The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-critical-angle-state-any-key-fo-77bb

stable pending witness
2026-05-29 06:55:19 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the critical angle. State any key formula.
68 chars

Generation

The critical angle is the angle of incidence in a denser medium at which light refracts along the boundary (at 90°) when entering a less dense medium. At angles greater than the critical angle, total internal reflection occurs instead of refraction. **Key formula:** sin θ_c = n₂/n₁ where θ_c is the critical angle, n₁ is the refractive index of the denser medium, and n₂ is the refractive index of the less dense medium (with n₁ > n₂).
25 tokens in · 129 tokens out · 3575 ms · $0.002

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
3582.3 ms
Base LLM
3575.3 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.002

Trail

06:55:19 received prompt_chars=68 verifiers=['scripture_anchors', 'theology_doctrine']
06:55:19 red_gate decision=pass reason=no disqualifying input patterns detected
06:55:23 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=129 latency_ms=3575.3 cost_usd=0.002
06:55:23 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:55:23 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:55:23 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:55:23 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:55:23 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:55:23 signed hash_algo=sha256 hash=sha256:2d97c5ea8427cbbee32eadf6655504713f3bf378a46715200f9b118115489f67

Content hash

sha256:2d97c5ea8427cbbee32eadf6655504713f3bf378a46715200f9b118115489f67

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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