The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-chromatic-aberration-state-any-key-0845

stable pending witness
2026-05-29 06:51:46 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain chromatic aberration. State any key formula.
70 chars

Generation

Chromatic aberration is an optical defect that occurs because a lens refracts different wavelengths of light by different amounts, causing them to focus at different points and creating colored fringes around objects. This happens because the refractive index of glass varies with wavelength, a phenomenon called dispersion. The key relationship is given by **Cauchy's equation**: n(λ) = A + B/λ² + C/λ⁴ + ..., where n is the refractive index and λ is the wavelength. The dispersive power is ω = (n_blue - n_red)/(n_yellow - 1), which quantifies how much chromatic aberration a material produces.
26 tokens in · 163 tokens out · 4262 ms · $0.0025

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
4270.3 ms
Base LLM
4262.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

06:51:46 received prompt_chars=70 verifiers=['scripture_anchors', 'theology_doctrine']
06:51:46 red_gate decision=pass reason=no disqualifying input patterns detected
06:51:51 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=163 latency_ms=4262.4 cost_usd=0.0025
06:51:51 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:51:51 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:51:51 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:51:51 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:51:51 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:51:51 signed hash_algo=sha256 hash=sha256:649bbab7a4cbbcef990ef7fe0617005ddc6991e6221c8364e40e416b03ccd7cd

Content hash

sha256:649bbab7a4cbbcef990ef7fe0617005ddc6991e6221c8364e40e416b03ccd7cd

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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