The Mechanism · Gated-generation receipt

gen-state-process-capability-index-cpk-precisely-and-explain-why-ca23

stable pending witness
2026-05-29 06:22:38 UTC · anthropic/claude-sonnet-4-5

Prompt

State process capability index (Cpk) precisely and explain why it matters in 2-3 sentences.
91 chars

Generation

# Process Capability Index (Cpk) **Cpk = min[(USL - μ)/3σ, (μ - LSL)/3σ]** Where: - USL = Upper Specification Limit - LSL = Lower Specification Limit - μ = Process mean - σ = Process standard deviation ## Why It Matters Cpk measures how well a process can consistently produce output within specification limits while accounting for process centering. A Cpk ≥ 1.33 indicates the process is capable of meeting customer requirements with minimal defects, while values below 1.0 signal that defects are likely and corrective action is needed. Unlike Cp, Cpk penalizes off-center processes, making it a critical metric for predicting real-world quality performance and defect rates.
30 tokens in · 191 tokens out · 5208 ms · $0.003

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
5215.0 ms
Base LLM
5208.0 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.003

Trail

06:22:38 received prompt_chars=91 verifiers=['scripture_anchors', 'theology_doctrine']
06:22:38 red_gate decision=pass reason=no disqualifying input patterns detected
06:22:43 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=191 latency_ms=5208.0 cost_usd=0.003
06:22:43 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:22:43 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:22:43 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:22:43 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:22:43 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:22:43 signed hash_algo=sha256 hash=sha256:548f0c30bd58495b565a42060ecc1d5a71e8b09aa3e17eb3fa8ad55513e1e325

Content hash

sha256:548f0c30bd58495b565a42060ecc1d5a71e8b09aa3e17eb3fa8ad55513e1e325

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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