The Mechanism · Gated-generation receipt

gen-briefly-explain-open-versus-closed-pipes-and-one-common-misc-3224

stable pending witness
2026-05-29 05:34:35 UTC · anthropic/claude-sonnet-4-5

Prompt

Briefly explain open versus closed pipes and one common misconception about it.
79 chars

Generation

# Open vs Closed Pipes **Closed pipes** have one end sealed and one end open. They support only **odd harmonics** (1st, 3rd, 5th, etc.) because a displacement node must form at the closed end and an antinode at the open end. **Open pipes** have both ends open. They support **all harmonics** (1st, 2nd, 3rd, etc.) because displacement antinodes form at both open ends. ## Common Misconception Many students believe that open pipes are "twice the frequency" of closed pipes. This is **incorrect**. The fundamental frequency of an open pipe is actually **twice** that of a closed pipe *of the same length*: - Closed pipe: f₁ = v/4L - Open pipe: f₁ = v/2L However, the confusion arises because the closed pipe's **3rd harmonic** (f₃ = 3v/4L) happens to be close to the open pipe's **2nd harmonic** (f₂ = v/L), not because there's a simple 2:1 relationship between all their frequencies.
22 tokens in · 265 tokens out · 6909 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
6916.8 ms
Base LLM
6909.5 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.004

Trail

05:34:35 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
05:34:35 red_gate decision=pass reason=no disqualifying input patterns detected
05:34:42 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=22 tokens_out=265 latency_ms=6909.5 cost_usd=0.004
05:34:42 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:34:42 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:34:42 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:34:42 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:34:42 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:34:42 signed hash_algo=sha256 hash=sha256:3c69b4210d3dc1fc1406dda55e975b8289247c96af7cc7197ce2e9c6aef68f45

Content hash

sha256:3c69b4210d3dc1fc1406dda55e975b8289247c96af7cc7197ce2e9c6aef68f45

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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