The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-fiber-optic-light-guiding-state-any-d9d0

stable pending witness
2026-05-29 09:01:46 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain fiber-optic light guiding. State any key formula.
75 chars

Generation

Fiber-optic light guiding relies on **total internal reflection**, where light traveling through a high refractive index core is repeatedly reflected at the boundary with a lower refractive index cladding, preventing it from escaping. This occurs when the angle of incidence exceeds the **critical angle** θc, given by: **sin θc = n₂/n₁** where n₁ is the core's refractive index and n₂ is the cladding's refractive index (n₁ > n₂). Light entering within the fiber's **acceptance cone** will propagate through the fiber by bouncing along its length, enabling long-distance transmission with minimal loss.
29 tokens in · 158 tokens out · 4562 ms · $0.0025

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
4574.8 ms
Base LLM
4561.5 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0025

Trail

09:01:46 received prompt_chars=75 verifiers=['scripture_anchors', 'theology_doctrine']
09:01:46 red_gate decision=pass reason=no disqualifying input patterns detected
09:01:51 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=158 latency_ms=4561.5 cost_usd=0.0025
09:01:51 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
09:01:51 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
09:01:51 floor_gate decision=pass reason=output above protective minimum; no mismatches
09:01:51 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
09:01:51 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
09:01:51 signed hash_algo=sha256 hash=sha256:40d3a7fb4e9fb7e9ebcce0c9d8b043e7fc5b276a2525b182e260d321b4e84391

Content hash

sha256:40d3a7fb4e9fb7e9ebcce0c9d8b043e7fc5b276a2525b182e260d321b4e84391

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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