{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:I445EYQXOQB7ECOP73Y4TPJMG6","short_pith_number":"pith:I445EYQX","canonical_record":{"source":{"id":"1604.06993","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-24T07:55:08Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"239d552bef148a9b8ea2457bda7be0977367fc265567e9798369d052ae98817b","abstract_canon_sha256":"08c7c424d8d3030f1d8865c3af23cacf9329c67268b1aafa5c5e4acdaf3c25da"},"schema_version":"1.0"},"canonical_sha256":"4739d262177403f209cffef1c9bd2c378849c590fef1552e706f725090f37ba3","source":{"kind":"arxiv","id":"1604.06993","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06993","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06993v5","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06993","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"pith_short_12","alias_value":"I445EYQXOQB7","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I445EYQXOQB7ECOP","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I445EYQX","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:I445EYQXOQB7ECOP73Y4TPJMG6","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06993","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-24T07:55:08Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"239d552bef148a9b8ea2457bda7be0977367fc265567e9798369d052ae98817b","abstract_canon_sha256":"08c7c424d8d3030f1d8865c3af23cacf9329c67268b1aafa5c5e4acdaf3c25da"},"schema_version":"1.0"},"canonical_sha256":"4739d262177403f209cffef1c9bd2c378849c590fef1552e706f725090f37ba3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:54.602616Z","signature_b64":"A79I9iCzvOPGANHbG12v9/D4flugXaNj1bvQKKewvtfIAF0ODK/+1G5J6StM60/iuux7ZRdvuwxOftS3NbngAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4739d262177403f209cffef1c9bd2c378849c590fef1552e706f725090f37ba3","last_reissued_at":"2026-05-18T00:48:54.601873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:54.601873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06993","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VEJL7inJ9X0S/2WjudQiZ07kx4hqXsEmIjiU3zMaF+ME3UAGJt1hmw2aEJC89C2MvF+WmL/wcGKdmDHgDXxJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:46:37.617425Z"},"content_sha256":"fee3e922f801a78e39a96066746c94d4b5ec301fd9710c3277a5947b2f8cae63","schema_version":"1.0","event_id":"sha256:fee3e922f801a78e39a96066746c94d4b5ec301fd9710c3277a5947b2f8cae63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:I445EYQXOQB7ECOP73Y4TPJMG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moment Generating Functions of Generalized Wireless Fading Channels and Applications in Wireless Communication Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ahmed Kulaib, Ali Hakam, Ehab Salahat, Nazar Ali","submitted_at":"2016-04-24T07:55:08Z","abstract_excerpt":"In this paper, new exact and approximate moment generating functions (MGF) expression for generalized fading models are derived. Specifically, we consider the ${\\eta}-{\\lambda}-{\\mu}$, ${\\alpha}-{\\mu}$, ${\\alpha}-{\\eta}-{\\mu}$, ${\\alpha}-{\\lambda}-{\\mu}$, ${\\alpha}-{\\kappa}-{\\mu}$, and ${\\alpha}-{\\lambda}-{\\eta}-{\\mu}$ generalized fading distributions to derive approximate MGF expressions. The new expressions are very accurate and, in contrast to earlier results in the literature, avoid any complicated special functions, e.g. the Meijer-$G$ and Fox $H$-functions. As such, the new MGF expressio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06993","kind":"arxiv","version":5},"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":"2026-05-18T00:48:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/wtCYPxCetJJSqArB4tXc7duCtM62l+ROTsmqAODR+C7CQLyalqXyKSjqMqyski7hNa+m6fdAeGjJicWmkRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:46:37.617762Z"},"content_sha256":"f795707a7a91ff913d00a3d3334bbfb4ef13302430668538fe094fb7e8f98514","schema_version":"1.0","event_id":"sha256:f795707a7a91ff913d00a3d3334bbfb4ef13302430668538fe094fb7e8f98514"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I445EYQXOQB7ECOP73Y4TPJMG6/bundle.json","state_url":"https://pith.science/pith/I445EYQXOQB7ECOP73Y4TPJMG