The Mechanism · Gated-generation receipt

gen-define-the-overtone-series-and-give-one-short-worked-example-90aa

stable pending witness
2026-05-29 08:53:54 UTC · anthropic/claude-sonnet-4-5

Prompt

Define the overtone series and give one short worked example.
61 chars

Generation

# Overtone Series The **overtone series** (or harmonic series) is the sequence of frequencies produced by a vibrating object, consisting of a fundamental frequency and whole-number multiples of that frequency. **Formula:** f_n = n × f₁ where: - f_n = frequency of the nth harmonic - n = 1, 2, 3, 4, ... (harmonic number) - f₁ = fundamental frequency ## Worked Example **Given:** A guitar string vibrates at a fundamental frequency of 110 Hz (low A) **Find the first 5 harmonics:** - **1st harmonic (fundamental):** f₁ = 1 × 110 = **110 Hz** (A2) - **2nd harmonic:** f₂ = 2 × 110 = **220 Hz** (A3, octave above) - **3rd harmonic:** f₃ = 3 × 110 = **330 Hz** (E4, fifth above) - **4th harmonic:** f₄ = 4 × 110 = **440 Hz** (A4, two octaves above) - **5th harmonic:** f₅ = 5 × 110 = **550 Hz** (C#5, major third) These harmonics sound simultaneously when the string is plucked, giving the note its characteristic timbre.
19 tokens in · 336 tokens out · 7132 ms · $0.0051

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
7139.4 ms
Base LLM
7132.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0051

Trail

08:53:54 received prompt_chars=61 verifiers=['scripture_anchors', 'theology_doctrine']
08:53:54 red_gate decision=pass reason=no disqualifying input patterns detected
08:54:01 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=336 latency_ms=7132.2 cost_usd=0.0051
08:54:01 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:54:01 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:54:01 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:54:01 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:54:01 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:54:01 signed hash_algo=sha256 hash=sha256:c40748b9ce984b851a438e20f601e136b87f3b6b83eb9546e7fcf2345c6e3445

Content hash

sha256:c40748b9ce984b851a438e20f601e136b87f3b6b83eb9546e7fcf2345c6e3445

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.

Bring another teaching · Run a discernment