{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6PRKPGAP25R6OEFVCINUKD62CO","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":"fe3176c97abc770d56ddbd1e7662a790ad9769fbbc7efd586ebd29323a7dce49","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-27T15:18:06Z","title_canon_sha256":"9c57b6914dc50393f2058d100b5e01e068a227090a7952df09192bfa7f7b27ae"},"schema_version":"1.0","source":{"id":"1511.08700","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08700","created_at":"2026-05-18T01:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08700v2","created_at":"2026-05-18T01:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08700","created_at":"2026-05-18T01:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"6PRKPGAP25R6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6PRKPGAP25R6OEFV","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6PRKPGAP","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:f3b6aabc518e93fba4b963304b74c360d69db57e1119ce26f31f3f979f3aa7ac","target":"graph","created_at":"2026-05-18T01:17:55Z","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":"We study amplify-and-forward (AF) relay networks operating with source and relay amplifier distortion, where the distortion dominates the noise power. The diversity order is shown to be $0$ for fixed-gain (FG) and $1$ for variable-gain (VG) if distortion occurs at the relay; if distortion occurs only at the source, the diversity order will be $1$ for both. With $\\epsilon_\\beta=N_0/\\eta_\\beta$ ($N_0$ the noise power, $\\eta_\\beta$ the distortion power at node $\\beta\\in\\{S,R\\}$, the source or relay), we demonstrate the emergence of what we call an $\\epsilon$-critical signal-to-noise plus distorti","authors_text":"David E. Simmons, Justin P. Coon","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-27T15:18:06Z","title":"Distortion Limited Amplify-and-forward Relay Networks and the $\\epsilon$-critical Phase Transition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08700","kind":"arxiv","version":2},"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:a269ca4a4a95370266ac1f2c6daa215baf72b3f0a09788e85b554a22efe346c6","target":"record","created_at":"2026-05-18T01:17:55Z","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":"fe3176c97abc770d56ddbd1e7662a790ad9769fbbc7efd586ebd29323a7dce49","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-27T15:18:06Z","title_canon_sha256":"9c57b6914dc50393f2058d100b5e01e068a227090a7952df09192bfa7f7b27ae"},"schema_version":"1.0","source":{"id":"1511.08700","kind":"arxiv","version":2}},"canonical_sha256":"f3e2a7980fd763e710b5121b450fda13a51b8d9b07f19fb7c72cb2dd3065f2f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3e2a7980fd763e710b5121b450fda13a51b8d9b07f19fb7c72cb2dd3065f2f3","first_computed_at":"2026-05-18T01:17:55.289962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:55.289962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6+UYBydw/TLnR6IGT0L9CVNrb2nMrGggyoRIbYsxJ1FyDYhXCcfTIaVmV9pIBeTK5YO9sqjFKM/NRLSCRhJmAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:55.290621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08700","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a269ca4a4a95370266ac1f2c6daa215baf72b3f0a09788e85b554a22efe346c6","sha256:f3b6aabc518e93fba4b963304b74c360d69db57e1119ce26f31f3f979f3aa7ac"],"state_sha256":"6b4524785e95816354b38db875d272b3dd8c427de2daa4e8c0e2f2714965dcdc"}