The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-thin-lens-equation-state-any-ke-c82e

stable pending witness
2026-05-29 07:28:53 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the thin-lens equation. State any key formula.
72 chars

Generation

The thin-lens equation relates the object distance, image distance, and focal length of a thin lens. It is expressed as **1/f = 1/do + 1/di**, where f is the focal length, do is the object distance from the lens, and di is the image distance from the lens. This equation allows you to calculate where an image will form when an object is placed at a certain distance from the lens. The sign conventions are important: real images have positive di values while virtual images have negative di values.
27 tokens in · 113 tokens out · 3239 ms · $0.0018

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
3246.2 ms
Base LLM
3239.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0018

Trail

07:28:53 received prompt_chars=72 verifiers=['scripture_anchors', 'theology_doctrine']
07:28:53 red_gate decision=pass reason=no disqualifying input patterns detected
07:28:56 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=113 latency_ms=3239.4 cost_usd=0.0018
07:28:56 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:28:56 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:28:56 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:28:56 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:28:56 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:28:56 signed hash_algo=sha256 hash=sha256:a24144cdf1bbea9727d5695b178795f428612a0f925245f85cff2bc625f4e7b6

Content hash

sha256:a24144cdf1bbea9727d5695b178795f428612a0f925245f85cff2bc625f4e7b6

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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