The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-luminosity-and-the-stefan-boltzmann-f3b6

stable pending witness
2026-05-29 08:27:15 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain luminosity and the Stefan-Boltzmann law. State any key formula.
89 chars

Generation

Luminosity is the total amount of energy a star (or other object) emits per unit time, measured in watts. The Stefan-Boltzmann law states that the luminosity of a blackbody is proportional to both its surface area and the fourth power of its temperature. The key formula is **L = 4πR²σT⁴**, where L is luminosity, R is radius, T is surface temperature, and σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W m⁻² K⁻⁴). This means even a small increase in temperature causes a dramatic increase in luminosity.
33 tokens in · 153 tokens out · 3317 ms · $0.0024

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
3324.2 ms
Base LLM
3316.7 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0024

Trail

08:27:15 received prompt_chars=89 verifiers=['scripture_anchors', 'theology_doctrine']
08:27:15 red_gate decision=pass reason=no disqualifying input patterns detected
08:27:18 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=33 tokens_out=153 latency_ms=3316.7 cost_usd=0.0024
08:27:18 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:27:18 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:27:18 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:27:18 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:27:18 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:27:18 signed hash_algo=sha256 hash=sha256:ba3df608602d301e129b409bad732165acc813d48f8bf090ab42397c433e5430

Content hash

sha256:ba3df608602d301e129b409bad732165acc813d48f8bf090ab42397c433e5430

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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