The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-doppler-effect-state-any-key-fo-5c22

stable pending witness
2026-05-29 04:56:39 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the Doppler effect. State any key formula.
68 chars

Generation

The Doppler effect is the change in frequency (or wavelength) of a wave observed when the source and observer are in relative motion. When the source moves toward the observer, the observed frequency increases (shorter wavelength), and when moving away, the frequency decreases (longer wavelength). This effect applies to all waves, including sound and light. The key formula for the observed frequency is: **f' = f(v ± v₀)/(v ∓ vₛ)**, where f' is the observed frequency, f is the source frequency, v is the wave speed, v₀ is the observer's speed, and vₛ is the source's speed. (Use upper signs when motion is toward each other, lower signs when moving apart.)
27 tokens in · 168 tokens out · 3816 ms · $0.0026

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
3822.8 ms
Base LLM
3815.8 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0026

Trail

04:56:39 received prompt_chars=68 verifiers=['scripture_anchors', 'theology_doctrine']
04:56:39 red_gate decision=pass reason=no disqualifying input patterns detected
04:56:43 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=168 latency_ms=3815.8 cost_usd=0.0026
04:56:43 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:56:43 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:56:43 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:56:43 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:56:43 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:56:43 signed hash_algo=sha256 hash=sha256:53d06662d0e428c3ce260c33361422ec36d85b4d4c225b1429a478aaafa6d771

Content hash

sha256:53d06662d0e428c3ce260c33361422ec36d85b4d4c225b1429a478aaafa6d771

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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