{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PYXFYFM3YA2L2TPXYATWVN7KBM","short_pith_number":"pith:PYXFYFM3","canonical_record":{"source":{"id":"1510.05557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-19T16:05:56Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d5dbcb87d14429ea48255c2c690c2c7dfcb8c2c2665286f1c1e7ca54642fc1f4","abstract_canon_sha256":"1cb0a744d17856363ffd62bd5c0e127e3ad3d42f39bf758b37b8001d78b715d4"},"schema_version":"1.0"},"canonical_sha256":"7e2e5c159bc034bd4df7c0276ab7ea0b037986751bc2fe7fdbd78ddde203ba89","source":{"kind":"arxiv","id":"1510.05557","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05557","created_at":"2026-05-18T00:58:34Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05557v1","created_at":"2026-05-18T00:58:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05557","created_at":"2026-05-18T00:58:34Z"},{"alias_kind":"pith_short_12","alias_value":"PYXFYFM3YA2L","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PYXFYFM3YA2L2TPX","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PYXFYFM3","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PYXFYFM3YA2L2TPXYATWVN7KBM","target":"record","payload":{"canonical_record":{"source":{"id":"1510.05557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-19T16:05:56Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d5dbcb87d14429ea48255c2c690c2c7dfcb8c2c2665286f1c1e7ca54642fc1f4","abstract_canon_sha256":"1cb0a744d17856363ffd62bd5c0e127e3ad3d42f39bf758b37b8001d78b715d4"},"schema_version":"1.0"},"canonical_sha256":"7e2e5c159bc034bd4df7c0276ab7ea0b037986751bc2fe7fdbd78ddde203ba89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:34.754554Z","signature_b64":"7BIgtlMwqK/T8Ape83N/3YttIPlA0hrNufspAVvmKHnLZMA2j29pdysqsAbyP5V78C4FfLqbqD+9iICC2De3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e2e5c159bc034bd4df7c0276ab7ea0b037986751bc2fe7fdbd78ddde203ba89","last_reissued_at":"2026-05-18T00:58:34.753804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:34.753804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.05557","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":"2026-05-18T00:58:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GuA1aBgGotgdozvw9rO6LqpRA2a+YwRz2d+QcB5nLAnQt6Hf7KSQIohhu6/8fj2cuOEngrx0ZOgLSvaQ9vL4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:06:29.542392Z"},"content_sha256":"88c500b035439c9260b13f5d738bf3e073049429def0143d376da5fc6011c7c5","schema_version":"1.0","event_id":"sha256:88c500b035439c9260b13f5d738bf3e073049429def0143d376da5fc6011c7c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PYXFYFM3YA2L2TPXYATWVN7KBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Saddle Point Approximation for Outage Probability Using Cumulant Generating Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ekram Hossain, Hina Tabassum, Sudarshan Guruacharya","submitted_at":"2015-10-19T16:05:56Z","abstract_excerpt":"This letter proposes the use of saddle point approximation (SPA) to evaluate the outage probability of wireless cellular networks. Unlike traditional numerical integration-based approaches, the SPA approach relies on cumulant generating functions (CGFs) and eliminates the need for explicit numerical integration. The approach is generic and can be applied to a wide variety of distributions, given that their CGFs exist. We illustrate the usefulness of SPA on channel fading distributions such as Nakagami-$m$, Nakagami-$q$ (Hoyt), and Rician distributions. Numerical results validate the accuracy o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05557","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":"2026-05-18T00:58:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Onw8Bxtkr2BN+tKpuHgqJVlvGsoaE1Nx2Wgrb9qWs9mBxL4ezcJ/+X+X8+BuO2bF5E3IPxfgxRcFK7uFllrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:06:29.542968Z"},"content_sha256":"9cda414531e0b3349dcc0d2dd0d9445a0bd31a996ba37bf36db4c87d66ed348c","schema_version":"1.0","event_id":"sha256:9cda414531e0b3349dcc0d2dd0d9445a0bd31a996ba37bf36db4c87d66ed348c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PYXFYFM3YA2L2TPXYATWVN7KBM/bundle.json","