{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:AZODDHXIIFKZWDNEDDCOEU52KX","short_pith_number":"pith:AZODDHXI","canonical_record":{"source":{"id":"1102.5086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-24T20:56:37Z","cross_cats_sorted":[],"title_canon_sha256":"ef445fdeb0cbfe55733975b375dc0ef93af47447960d426fe5d95314c94a065e","abstract_canon_sha256":"7e08865815ed918c2294cc1563765a08ba382736d6f4cd42da8da990148a76ad"},"schema_version":"1.0"},"canonical_sha256":"065c319ee841559b0da418c4e253ba55cfa740678bbba149ce22a79dd75a1fc7","source":{"kind":"arxiv","id":"1102.5086","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5086","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5086v1","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5086","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"AZODDHXIIFKZ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AZODDHXIIFKZWDNE","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AZODDHXI","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:AZODDHXIIFKZWDNEDDCOEU52KX","target":"record","payload":{"canonical_record":{"source":{"id":"1102.5086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-24T20:56:37Z","cross_cats_sorted":[],"title_canon_sha256":"ef445fdeb0cbfe55733975b375dc0ef93af47447960d426fe5d95314c94a065e","abstract_canon_sha256":"7e08865815ed918c2294cc1563765a08ba382736d6f4cd42da8da990148a76ad"},"schema_version":"1.0"},"canonical_sha256":"065c319ee841559b0da418c4e253ba55cfa740678bbba149ce22a79dd75a1fc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:57.442905Z","signature_b64":"sCyHweRgzekPtXQ8AnR6RvzPEfVREwDKIDtFxH8Rl4QeD+1LtLLdvQzNYzcmfOlR+ef2MJCOJSdhut+jJco0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"065c319ee841559b0da418c4e253ba55cfa740678bbba149ce22a79dd75a1fc7","last_reissued_at":"2026-05-18T04:27:57.442240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:57.442240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.5086","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":"2026-05-18T04:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LUmlK13L1RYnKrohF6XGVgvaJ0letCGK8fX8+9csDlsGyZxdqLy4SStbdsh5FrGB0EmCVJo8kbZU6IHmyc9wBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:11:17.837914Z"},"content_sha256":"c376f09ccb08f90eb10ec456ec9f519df588a7a2875c28ba8692bf50ca7fdb7a","schema_version":"1.0","event_id":"sha256:c376f09ccb08f90eb10ec456ec9f519df588a7a2875c28ba8692bf50ca7fdb7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:AZODDHXIIFKZWDNEDDCOEU52KX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Determination of the Plancherel measure for Lebedev-Whittaker transforms on GL(n)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alex Kontorovich, Dorian Goldfeld","submitted_at":"2011-02-24T20:56:37Z","abstract_excerpt":"We give a simple derivation of the Plancherel measure for Lebedev-Whittaker transforms on GL(n)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5086","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":"2026-05-18T04:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KwdKH7Rd9N0Q2QnyX5LloDRF+iU/joLekFWxZDzumQCS5mVyWg4+u7PspiCChqxU8oeMSqSpFmhS8decBGqKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:11:17.838255Z"},"content_sha256":"3df760a6a9de22666220b34761629273e5c7c13b68e552a416ea303089536b59","schema_version":"1.0","event_id":"sha256:3df760a6a9de22666220b34761629273e5c7c13b68e552a416ea303089536b59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AZODDHXIIFKZWDNEDDCOEU52KX/bundle.json","state_url":"https://pith.science/pith/AZODDHXIIFKZWDNEDDCOEU52KX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AZODDHXIIFKZWDNEDDCOEU52KX/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":"2026-06-03T08:11:17Z","links":{"resolver":"https://pith.science/pith/AZODDHXIIFKZWDNEDDCOEU52KX","bundle":"https://pith.science/pith/AZODDHXIIFKZWDNEDDCOEU52KX/bundle.json","state":"https://pith.science/pith/AZODDHXIIFKZWDNEDDCOEU52KX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AZODDHXIIFKZWDNEDDCOEU52KX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AZODDHXIIFKZWDNEDDCOEU52KX","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":"7e08865815ed918c2294cc1563765a08ba382736d6f4cd42da8da990148a76ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-24T20:56:37Z","title_canon_sha256":"ef445fdeb0cbfe55733975b375dc0ef93af47447960d426fe5d95314c94a065e"},"schema_version":"1.0","source":{"id":"1102.5086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5086","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5086v1","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5086","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"AZODDHXIIFKZ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AZODDHXIIFKZWDNE","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AZODDHXI","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:3df760a6a9de22666220b34761629273e5c7c13b68e552a416ea303089536b59","target":"graph","created_at":"2026-05-18T04:27:57Z","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":"We give a simple derivation of the Plancherel measure for Lebedev-Whittaker transforms on GL(n).","authors_text":"Alex Kontorovich, Dorian Goldfeld","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-24T20:56:37Z","title":"On the Determination of the Plancherel measure for Lebedev-Whittaker transforms on GL(n)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5086","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:c376f09ccb08f90eb10ec456ec9f519df588a7a2875c28ba8692bf50ca7fdb7a","target":"record","created_at":"2026-05-18T04:27:57Z","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":"7e08865815ed918c2294cc1563765a08ba382736d6f4cd42da8da990148a76ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-24T20:56:37Z","title_canon_sha256":"ef445fdeb0cbfe55733975b375dc0ef93af47447960d426fe5d95314c94a065e"},"schema_version":"1.0","source":{"id":"1102.5086","kind":"arxiv","version":1}},"canonical_sha256":"065c319ee841559b0da418c4e253ba55cfa740678bbba149ce22a79dd75a1fc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"065c319ee841559b0da418c4e253ba55cfa740678bbba149ce22a79dd75a1fc7","first_computed_at":"2026-05-18T04:27:57.442240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:57.442240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sCyHweRgzekPtXQ8AnR6RvzPEfVREwDKIDtFxH8Rl4QeD+1LtLLdvQzNYzcmfOlR+ef2MJCOJSdhut+jJco0AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:57.442905Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c376f09ccb08f90eb10ec456ec9f519df588a7a2875c28ba8692bf50ca7fdb7a","sha256:3df760a6a9de22666220b34761629273e5c7c13b68e552a416ea303089536b59"],"state_sha256":"6ca64641a5674ab0e3979daf146a392da0be4a99b4d51bdc932ae098902414a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2udQ6C1YvMQVVIKBxuUGveEYSlOqPIpn7jz8+Y9kO43wtyUQjePRgYQoCEiZeYqu5q+CSoXv2XDkYpNQQAnyBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:11:17.840248Z","bundle_sha256":"0b3b2c86ed99842251e68b5857af20faaab258dcf1aab4dbaf10887fc5468fff"}}