The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-yield-curve-state-any-key-formu-6426

stable pending witness
2026-05-29 08:18:25 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the yield curve. State any key formula.
65 chars

Generation

The yield curve is a graph plotting interest rates (yields) of bonds against their time to maturity, typically for government bonds. A normal upward-sloping curve indicates longer-term bonds have higher yields than short-term ones, reflecting greater risk and inflation expectations over time. The curve's shape helps predict economic conditions: an inverted curve (short rates > long rates) often signals recession, while a steep curve suggests economic expansion. **Key formula**: The **expectations hypothesis** states that long-term rates equal the average of expected future short-term rates: (1 + y_n)^n = (1 + y_1)(1 + E[r_2])...(1 + E[r_n]), where y_n is the n-year yield and E[r_i] represents expected future 1-year rates.
25 tokens in · 185 tokens out · 5818 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
5824.8 ms
Base LLM
5817.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0029

Trail

08:18:25 received prompt_chars=65 verifiers=['scripture_anchors', 'theology_doctrine']
08:18:25 red_gate decision=pass reason=no disqualifying input patterns detected
08:18:31 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=185 latency_ms=5817.6 cost_usd=0.0029
08:18:31 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:18:31 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:18:31 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:18:31 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:18:31 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:18:31 signed hash_algo=sha256 hash=sha256:c0848a84224e8107b9d6a81fd5b5062ee654c63992b2805df99950ecf4a04d0c

Content hash

sha256:c0848a84224e8107b9d6a81fd5b5062ee654c63992b2805df99950ecf4a04d0c

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.

Bring another teaching · Run a discernment