The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-celestial-sphere-and-coordinate-0038

stable pending witness
2026-05-29 04:48:10 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the celestial sphere and coordinates. State any key formula.
86 chars

Generation

The celestial sphere is an imaginary sphere of arbitrary radius centered on Earth, onto which all celestial objects are projected for mapping purposes. Astronomers use two main coordinate systems on this sphere: the **altitude-azimuth system** (local, using altitude above horizon and azimuth angle) and the **equatorial system** (fixed to Earth's rotation, using declination δ and right ascension α). A key conversion formula relates altitude (a), azimuth (A), declination (δ), hour angle (H), and observer latitude (φ): **sin(a) = sin(δ)sin(φ) + cos(δ)cos(φ)cos(H)** This formula allows conversion between local horizontal coordinates and equatorial coordinates.
28 tokens in · 171 tokens out · 4432 ms · $0.0026

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
4439.0 ms
Base LLM
4431.6 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0026

Trail

04:48:10 received prompt_chars=86 verifiers=['scripture_anchors', 'theology_doctrine']
04:48:10 red_gate decision=pass reason=no disqualifying input patterns detected
04:48:15 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=171 latency_ms=4431.6 cost_usd=0.0026
04:48:15 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:48:15 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:48:15 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:48:15 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:48:15 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:48:15 signed hash_algo=sha256 hash=sha256:71ac432060c528a8c70db5841430208d34400e1aae77817776c167db1a0a0c58

Content hash

sha256:71ac432060c528a8c70db5841430208d34400e1aae77817776c167db1a0a0c58

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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