The Mechanism · Gated-generation receipt

gen-explain-a-chi-squared-test-as-you-would-to-a-capable-student-6f08

stable pending witness
2026-05-29 08:44:46 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain a chi-squared test as you would to a capable student, in 3-4 sentences.
79 chars

Generation

A chi-squared test helps you determine whether differences between observed data and what you'd expect by chance are statistically significant or just due to random variation. You calculate it by comparing your actual observations to expected values, squaring the differences, dividing by the expected values, and summing everything up—this gives you a test statistic. You then compare this statistic to a chi-squared distribution to get a p-value, which tells you the probability that any differences you see are just due to chance. It's commonly used for categorical data, like testing whether two variables are independent or whether your data fits an expected distribution.
30 tokens in · 131 tokens out · 4631 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
4638.7 ms
Base LLM
4631.3 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0021

Trail

08:44:46 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
08:44:46 red_gate decision=pass reason=no disqualifying input patterns detected
08:44:51 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=131 latency_ms=4631.3 cost_usd=0.0021
08:44:51 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:44:51 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:44:51 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:44:51 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:44:51 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:44:51 signed hash_algo=sha256 hash=sha256:0ad96be47a7325a28c8463cd208dffdf8823109e1636ca65e33c9db15c160797

Content hash

sha256:0ad96be47a7325a28c8463cd208dffdf8823109e1636ca65e33c9db15c160797

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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