The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-resolving-power-of-a-telescope-da9c

stable pending witness
2026-05-29 04:54:42 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the resolving power of a telescope. State any key formula.
84 chars

Generation

Resolving power is a telescope's ability to distinguish two closely spaced objects as separate entities rather than as a single blurred image. It is fundamentally limited by diffraction, which causes light from point sources to spread into characteristic patterns. The minimum angular separation (θ) that can be resolved is given by the **Rayleigh criterion**: θ = 1.22λ/D, where λ is the wavelength of light and D is the diameter of the telescope's aperture. Larger apertures provide better resolving power by allowing smaller angles to be distinguished.
29 tokens in · 125 tokens out · 3892 ms · $0.002

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
3904.5 ms
Base LLM
3891.8 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.002

Trail

04:54:42 received prompt_chars=84 verifiers=['scripture_anchors', 'theology_doctrine']
04:54:42 red_gate decision=pass reason=no disqualifying input patterns detected
04:54:46 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=125 latency_ms=3891.8 cost_usd=0.002
04:54:46 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:54:46 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:54:46 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:54:46 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:54:46 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:54:46 signed hash_algo=sha256 hash=sha256:20651b9dd3bf729cd2c1ae2404b90093cb77ec45c3f1d05700ba5e73358b2405

Content hash

sha256:20651b9dd3bf729cd2c1ae2404b90093cb77ec45c3f1d05700ba5e73358b2405

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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