state_url":"https://pith.science/pith/PYXFYFM3YA2L2TPXYATWVN7KBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PYXFYFM3YA2L2TPXYATWVN7KBM/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":"2026-05-31T05:06:29Z","links":{"resolver":"https://pith.science/pith/PYXFYFM3YA2L2TPXYATWVN7KBM","bundle":"https://pith.science/pith/PYXFYFM3YA2L2TPXYATWVN7KBM/bundle.json","state":"https://pith.science/pith/PYXFYFM3YA2L2TPXYATWVN7KBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PYXFYFM3YA2L2TPXYATWVN7KBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PYXFYFM3YA2L2TPXYATWVN7KBM","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":"1cb0a744d17856363ffd62bd5c0e127e3ad3d42f39bf758b37b8001d78b715d4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-19T16:05:56Z","title_canon_sha256":"d5dbcb87d14429ea48255c2c690c2c7dfcb8c2c2665286f1c1e7ca54642fc1f4"},"schema_version":"1.0","source":{"id":"1510.05557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05557","created_at":"2026-05-18T00:58:34Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05557v1","created_at":"2026-05-18T00:58:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05557","created_at":"2026-05-18T00:58:34Z"},{"alias_kind":"pith_short_12","alias_value":"PYXFYFM3YA2L","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PYXFYFM3YA2L2TPX","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PYXFYFM3","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:9cda414531e0b3349dcc0d2dd0d9445a0bd31a996ba37bf36db4c87d66ed348c","target":"graph","created_at":"2026-05-18T00:58:34Z","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":"This letter proposes the use of saddle point approximation (SPA) to evaluate the outage probability of wireless cellular networks. Unlike traditional numerical integration-based approaches, the SPA approach relies on cumulant generating functions (CGFs) and eliminates the need for explicit numerical integration. The approach is generic and can be applied to a wide variety of distributions, given that their CGFs exist. We illustrate the usefulness of SPA on channel fading distributions such as Nakagami-$m$, Nakagami-$q$ (Hoyt), and Rician distributions. Numerical results validate the accuracy o","authors_text":"Ekram Hossain, Hina Tabassum, Sudarshan Guruacharya","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-19T16:05:56Z","title":"Saddle Point Approximation for Outage Probability Using Cumulant Generating Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05557","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":"sha256:88c500b035439c9260b13f5d738bf3e073049429def0143d376da5fc6011c7c5","target":"record","created_at":"2026-05-18T00:58:34Z","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":"1cb0a744d17856363ffd62bd5c0e127e3ad3d42f39bf758b37b8001d78b715d4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-19T16:05:56Z","title_canon_sha256":"d5dbcb87d14429ea48255c2c690c2c7dfcb8c2c2665286f1c1e7ca54642fc1f4"},"schema_version":"1.0","source":{"id":"1510.05557","kind":"arxiv","version":1}},"canonical_sha256":"7e2e5c159bc034bd4df7c0276ab7ea0b037986751bc2fe7fdbd78ddde203ba89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e2e5c159bc034bd4df7c0276ab7ea0b037986751bc2fe7fdbd78ddde203ba89","first_computed_at":"2026-05-18T00:58:34.753804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:34.753804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7BIgtlMwqK/T8Ape83N/3YttIPlA0hrNufspAVvmKHnLZMA2j29pdysqsAbyP5V78C4FfLqbqD+9iICC2De3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:34.754554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88c500b035439c9260b13f5d738bf3e073049429def0143d376da5fc6011c7c5","sha256:9cda414531e0b3349dcc0d2dd0d9445a0bd31a996ba37bf36db4c87d66ed348c"],"state_sha256":"2c42237a31bdcf93dc12b0377e9046d369a6d6ac2fe5dddc074024c9521bc213"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mxxYFsV61jqg8pJWQwiis1ytmZaYK2R7IacsQ49MCXbB50ZSlki7OZCEfx1LGGBnvZFpoKrBgsmJuhQ5jb02Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:06:29.545349Z","bundle_sha256":"e62e04321a697053bea22113a19aaff8c65c5a1890a395f7734f74a0c7fc046b"}}