{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GPRKCXZGZURPQMBBCHOHUJG63C","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":"d65dfc101d25219a1d84a8a26324b62ff3a92742f5d6627477f972f261f79a8c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-13T16:06:19Z","title_canon_sha256":"8b65271ed94e381ec346564ba847b406289bed30abf9f18710abb6cf43189c7b"},"schema_version":"1.0","source":{"id":"1506.04283","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04283","created_at":"2026-05-18T01:49:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04283v1","created_at":"2026-05-18T01:49:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04283","created_at":"2026-05-18T01:49:55Z"},{"alias_kind":"pith_short_12","alias_value":"GPRKCXZGZURP","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GPRKCXZGZURPQMBB","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GPRKCXZG","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:bea1d51f7f1dcdc0f4a303d47cc21c3da9fd52f71304b640f8aae2a88f802b36","target":"graph","created_at":"2026-05-18T01:49:55Z","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":"Using fractional-calculus mathematics, a novel approach is introduced to rewrite modified Bessel functions in series form using simple elementary functions. Then, a statistical characterization of the total receive-SNR at the destination, corresponding to the source-relay-destination and the source-destination link SNR, is provided for a general relaying scenario, in which the destination exploits a maximum ratio combining (MRC) receiver. Using the novel statistical model for the total receive SNR at the destination, accurate and simple analytical expressions for the outage probability, the bi","authors_text":"Mehdi M. Molu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-13T16:06:19Z","title":"Series Representation of Modified Bessel Functions and Its Application in AF Cooperative systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04283","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":"sha256:99c59885417d52a0fe3aab4614f4a83e1ce4f21bab65dae8d6290b12352fae78","target":"record","created_at":"2026-05-18T01:49:55Z","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":"d65dfc101d25219a1d84a8a26324b62ff3a92742f5d6627477f972f261f79a8c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-13T16:06:19Z","title_canon_sha256":"8b65271ed94e381ec346564ba847b406289bed30abf9f18710abb6cf43189c7b"},"schema_version":"1.0","source":{"id":"1506.04283","kind":"arxiv","version":1}},"canonical_sha256":"33e2a15f26cd22f8302111dc7a24ded8889ac27628097b6276faedd3137cdf87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33e2a15f26cd22f8302111dc7a24ded8889ac27628097b6276faedd3137cdf87","first_computed_at":"2026-05-18T01:49:55.026186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:55.026186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lG16JTSUFfOjz8YEetLLcVErQSJagZ491CKZ+JSfSptnLOnlIveSguY2kE21+F+mxjedceUOxRfpL1RKQQEtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:55.026850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04283","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99c59885417d52a0fe3aab4614f4a83e1ce4f21bab65dae8d6290b12352fae78","sha256:bea1d51f7f1dcdc0f4a303d47cc21c3da9fd52f71304b640f8aae2a88f802b36"],"state_sha256":"5588a19b891a103fc9cc9c90d4281f275f577b89c61357fb20fbafd11eb46861"}