The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-index-of-refraction-state-any-k-94d5

stable pending witness
2026-05-29 02:40:28 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the index of refraction. State any key formula.
73 chars

Generation

The index of refraction (n) is a measure of how much light slows down and bends when entering a material compared to its speed in a vacuum. It is defined by the formula **n = c/v**, where c is the speed of light in vacuum and v is the speed of light in the material. Since light always travels slower in materials than in vacuum, the index of refraction is always greater than or equal to 1. A related key formula is **Snell's Law: n₁sin(θ₁) = n₂sin(θ₂)**, which describes how light bends at the interface between two materials with different indices of refraction.
27 tokens in · 148 tokens out · 3282 ms · $0.0023

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
3294.5 ms
Base LLM
3282.4 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0023

Trail

02:40:28 received prompt_chars=73 verifiers=['scripture_anchors', 'theology_doctrine']
02:40:28 red_gate decision=pass reason=no disqualifying input patterns detected
02:40:32 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=148 latency_ms=3282.4 cost_usd=0.0023
02:40:32 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:40:32 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:40:32 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:40:32 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:40:32 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:40:32 signed hash_algo=sha256 hash=sha256:8934cc36b5fdece5b44fe7ebe0f6fb1ce8afd210965b546001489537115ee52c

Content hash

sha256:8934cc36b5fdece5b44fe7ebe0f6fb1ce8afd210965b546001489537115ee52c

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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