The Mechanism · Gated-generation receipt

gen-explain-a-convex-function-as-you-would-to-a-capable-student-4e1a

stable pending witness
2026-05-29 02:59:47 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain a convex function as you would to a capable student, in 3-4 sentences.
78 chars

Generation

A convex function is one where the line segment connecting any two points on the graph always lies above (or on) the graph itself. Imagine a U-shaped curve like f(x) = x²—if you pick any two points and draw a straight line between them, that line never dips below the curve. Mathematically, this means f(tx + (1-t)y) ≤ tf(x) + (1-t)f(y) for any points x and y and any t between 0 and 1. This property makes convex functions special because they have no local minima that aren't also global minima, which is extremely useful in optimization.
29 tokens in · 151 tokens out · 4123 ms · $0.0024

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
4130.6 ms
Base LLM
4123.0 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0024

Trail

02:59:47 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
02:59:47 red_gate decision=pass reason=no disqualifying input patterns detected
02:59:51 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=151 latency_ms=4123.0 cost_usd=0.0024
02:59:51 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:59:51 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:59:51 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:59:51 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:59:51 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:59:51 signed hash_algo=sha256 hash=sha256:0724ceafa8079fadcddf87cf73a5e6f619ce185c893c78fb498214e93b9369c6

Content hash

sha256:0724ceafa8079fadcddf87cf73a5e6f619ce185c893c78fb498214e93b9369c6

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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