The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-latitude-and-longitude-state-any-ke-a755

stable pending witness
2026-05-29 06:54:31 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain latitude and longitude. State any key formula.
72 chars

Generation

Latitude and longitude are coordinates used to specify any location on Earth's surface. Latitude measures the angular distance north or south of the equator (0° to 90°), while longitude measures the angular distance east or west of the Prime Meridian (0° to 180°). Together, they form a grid system where any point can be expressed as (latitude, longitude). A key formula for calculating the great-circle distance between two points is the **haversine formula**: d = 2r × arcsin(√[sin²(Δφ/2) + cos(φ₁)cos(φ₂)sin²(Δλ/2)]), where φ is latitude, λ is longitude, r is Earth's radius, and d is the distance.
25 tokens in · 173 tokens out · 3689 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
3694.8 ms
Base LLM
3689.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0027

Trail

06:54:31 received prompt_chars=72 verifiers=['scripture_anchors', 'theology_doctrine']
06:54:31 red_gate decision=pass reason=no disqualifying input patterns detected
06:54:35 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=173 latency_ms=3689.3 cost_usd=0.0027
06:54:35 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:54:35 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:54:35 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:54:35 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:54:35 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:54:35 signed hash_algo=sha256 hash=sha256:b5283df4e6825365ac2d3fb8dcf5a9e9442da3136dfa37c598c18c00076b1f37

Content hash

sha256:b5283df4e6825365ac2d3fb8dcf5a9e9442da3136dfa37c598c18c00076b1f37

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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