The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-spherical-aberration-state-any-key-511f

stable pending witness
2026-05-29 07:48:37 UTC · anthropic/claude-sonnet-4-5

Prompt

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

Generation

Spherical aberration occurs when light rays passing through different zones of a spherical lens or mirror fail to converge at a single focal point—rays near the edge focus closer to the lens than paraxial (near-axis) rays. This happens because spherical surfaces are mathematically convenient but not optically ideal for focusing. The longitudinal spherical aberration (LSA) for a thin lens can be approximated by: **LSA ≈ -h²/(8nf³) × (n-1) × shape factors** where h is the ray height, n is the refractive index, and f is the focal length. Spherical aberration can be minimized using aspheric lenses, aperture stops, or corrected lens combinations.
26 tokens in · 168 tokens out · 5622 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
5630.1 ms
Base LLM
5622.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0026

Trail

07:48:37 received prompt_chars=70 verifiers=['scripture_anchors', 'theology_doctrine']
07:48:37 red_gate decision=pass reason=no disqualifying input patterns detected
07:48:43 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=168 latency_ms=5622.1 cost_usd=0.0026
07:48:43 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:48:43 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:48:43 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:48:43 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:48:43 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:48:43 signed hash_algo=sha256 hash=sha256:b9ab7dbdee05f51ba2c6d01b617a84868ac9eebb038dac9ef514cd3d29a50aaf

Content hash

sha256:b9ab7dbdee05f51ba2c6d01b617a84868ac9eebb038dac9ef514cd3d29a50aaf

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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