The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-polygon-angle-sums-state-any-key-fo-4a13

stable pending witness
2026-05-29 06:17:13 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain polygon angle sums. State any key formula.
68 chars

Generation

# Polygon Angle Sums The sum of interior angles in a polygon depends on the number of sides. **The key formula is: Sum = (n - 2) × 180°**, where n is the number of sides. This works because any polygon can be divided into (n - 2) triangles from a single vertex, and since each triangle has angles summing to 180°, you multiply accordingly. For example, a pentagon (5 sides) has interior angles summing to (5 - 2) × 180° = 540°.
26 tokens in · 125 tokens out · 3450 ms · $0.002

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
3460.8 ms
Base LLM
3449.6 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.002

Trail

06:17:13 received prompt_chars=68 verifiers=['scripture_anchors', 'theology_doctrine']
06:17:13 red_gate decision=pass reason=no disqualifying input patterns detected
06:17:17 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=125 latency_ms=3449.6 cost_usd=0.002
06:17:17 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:17:17 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:17:17 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:17:17 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:17:17 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:17:17 signed hash_algo=sha256 hash=sha256:33d91bc12cc564adac27ec2eb59a32c071bc6802971c557db43481aabc391389

Content hash

sha256:33d91bc12cc564adac27ec2eb59a32c071bc6802971c557db43481aabc391389

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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