The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-gaussian-curvature-answer-concis-4760

stable pending witness
2026-05-29 02:13:20 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of Gaussian curvature? Answer concisely in 2-3 sentences.
82 chars

Generation

Gaussian curvature measures the intrinsic curvature of a surface at a point, determining whether it curves like a sphere (positive), a saddle (negative), or a plane (zero). Its significance lies in being an intrinsic property—it remains unchanged under bending without stretching, as stated in Gauss's Theorema Egregium. This makes it fundamental to differential geometry, general relativity, and understanding the geometric properties of surfaces.
30 tokens in · 101 tokens out · 2812 ms · $0.0016

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
2819.6 ms
Base LLM
2811.5 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0016

Trail

02:13:20 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
02:13:20 red_gate decision=pass reason=no disqualifying input patterns detected
02:13:23 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=101 latency_ms=2811.5 cost_usd=0.0016
02:13:23 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:13:23 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:13:23 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:13:23 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:13:23 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:13:23 signed hash_algo=sha256 hash=sha256:4345cf9e52a5d80615bed474c407dca686aaa5f2e8d1a52ee1e22b0a050dcd1f

Content hash

sha256:4345cf9e52a5d80615bed474c407dca686aaa5f2e8d1a52ee1e22b0a050dcd1f

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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