The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-thin-lens-equation-answer-co-7ae9

stable pending witness
2026-05-29 07:18:36 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the thin-lens equation? Answer concisely in 2-3 sentences.
86 chars

Generation

The thin-lens equation (1/f = 1/do + 1/di) relates the focal length of a lens to the object and image distances, allowing us to predict where an image will form and its characteristics. It is fundamental to understanding and designing optical systems like cameras, eyeglasses, microscopes, and telescopes. This equation applies when the lens thickness is negligible compared to the object and image distances.
30 tokens in · 92 tokens out · 2655 ms · $0.0015

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
2661.0 ms
Base LLM
2655.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0015

Trail

07:18:36 received prompt_chars=86 verifiers=['scripture_anchors', 'theology_doctrine']
07:18:36 red_gate decision=pass reason=no disqualifying input patterns detected
07:18:39 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=92 latency_ms=2655.1 cost_usd=0.0015
07:18:39 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:18:39 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:18:39 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:18:39 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:18:39 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:18:39 signed hash_algo=sha256 hash=sha256:5de17782d232dbf7d847f74395d9edcc6016b18b8a6c0f6984a7140b99203f30

Content hash

sha256:5de17782d232dbf7d847f74395d9edcc6016b18b8a6c0f6984a7140b99203f30

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.

Bring another teaching · Run a discernment