The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-a-convex-function-answer-concise-64c5

stable pending witness
2026-05-29 04:22:44 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of a convex function? Answer concisely in 2-3 sentences.
81 chars

Generation

A convex function has the property that any line segment connecting two points on its graph lies above or on the graph itself. This property ensures that any local minimum is also a global minimum, making convex functions particularly important in optimization problems where finding the best solution is guaranteed to be tractable. Convex functions appear throughout mathematics, economics, and machine learning due to these favorable computational and theoretical properties.
29 tokens in · 84 tokens out · 2820 ms · $0.0013

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
2827.1 ms
Base LLM
2820.1 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

04:22:44 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
04:22:44 red_gate decision=pass reason=no disqualifying input patterns detected
04:22:47 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=84 latency_ms=2820.1 cost_usd=0.0013
04:22:47 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:22:47 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:22:47 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:22:47 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:22:47 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:22:47 signed hash_algo=sha256 hash=sha256:848d6e5da97b5586fd6d99f95429db93b0c7695f09e79e99bffd4829fb86d63f

Content hash

sha256:848d6e5da97b5586fd6d99f95429db93b0c7695f09e79e99bffd4829fb86d63f

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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