The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-distance-formula-answer-conc-3923

stable pending witness
2026-05-29 04:28:16 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the distance formula? Answer concisely in 2-3 sentences.
84 chars

Generation

The distance formula calculates the straight-line distance between two points in coordinate space, derived from the Pythagorean theorem. It's fundamental to mathematics, physics, and engineering for measuring spatial relationships, analyzing geometric shapes, and solving real-world problems involving position and movement. This formula extends beyond 2D planes to higher dimensions, making it essential for fields like computer graphics, navigation, and data science.
28 tokens in · 87 tokens out · 2473 ms · $0.0014

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
2479.9 ms
Base LLM
2472.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0014

Trail

04:28:16 received prompt_chars=84 verifiers=['scripture_anchors', 'theology_doctrine']
04:28:16 red_gate decision=pass reason=no disqualifying input patterns detected
04:28:19 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=87 latency_ms=2472.6 cost_usd=0.0014
04:28:19 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:28:19 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:28:19 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:28:19 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:28:19 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:28:19 signed hash_algo=sha256 hash=sha256:3a45223a86fc7ecef0d55bcd0d95cded30feac6c4c6e44abe76c1a00d069dd46

Content hash

sha256:3a45223a86fc7ecef0d55bcd0d95cded30feac6c4c6e44abe76c1a00d069dd46

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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