The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-beat-frequency-state-any-key-formul-0eb2

stable pending witness
2026-05-29 08:43:32 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain beat frequency. State any key formula.
64 chars

Generation

Beat frequency occurs when two waves of slightly different frequencies interfere, creating a periodic variation in amplitude that we perceive as a "wobbling" or pulsing sound. The beats result from alternating constructive and destructive interference as the waves move in and out of phase with each other. **Key formula:** f_beat = |f₁ - f₂| where f₁ and f₂ are the frequencies of the two interfering waves. The beat frequency equals the absolute difference between the two original frequencies.
24 tokens in · 117 tokens out · 3479 ms · $0.0018

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
3487.6 ms
Base LLM
3479.1 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0018

Trail

08:43:32 received prompt_chars=64 verifiers=['scripture_anchors', 'theology_doctrine']
08:43:32 red_gate decision=pass reason=no disqualifying input patterns detected
08:43:35 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=117 latency_ms=3479.1 cost_usd=0.0018
08:43:35 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:43:35 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:43:35 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:43:35 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:43:35 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:43:35 signed hash_algo=sha256 hash=sha256:b3ab37efde44768f3745afa183ddf82d036b724d0774faba1e5a02fb9406dd9e

Content hash

sha256:b3ab37efde44768f3745afa183ddf82d036b724d0774faba1e5a02fb9406dd9e

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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