The Mechanism · Gated-generation receipt

gen-state-the-riemann-integral-precisely-and-explain-why-it-matt-fc67

stable pending witness
2026-05-29 08:26:13 UTC · anthropic/claude-sonnet-4-5

Prompt

State the Riemann integral precisely and explain why it matters in 2-3 sentences.
81 chars

Generation

# The Riemann Integral **Definition:** For a bounded function *f* on [*a*, *b*], the Riemann integral ∫ₐᵇ *f*(*x*)*dx* equals *L* if for every ε > 0, there exists δ > 0 such that for any partition with mesh less than δ, every Riemann sum satisfies |*S* - *L*| < ε. **Why it matters:** The Riemann integral rigorously formalizes the intuitive notion of "area under a curve," providing a precise foundation for calculus that replaced centuries of informal reasoning. It enables us to calculate physical quantities like work, mass, and probability, and serves as the gateway to more advanced integration theories in analysis.
27 tokens in · 177 tokens out · 5052 ms · $0.0027

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
5059.2 ms
Base LLM
5052.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0027

Trail

08:26:13 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
08:26:13 red_gate decision=pass reason=no disqualifying input patterns detected
08:26:18 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=177 latency_ms=5052.3 cost_usd=0.0027
08:26:18 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:26:18 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:26:18 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:26:18 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:26:18 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:26:18 signed hash_algo=sha256 hash=sha256:ecbca28cb178dfee2871e239954fcc34db897f30c1a6c47eeeed591ed2b29e46

Content hash

sha256:ecbca28cb178dfee2871e239954fcc34db897f30c1a6c47eeeed591ed2b29e46

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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