The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-type-i-and-type-ii-errors-state-any-b24b

stable pending witness
2026-05-29 05:38:48 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain type I and type II errors. State any key formula.
75 chars

Generation

# Type I and Type II Errors **Type I Error (α)** occurs when we reject a true null hypothesis—a "false positive." This is controlled by the significance level, typically set at α = 0.05. **Type II Error (β)** occurs when we fail to reject a false null hypothesis—a "false negative." The probability of correctly rejecting a false null hypothesis is called **power**, given by the formula: **Power = 1 - β**. The two error types have an inverse relationship: decreasing one typically increases the other, requiring a balance based on the context of the test.
28 tokens in · 135 tokens out · 3820 ms · $0.0021

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
3834.2 ms
Base LLM
3819.9 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0021

Trail

05:38:48 received prompt_chars=75 verifiers=['scripture_anchors', 'theology_doctrine']
05:38:48 red_gate decision=pass reason=no disqualifying input patterns detected
05:38:52 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=135 latency_ms=3819.9 cost_usd=0.0021
05:38:52 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:38:52 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:38:52 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:38:52 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:38:52 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:38:52 signed hash_algo=sha256 hash=sha256:498f405ef37daf837d12d0312d79d2eabb127d1057164923da484716737c5b93

Content hash

sha256:498f405ef37daf837d12d0312d79d2eabb127d1057164923da484716737c5b93

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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