The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-process-capability-index-cpk-state-d784

stable pending witness
2026-05-29 02:39:45 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain process capability index (Cpk). State any key formula.
80 chars

Generation

Process capability index (Cpk) measures how well a process can meet specification limits, accounting for both process variation and centering. It indicates the relationship between the process spread (natural variation) and the specification limits, with higher values indicating better capability. A Cpk ≥ 1.33 is generally considered acceptable for most processes, while Cpk ≥ 1.67 indicates excellent capability. **Key formula:** Cpk = min[(USL - μ)/(3σ), (μ - LSL)/(3σ)] where USL = upper specification limit, LSL = lower specification limit, μ = process mean, and σ = process standard deviation.
29 tokens in · 156 tokens out · 5552 ms · $0.0024

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
5564.3 ms
Base LLM
5551.9 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0024

Trail

02:39:45 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
02:39:45 red_gate decision=pass reason=no disqualifying input patterns detected
02:39:51 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=156 latency_ms=5551.9 cost_usd=0.0024
02:39:51 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:39:51 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:39:51 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:39:51 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:39:51 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:39:51 signed hash_algo=sha256 hash=sha256:e605791d50803b4cdc70b030003383f22070a84fbe4594ad2525d1395e83a19f

Content hash

sha256:e605791d50803b4cdc70b030003383f22070a84fbe4594ad2525d1395e83a19f

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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