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I445EYQXOQB7ECOP73Y4TPJMG6/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":"2026-06-29T08:46:37Z","links":{"resolver":"https://pith.science/pith/I445EYQXOQB7ECOP73Y4TPJMG6","bundle":"https://pith.science/pith/I445EYQXOQB7ECOP73Y4TPJMG6/bundle.json","state":"https://pith.science/pith/I445EYQXOQB7ECOP73Y4TPJMG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I445EYQXOQB7ECOP73Y4TPJMG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I445EYQXOQB7ECOP73Y4TPJMG6","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":"08c7c424d8d3030f1d8865c3af23cacf9329c67268b1aafa5c5e4acdaf3c25da","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-24T07:55:08Z","title_canon_sha256":"239d552bef148a9b8ea2457bda7be0977367fc265567e9798369d052ae98817b"},"schema_version":"1.0","source":{"id":"1604.06993","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06993","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06993v5","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06993","created_at":"2026-05-18T00:48:54Z"},{"alias_kind":"pith_short_12","alias_value":"I445EYQXOQB7","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I445EYQXOQB7ECOP","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I445EYQX","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:f795707a7a91ff913d00a3d3334bbfb4ef13302430668538fe094fb7e8f98514","target":"graph","created_at":"2026-05-18T00:48:54Z","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":"In this paper, new exact and approximate moment generating functions (MGF) expression for generalized fading models are derived. Specifically, we consider the ${\\eta}-{\\lambda}-{\\mu}$, ${\\alpha}-{\\mu}$, ${\\alpha}-{\\eta}-{\\mu}$, ${\\alpha}-{\\lambda}-{\\mu}$, ${\\alpha}-{\\kappa}-{\\mu}$, and ${\\alpha}-{\\lambda}-{\\eta}-{\\mu}$ generalized fading distributions to derive approximate MGF expressions. The new expressions are very accurate and, in contrast to earlier results in the literature, avoid any complicated special functions, e.g. the Meijer-$G$ and Fox $H$-functions. As such, the new MGF expressio","authors_text":"Ahmed Kulaib, Ali Hakam, Ehab Salahat, Nazar Ali","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-24T07:55:08Z","title":"Moment Generating Functions of Generalized Wireless Fading Channels and Applications in Wireless Communication Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06993","kind":"arxiv","version":5},"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:fee3e922f801a78e39a96066746c94d4b5ec301fd9710c3277a5947b2f8cae63","target":"record","created_at":"2026-05-18T00:48:54Z","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":"08c7c424d8d3030f1d8865c3af23cacf9329c67268b1aafa5c5e4acdaf3c25da","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-24T07:55:08Z","title_canon_sha256":"239d552bef148a9b8ea2457bda7be0977367fc265567e9798369d052ae98817b"},"schema_version":"1.0","source":{"id":"1604.06993","kind":"arxiv","version":5}},"canonical_sha256":"4739d262177403f209cffef1c9bd2c378849c590fef1552e706f725090f37ba3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4739d262177403f209cffef1c9bd2c378849c590fef1552e706f725090f37ba3","first_computed_at":"2026-05-18T00:48:54.601873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:54.601873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A79I9iCzvOPGANHbG12v9/D4flugXaNj1bvQKKewvtfIAF0ODK/+1G5J6StM60/iuux7ZRdvuwxOftS3NbngAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:54.602616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06993","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fee3e922f801a78e39a96066746c94d4b5ec301fd9710c3277a5947b2f8cae63","sha256:f795707a7a91ff913d00a3d3334bbfb4ef13302430668538fe094fb7e8f98514"],"state_sha256":"1a8282f11801e017e6b9a1dee355000d02b7741cc9a5c62cf3cadad53dc943f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHFhc4aGU4243r6eID0wmZykNFVO6REto6YwKxrBqHDk/2xAcEXgFN/GgMPB6xVPCRyFo9MSoEc4tI65RmQ6BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T08:46:37.619639Z","bundle_sha256":"fdd757acfb15ca0d4951233be9bd9ee929103ac9d9a47c5df3ac86bb6274277c"}}