The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-histogram-state-any-key-formula-bfc3

stable pending witness
2026-05-29 02:30:45 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the histogram. State any key formula.
63 chars

Generation

A histogram is a graphical representation that displays the frequency distribution of continuous data by dividing it into intervals (bins) and showing the count or frequency of observations in each bin using adjacent bars. The key formula for determining the optimal bin width is **Sturges' rule: k = 1 + 3.322 log₁₀(n)**, where k is the number of bins and n is the sample size. The height of each bar represents the frequency (count) or relative frequency (proportion) of data points falling within that interval. Histograms are useful for visualizing the shape, central tendency, and spread of a dataset.
24 tokens in · 139 tokens out · 3744 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
3750.9 ms
Base LLM
3744.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

02:30:45 received prompt_chars=63 verifiers=['scripture_anchors', 'theology_doctrine']
02:30:45 red_gate decision=pass reason=no disqualifying input patterns detected
02:30:49 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=139 latency_ms=3744.4 cost_usd=0.0022
02:30:49 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:30:49 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:30:49 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:30:49 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:30:49 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:30:49 signed hash_algo=sha256 hash=sha256:f939c2bbd98175670e228b7cd363150049c586c7fbfa512ce51c50564f017ade

Content hash

sha256:f939c2bbd98175670e228b7cd363150049c586c7fbfa512ce51c50564f017ade

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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