The Mechanism · Gated-generation receipt

gen-state-the-distance-formula-precisely-and-explain-why-it-matt-a01a

stable pending witness
2026-05-29 08:21:44 UTC · anthropic/claude-sonnet-4-5

Prompt

State the distance formula precisely and explain why it matters in 2-3 sentences.
81 chars

Generation

## Distance Formula The distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is: **d = √[(x₂ - x₁)² + (y₂ - y₁)²]** This formula matters because it allows us to calculate exact measurements between any two points in space, forming the foundation for coordinate geometry, navigation systems, and computer graphics. It's derived from the Pythagorean theorem and extends our ability to quantify spatial relationships in mathematics, physics, and countless real-world applications.
25 tokens in · 132 tokens out · 3526 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
3534.4 ms
Base LLM
3526.4 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0021

Trail

08:21:44 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
08:21:44 red_gate decision=pass reason=no disqualifying input patterns detected
08:21:48 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=132 latency_ms=3526.4 cost_usd=0.0021
08:21:48 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:21:48 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:21:48 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:21:48 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:21:48 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:21:48 signed hash_algo=sha256 hash=sha256:3e8343a87d1ab3bf5cd8114fb8fe841b9d8b993ca53ee9950a2406b47fd91a72

Content hash

sha256:3e8343a87d1ab3bf5cd8114fb8fe841b9d8b993ca53ee9950a2406b47fd91a72

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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