{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:KT6FCZ7Z3BMJV7SA3VS4EY4PKO","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":"3a6161cb0c579166f32c29c15598b367a01ee2a72777bff14253d4e9a0547403","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-04-18T16:34:54Z","title_canon_sha256":"fb6abd21c964e58107a9b7ed69826c319d263d39a3b370e30895ebe91a6642c9"},"schema_version":"1.0","source":{"id":"2004.08660","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.08660","created_at":"2026-07-05T00:56:08Z"},{"alias_kind":"arxiv_version","alias_value":"2004.08660v1","created_at":"2026-07-05T00:56:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.08660","created_at":"2026-07-05T00:56:08Z"},{"alias_kind":"pith_short_12","alias_value":"KT6FCZ7Z3BMJ","created_at":"2026-07-05T00:56:08Z"},{"alias_kind":"pith_short_16","alias_value":"KT6FCZ7Z3BMJV7SA","created_at":"2026-07-05T00:56:08Z"},{"alias_kind":"pith_short_8","alias_value":"KT6FCZ7Z","created_at":"2026-07-05T00:56:08Z"}],"graph_snapshots":[{"event_id":"sha256:186fad596a51134e879ee032a85fb682aab2e795cc53ed309e76fbd83fff42f9","target":"graph","created_at":"2026-07-05T00:56:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2004.08660/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce the degenerate gamma random variables which are connected with the degenerate gamma functions and the degenerate exponential functions, and deduce the expectation and variance of those random variables.","authors_text":"Dae San Kim, Hyunseok Lee, Jongkyum Kwon, Taekyun Kim","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-04-18T16:34:54Z","title":"A note on degenerate gamma random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.08660","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:aaec8a8469caa1bd828180d5491c9f4b1f253d245398fb474b8e0d908d5bfef0","target":"record","created_at":"2026-07-05T00:56:08Z","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":"3a6161cb0c579166f32c29c15598b367a01ee2a72777bff14253d4e9a0547403","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-04-18T16:34:54Z","title_canon_sha256":"fb6abd21c964e58107a9b7ed69826c319d263d39a3b370e30895ebe91a6642c9"},"schema_version":"1.0","source":{"id":"2004.08660","kind":"arxiv","version":1}},"canonical_sha256":"54fc5167f9d8589afe40dd65c2638f53843aaa3165dae90d199e98f5638562c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54fc5167f9d8589afe40dd65c2638f53843aaa3165dae90d199e98f5638562c5","first_computed_at":"2026-07-05T00:56:08.249255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:56:08.249255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wjZ83lbyKWhIHQRKyuo57LJTe95h59oxJRePwZGPF4cBoOlieZgh7L/0bRU1JNL7jMNVqiQuuNL13is1kQ/CAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:56:08.249738Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.08660","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaec8a8469caa1bd828180d5491c9f4b1f253d245398fb474b8e0d908d5bfef0","sha256:186fad596a51134e879ee032a85fb682aab2e795cc53ed309e76fbd83fff42f9"],"state_sha256":"f11fcebfb6a7a39fbcc7e067c05efa724dd7d3f5bd13be34f803f29c58670668"}