The Mechanism · Gated-generation receipt

gen-explain-polygon-angle-sums-as-you-would-to-a-capable-student-70e6

stable pending witness
2026-05-29 07:34:16 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain polygon angle sums as you would to a capable student, in 3-4 sentences.
79 chars

Generation

Here's how polygon angle sums work: If you pick any vertex of a polygon and draw diagonals to all the non-adjacent vertices, you'll divide the polygon into triangles—specifically, a polygon with *n* sides splits into *(n-2)* triangles. Since each triangle contains 180°, the total interior angle sum is **(n-2) × 180°**. For example, a hexagon (6 sides) has (6-2) × 180° = 720° total, which you can verify by dividing it into 4 triangles.
29 tokens in · 131 tokens out · 3516 ms · $0.0021

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
3524.4 ms
Base LLM
3516.4 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0021

Trail

07:34:16 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
07:34:16 red_gate decision=pass reason=no disqualifying input patterns detected
07:34:20 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=131 latency_ms=3516.4 cost_usd=0.0021
07:34:20 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:34:20 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:34:20 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:34:20 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:34:20 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:34:20 signed hash_algo=sha256 hash=sha256:1fa791cdc356c8a3ddaca6c4488d6a398de1e20bf503ba194224a3ca5f428841

Content hash

sha256:1fa791cdc356c8a3ddaca6c4488d6a398de1e20bf503ba194224a3ca5f428841

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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