The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-chi-squared-test-state-any-key-fo-d242

stable pending witness
2026-05-29 03:03:18 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a chi-squared test. State any key formula.
68 chars

Generation

A chi-squared test is a statistical method used to determine whether there is a significant association between categorical variables or whether observed frequencies differ from expected frequencies. The test compares observed data to what would be expected under a null hypothesis of independence or no difference. The key formula is: **χ² = Σ[(O - E)² / E]** where O represents observed frequencies, E represents expected frequencies, and the sum is taken across all categories. The resulting χ² statistic is compared to a chi-squared distribution to determine statistical significance.
27 tokens in · 120 tokens out · 5181 ms · $0.0019

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
5188.5 ms
Base LLM
5181.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0019

Trail

03:03:18 received prompt_chars=68 verifiers=['scripture_anchors', 'theology_doctrine']
03:03:18 red_gate decision=pass reason=no disqualifying input patterns detected
03:03:23 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=120 latency_ms=5181.1 cost_usd=0.0019
03:03:23 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:03:23 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:03:23 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:03:23 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:03:23 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:03:23 signed hash_algo=sha256 hash=sha256:cf6ff0a53e94bd4db840e75122e9fad9614f7cef532e6db1b4ffa8c0cdae3e74

Content hash

sha256:cf6ff0a53e94bd4db840e75122e9fad9614f7cef532e6db1b4ffa8c0cdae3e74

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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