The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-great-circle-distance-state-any-52dd

stable pending witness
2026-05-29 05:31:18 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the great-circle distance. State any key formula.
75 chars

Generation

# Great-Circle Distance The great-circle distance is the shortest path between two points on the surface of a sphere, measured along the sphere's surface. This path follows a "great circle"—a circle whose center coincides with the sphere's center (like the equator or lines of longitude). The distance can be calculated using the **Haversine formula**: **d = 2r · arcsin(√[sin²(Δφ/2) + cos(φ₁)·cos(φ₂)·sin²(Δλ/2)])** where *r* is the sphere's radius, *φ₁* and *φ₂* are the latitudes, and *Δλ* is the difference in longitudes.
27 tokens in · 176 tokens out · 4834 ms · $0.0027

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
4844.0 ms
Base LLM
4834.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0027

Trail

05:31:18 received prompt_chars=75 verifiers=['scripture_anchors', 'theology_doctrine']
05:31:18 red_gate decision=pass reason=no disqualifying input patterns detected
05:31:22 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=176 latency_ms=4834.2 cost_usd=0.0027
05:31:22 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:31:22 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:31:22 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:31:22 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:31:22 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:31:22 signed hash_algo=sha256 hash=sha256:62ce6f36c1c9fccb0889c171def7fa3ae7e4e2af4ef22b702f396f26abed36ab

Content hash

sha256:62ce6f36c1c9fccb0889c171def7fa3ae7e4e2af4ef22b702f396f26abed36ab

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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