The Mechanism · Gated-generation receipt

gen-state-the-economic-order-quantity-precisely-and-explain-why-e32b

stable pending witness
2026-05-29 08:25:56 UTC · anthropic/claude-sonnet-4-5

Prompt

State the economic order quantity precisely and explain why it matters in 2-3 sentences.
88 chars

Generation

# Economic Order Quantity (EOQ) **Formula:** EOQ = √(2DS/H) Where: - D = Annual demand - S = Order cost per purchase order - H = Annual holding cost per unit ## Why It Matters EOQ identifies the optimal order size that minimizes total inventory costs by balancing two competing expenses: ordering costs (which decrease with larger, less frequent orders) and holding costs (which increase with larger inventory levels). Using EOQ helps businesses reduce waste, free up working capital, and improve cash flow by avoiding both excessive inventory storage and frequent costly reorders.
26 tokens in · 132 tokens out · 4544 ms · $0.0021

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
4551.1 ms
Base LLM
4544.0 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

08:25:56 received prompt_chars=88 verifiers=['scripture_anchors', 'theology_doctrine']
08:25:56 red_gate decision=pass reason=no disqualifying input patterns detected
08:26:01 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=132 latency_ms=4544.0 cost_usd=0.0021
08:26:01 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:26:01 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:26:01 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:26:01 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:26:01 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:26:01 signed hash_algo=sha256 hash=sha256:c696e3789150074ac1667d9b46ec6d6ed592da29e946d927a197976fc1a1819c

Content hash

sha256:c696e3789150074ac1667d9b46ec6d6ed592da29e946d927a197976fc1a1819c

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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