The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-simple-harmonic-motion-state-any-ke-d463

hold
2026-05-29 04:12:23 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain simple harmonic motion. State any key formula.
72 chars

Generation

Simple harmonic motion (SHM) is a type of periodic motion where a restoring force is directly proportional to the displacement from equilibrium and acts toward that equilibrium position. Common examples include a mass on a spring and a pendulum undergoing small oscillations. The motion follows a sinusoidal pattern in time, described by the position equation **x(t) = A cos(ωt + φ)**, where A is amplitude, ω is angular frequency, and φ is the phase constant. The restoring force follows **F = -kx** (Hooke's law for a spring), leading to an angular frequency of **ω = √(k/m)** for a mass-spring system.
26 tokens in · 158 tokens out · 3609 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
3618.4 ms
Base LLM
3608.6 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0024

Trail

04:12:23 received prompt_chars=72 verifiers=['scripture_anchors', 'theology_doctrine']
04:12:23 red_gate decision=pass reason=no disqualifying input patterns detected
04:12:26 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=158 latency_ms=3608.6 cost_usd=0.0024
04:12:26 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:12:26 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:12:26 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:12:26 way_gate decision=wait reason=output contains coercion language: ['force']
04:12:26 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:12:26 signed hash_algo=sha256 hash=sha256:e6bcd9589b4021639f19a94b2e0381061ee11f420636ea24f3537c83f8d357e5

Content hash

sha256:e6bcd9589b4021639f19a94b2e0381061ee11f420636ea24f3537c83f8d357e5

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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