The Mechanism · Gated-generation receipt

gen-state-a-convex-function-precisely-and-explain-why-it-matters-91a6

stable pending witness
2026-05-29 08:02:16 UTC · anthropic/claude-sonnet-4-5

Prompt

State a convex function precisely and explain why it matters in 2-3 sentences.
78 chars

Generation

# Convex Function **Definition:** A function f: ℝⁿ → ℝ is convex if for all points x, y in its domain and all λ ∈ [0,1]: f(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y) Geometrically, the line segment connecting any two points on the graph lies above (or on) the graph itself. **Why it matters:** Convex functions are crucial because any local minimum is also a global minimum, making optimization problems computationally tractable. This property underlies much of machine learning, economics, and engineering design, where we can efficiently find optimal solutions using gradient descent and related algorithms.
26 tokens in · 174 tokens out · 4338 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
4345.2 ms
Base LLM
4338.5 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0027

Trail

08:02:16 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
08:02:16 red_gate decision=pass reason=no disqualifying input patterns detected
08:02:20 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=174 latency_ms=4338.5 cost_usd=0.0027
08:02:20 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:02:20 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:02:20 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:02:20 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:02:20 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:02:20 signed hash_algo=sha256 hash=sha256:2b38b3c91a475a96ed1901b98cf592dab9399ee15a9c88b74448a167cc2ce131

Content hash

sha256:2b38b3c91a475a96ed1901b98cf592dab9399ee15a9c88b74448a167cc2ce131

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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