The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-an-anova-state-any-key-formula-16c4

stable pending witness
2026-05-29 08:21:21 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain an ANOVA. State any key formula.
58 chars

Generation

ANOVA (Analysis of Variance) is a statistical test used to determine whether there are significant differences between the means of three or more groups. It works by comparing the variation between groups to the variation within groups—if between-group variation is substantially larger than within-group variation, this suggests the groups have different means. The key formula is the **F-statistic**: **F = MS_between / MS_within** where MS_between is the mean square between groups (variance between group means) and MS_within is the mean square within groups (average variance within each group). A large F-value indicates significant differences among group means.
26 tokens in · 140 tokens out · 7298 ms · $0.0022

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
7304.6 ms
Base LLM
7297.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

08:21:21 received prompt_chars=58 verifiers=['scripture_anchors', 'theology_doctrine']
08:21:21 red_gate decision=pass reason=no disqualifying input patterns detected
08:21:28 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=140 latency_ms=7297.7 cost_usd=0.0022
08:21:28 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:21:28 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:21:28 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:21:28 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:21:28 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:21:28 signed hash_algo=sha256 hash=sha256:7a9ef14a5729b775de928e3159e431ade70d7b82f6f75fde75e417e63cbe20c7

Content hash

sha256:7a9ef14a5729b775de928e3159e431ade70d7b82f6f75fde75e417e63cbe20c7

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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