The Mechanism · Gated-generation receipt

gen-define-chromatic-aberration-and-give-one-short-worked-exampl-ea0d

stable pending witness
2026-05-29 02:52:23 UTC · anthropic/claude-sonnet-4-5

Prompt

Define chromatic aberration and give one short worked example.
62 chars

Generation

# Chromatic Aberration **Definition:** Chromatic aberration is an optical defect that occurs because a lens refracts different wavelengths (colors) of light by different amounts, causing them to focus at different points. This happens because the refractive index of glass varies with wavelength (dispersion). ## Worked Example **Problem:** A thin converging lens has focal lengths of 50.0 cm for red light and 48.0 cm for blue light. If a white light point source is placed 100 cm from the lens, what is the longitudinal chromatic aberration? **Solution:** Using the thin lens equation: 1/f = 1/v + 1/u For red light (f_r = 50.0 cm, u = -100 cm): - 1/50 = 1/v_r - 1/100 - 1/v_r = 1/50 + 1/100 = 3/100 - **v_r = 33.3 cm** For blue light (f_b = 48.0 cm, u = -100 cm): - 1/48 = 1/v_b - 1/100 - 1/v_b = 1/48 + 1/100 = 37/1200 - **v_b = 32.4 cm** **Longitudinal chromatic aberration = v_r - v_b = 33.3 - 32.4 = 0.9 cm** The red and blue images are separated by 0.9 cm along the optical axis, causing color fringing in the image.
19 tokens in · 388 tokens out · 7726 ms · $0.0059

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
7736.1 ms
Base LLM
7726.5 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0059

Trail

02:52:23 received prompt_chars=62 verifiers=['scripture_anchors', 'theology_doctrine']
02:52:23 red_gate decision=pass reason=no disqualifying input patterns detected
02:52:31 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=388 latency_ms=7726.5 cost_usd=0.0059
02:52:31 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:52:31 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:52:31 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:52:31 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:52:31 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:52:31 signed hash_algo=sha256 hash=sha256:b038046589e9b850a24ba34934a6d12577481c74b6b15ac13f3b4a3219cf7512

Content hash

sha256:b038046589e9b850a24ba34934a6d12577481c74b6b15ac13f3b4a3219cf7512

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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