The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-capital-asset-pricing-model-sta-fac4

stable pending witness
2026-05-29 08:55:31 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the capital asset pricing model. State any key formula.
81 chars

Generation

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks. It posits that investors require higher expected returns for taking on additional systematic (market) risk that cannot be diversified away. The key formula is: **E(Ri) = Rf + βi[E(Rm) - Rf]** Where E(Ri) is the expected return on asset i, Rf is the risk-free rate, βi measures the asset's sensitivity to market movements, and E(Rm) is the expected market return. The term [E(Rm) - Rf] represents the market risk premium.
27 tokens in · 148 tokens out · 3622 ms · $0.0023

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
3629.4 ms
Base LLM
3621.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0023

Trail

08:55:31 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
08:55:31 red_gate decision=pass reason=no disqualifying input patterns detected
08:55:35 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=148 latency_ms=3621.9 cost_usd=0.0023
08:55:35 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:55:35 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:55:35 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:55:35 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:55:35 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:55:35 signed hash_algo=sha256 hash=sha256:e9154f9badb8f542ff299e76464da7c708988282356fee515840e86482b74fe9

Content hash

sha256:e9154f9badb8f542ff299e76464da7c708988282356fee515840e86482b74fe9

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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