The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-distance-formula-state-any-key-16a8

stable pending witness
2026-05-29 05:35:29 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the distance formula. State any key formula.
70 chars

Generation

The distance formula calculates the straight-line distance between two points in a coordinate plane. It is derived from the Pythagorean theorem by treating the horizontal and vertical distances between points as legs of a right triangle. **Key Formula:** For two points (x₁, y₁) and (x₂, y₂), the distance d is: **d = √[(x₂ - x₁)² + (y₂ - y₁)²]** This formula finds the length of the hypotenuse connecting the two points.
25 tokens in · 128 tokens out · 8164 ms · $0.002

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
8171.0 ms
Base LLM
8163.6 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.002

Trail

05:35:29 received prompt_chars=70 verifiers=['scripture_anchors', 'theology_doctrine']
05:35:29 red_gate decision=pass reason=no disqualifying input patterns detected
05:35:37 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=128 latency_ms=8163.6 cost_usd=0.002
05:35:37 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:35:37 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:35:37 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:35:37 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:35:37 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:35:37 signed hash_algo=sha256 hash=sha256:3e8f7fec86692c9dbe532694760149da2e6ea7100ae78a6b6d03d9ceed20d0ef

Content hash

sha256:3e8f7fec86692c9dbe532694760149da2e6ea7100ae78a6b6d03d9ceed20d0ef

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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