The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-resonance-frequency-state-any-key-f-6333

hold
2026-05-29 03:37:58 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain resonance frequency. State any key formula.
69 chars

Generation

Resonance frequency is the natural frequency at which a system tends to oscillate with maximum amplitude when disturbed or driven by an external periodic force. At this frequency, even small periodic driving forces can produce large amplitude oscillations because the system absorbs energy most efficiently. The key formula for a simple harmonic oscillator (like a mass-spring system) is: **f₀ = (1/2π)√(k/m)** where f₀ is the resonance frequency, k is the spring constant (or restoring force constant), and m is the mass. For LC circuits, the analogous formula is f₀ = (1/2π)√(1/LC).
25 tokens in · 154 tokens out · 3774 ms · $0.0024

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
wait
output contains coercion language: ['force']
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
3780.8 ms
Base LLM
3773.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0024

Trail

03:37:58 received prompt_chars=69 verifiers=['scripture_anchors', 'theology_doctrine']
03:37:58 red_gate decision=pass reason=no disqualifying input patterns detected
03:38:01 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=154 latency_ms=3773.6 cost_usd=0.0024
03:38:01 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:38:01 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:38:01 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:38:01 way_gate decision=wait reason=output contains coercion language: ['force']
03:38:01 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:38:01 signed hash_algo=sha256 hash=sha256:87e46bea8f90e01c23d19aa6aa928687f9e94b3c86f22e8b886cdf3a2a6b5749

Content hash

sha256:87e46bea8f90e01c23d19aa6aa928687f9e94b3c86f22e8b886cdf3a2a6b5749

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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