The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-acoustic-impedance-state-any-key-fo-4032

stable pending witness
2026-05-29 03:08:29 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain acoustic impedance. State any key formula.
68 chars

Generation

Acoustic impedance (Z) is a material property that describes how much a medium resists the propagation of sound waves through it. It is defined as the product of the material's density (ρ) and the speed of sound in that material (c): **Z = ρc**. When sound encounters a boundary between two materials with different acoustic impedances, some of the sound is reflected and some is transmitted, with greater impedance mismatch causing more reflection. This principle is critical in applications like ultrasound imaging and sonar.
25 tokens in · 117 tokens out · 3859 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
3866.6 ms
Base LLM
3858.8 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0018

Trail

03:08:29 received prompt_chars=68 verifiers=['scripture_anchors', 'theology_doctrine']
03:08:29 red_gate decision=pass reason=no disqualifying input patterns detected
03:08:33 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=117 latency_ms=3858.8 cost_usd=0.0018
03:08:33 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:08:33 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:08:33 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:08:33 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:08:33 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:08:33 signed hash_algo=sha256 hash=sha256:7a090e7736f98a751ed9421f7667b9e3d56d020ae4ac90b785f2b68d33087640

Content hash

sha256:7a090e7736f98a751ed9421f7667b9e3d56d020ae4ac90b785f2b68d33087640

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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