The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-convex-function-state-any-key-for-0dad

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

Prompt

In 3-4 sentences, explain a convex function. State any key formula.
67 chars

Generation

A convex function is one where a line segment connecting any two points on the graph lies above or on the graph itself. Intuitively, the function "curves upward" or is bowl-shaped. **Key formula**: A function f is convex if for any two points x₁ and x₂, and any λ ∈ [0,1]: **f(λx₁ + (1-λ)x₂) ≤ λf(x₁) + (1-λ)f(x₂)** For twice-differentiable functions, f is convex if and only if its second derivative f''(x) ≥ 0 everywhere.
26 tokens in · 163 tokens out · 4099 ms · $0.0025

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
4109.4 ms
Base LLM
4099.3 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0025

Trail

08:08:02 received prompt_chars=67 verifiers=['scripture_anchors', 'theology_doctrine']
08:08:02 red_gate decision=pass reason=no disqualifying input patterns detected
08:08:07 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=163 latency_ms=4099.3 cost_usd=0.0025
08:08:07 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:08:07 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:08:07 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:08:07 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:08:07 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:08:07 signed hash_algo=sha256 hash=sha256:80d8d5f5c23f7e2b9b8be335090dbd5dbd6266d056b549c7b1c2fc0364b10e2b

Content hash

sha256:80d8d5f5c23f7e2b9b8be335090dbd5dbd6266d056b549c7b1c2fc0364b10e2b

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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