The Mechanism · Gated-generation receipt

gen-define-polygon-angle-sums-and-give-one-short-worked-example-0fa1

stable pending witness
2026-05-29 03:54:59 UTC · anthropic/claude-sonnet-4-5

Prompt

Define polygon angle sums and give one short worked example.
60 chars

Generation

# Polygon Angle Sums ## Definition The **sum of interior angles** of a polygon with *n* sides is given by the formula: **Sum = (n - 2) × 180°** This works because any polygon can be divided into (n - 2) triangles from one vertex, and each triangle contains 180°. ## Worked Example **Find the sum of interior angles of a hexagon.** - A hexagon has n = 6 sides - Sum = (6 - 2) × 180° - Sum = 4 × 180° - **Sum = 720°** --- *Note: For a regular polygon (all angles equal), each interior angle = Sum ÷ n*
19 tokens in · 172 tokens out · 4232 ms · $0.0026

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
4241.5 ms
Base LLM
4231.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0026

Trail

03:54:59 received prompt_chars=60 verifiers=['scripture_anchors', 'theology_doctrine']
03:54:59 red_gate decision=pass reason=no disqualifying input patterns detected
03:55:03 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=172 latency_ms=4231.7 cost_usd=0.0026
03:55:03 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:55:03 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:55:03 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:55:03 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:55:03 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:55:03 signed hash_algo=sha256 hash=sha256:5e1714c5019fa8d6fc09fbdfa3b3ff4897200b0a2a0191c3ce84fed9db56face

Content hash

sha256:5e1714c5019fa8d6fc09fbdfa3b3ff4897200b0a2a0191c3ce84fed9db56face

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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