The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-doppler-shift-in-spectra-state-15eb

stable pending witness
2026-05-29 08:18:47 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the Doppler shift in spectra. State any key formula.
78 chars

Generation

The Doppler shift occurs when the wavelength of light from a moving object is stretched or compressed due to the object's motion relative to the observer. Light from objects moving away from us is redshifted (wavelengths become longer), while light from approaching objects is blueshifted (wavelengths become shorter). The key formula for the radial velocity is: **v = c × (Δλ/λ₀)** where v is the radial velocity, c is the speed of light, Δλ is the change in wavelength, and λ₀ is the rest wavelength. This relationship allows astronomers to measure velocities of stars and galaxies from their spectral lines.
30 tokens in · 158 tokens out · 4054 ms · $0.0025

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
4064.6 ms
Base LLM
4054.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

08:18:47 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
08:18:47 red_gate decision=pass reason=no disqualifying input patterns detected
08:18:52 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=158 latency_ms=4054.4 cost_usd=0.0025
08:18:52 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:18:52 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:18:52 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:18:52 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:18:52 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:18:52 signed hash_algo=sha256 hash=sha256:fe56f653f00516791bf718471861294cb98567d5a53c228fbc03b33d326147b5

Content hash

sha256:fe56f653f00516791bf718471861294cb98567d5a53c228fbc03b33d326147b5

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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