779e5de1","target":"record","created_at":"2026-05-18T03:33:47Z","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":"f1ce663f61e5d2168d8992cbf619a3aa1b69ef4c1f95b3749cb147e3ff4973c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-09-18T23:53:56Z","title_canon_sha256":"5a4eae181f58a732e1164ed1321ccd5e6260b04ccb35bb768d2cbcafdb455ef2"},"schema_version":"1.0","source":{"id":"1209.4122","kind":"arxiv","version":1}},"canonical_sha256":"7d4f1f4ce6f13dafd2b00213ea4610c381824a1b9ba21fb8993278def2b9a704","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d4f1f4ce6f13dafd2b00213ea4610c381824a1b9ba21fb8993278def2b9a704","first_computed_at":"2026-05-18T03:33:47.970373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:47.970373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ULsYf87t/osIGxg8WtOXBb49So6QAXFx/etOYI5X0hGHf5X3kP4LoXeovPdqlxJAmO1MTQWzvKhHuu1bK1UpCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:47.971127Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4122","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b142c051c8120d5adc0cb08b1bdb2deb122a08ce6a92a595889cadd779e5de1","sha256:e31edf0105a99fce2156e7db486a73c35f45db792b4103dee82e9a1178387d9d"],"state_sha256":"33f92e12a564b5fb4f9db778e23bc0bca679ca429a7a490ee41e84a7a23e3e13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lmfKF5PmYtZW/XQXcL9uRd6BJmY2kERDKpETc5jwICJm2/9ff7OO3wbQkcSWUtv7q1KqsMu3zhpg+k3U0uO4AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:42:50.712054Z","bundle_sha256":"e3d601ed6336f4dd955f94779eb3d78afc6b80ea6946d8dd404e2c066bd55acc"}}