The Mechanism · Gated-generation receipt

gen-define-wavelength-and-frequency-and-give-one-short-worked-ex-2da0

stable pending witness
2026-05-29 08:19:26 UTC · anthropic/claude-sonnet-4-5

Prompt

Define wavelength and frequency and give one short worked example.
66 chars

Generation

# Wavelength and Frequency **Wavelength (λ)**: The distance between two consecutive identical points on a wave (e.g., crest to crest or trough to trough). Measured in meters (m). **Frequency (f)**: The number of complete wave cycles that pass a fixed point per second. Measured in Hertz (Hz), where 1 Hz = 1 cycle/second. ## Relationship These are related by the wave equation: $$v = f \lambda$$ where *v* is the wave speed. --- ## Worked Example **Question**: A sound wave has a frequency of 440 Hz (musical note A). If the speed of sound in air is 340 m/s, what is the wavelength? **Solution**: - Given: f = 440 Hz, v = 340 m/s - Using v = fλ - Rearrange: λ = v/f - λ = 340/440 - **λ = 0.77 m** The wavelength of this sound wave is 0.77 meters (or 77 cm).
19 tokens in · 266 tokens out · 4890 ms · $0.004

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
4899.5 ms
Base LLM
4890.4 ms
Verifiers
0.6 ms
Gates
0.1 ms
Cost
$0.004

Trail

08:19:26 received prompt_chars=66 verifiers=['scripture_anchors', 'theology_doctrine']
08:19:26 red_gate decision=pass reason=no disqualifying input patterns detected
08:19:31 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=266 latency_ms=4890.4 cost_usd=0.004
08:19:31 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:19:31 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:19:31 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:19:31 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:19:31 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:19:31 signed hash_algo=sha256 hash=sha256:347b1f2f1382fa547c9f515a67a1fb20d1348689b4a2e4b4fa854b3eef30bf2b

Content hash

sha256:347b1f2f1382fa547c9f515a67a1fb20d1348689b4a2e4b4fa854b3eef30bf2b

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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