The Mechanism · Gated-generation receipt

gen-state-the-capital-asset-pricing-model-precisely-and-explain-635e

stable pending witness
2026-05-29 07:25:38 UTC · anthropic/claude-sonnet-4-5

Prompt

State the capital asset pricing model precisely and explain why it matters in 2-3 sentences.
92 chars

Generation

# Capital Asset Pricing Model (CAPM) **Formula:** E(Ri) = Rf + βi[E(Rm) - Rf] Where: - E(Ri) = Expected return on asset i - Rf = Risk-free rate - βi = Beta of asset i (systematic risk) - E(Rm) = Expected return on the market portfolio ## Why It Matters CAPM provides a fundamental framework for pricing risky assets by establishing that only systematic (market) risk should be rewarded with higher returns, while diversifiable risk should not. It allows investors and companies to determine required rates of return for investments and is widely used in corporate finance for capital budgeting decisions and calculating the cost of equity. Despite its limitations, CAPM remains the dominant model for understanding the risk-return tradeoff in financial markets.
27 tokens in · 191 tokens out · 4895 ms · $0.0029

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
4901.1 ms
Base LLM
4895.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0029

Trail

07:25:38 received prompt_chars=92 verifiers=['scripture_anchors', 'theology_doctrine']
07:25:38 red_gate decision=pass reason=no disqualifying input patterns detected
07:25:43 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=191 latency_ms=4895.1 cost_usd=0.0029
07:25:43 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:25:43 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:25:43 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:25:43 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:25:43 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:25:43 signed hash_algo=sha256 hash=sha256:68352811ac0309fc844c6cc1bced7e9ecfad76d82fc23e9e7ff21d6cf0d85ee6

Content hash

sha256:68352811ac0309fc844c6cc1bced7e9ecfad76d82fc23e9e7ff21d6cf0d85ee6

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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