The Mechanism · Gated-generation receipt

gen-state-polygon-angle-sums-precisely-and-explain-why-it-matter-728c

stable pending witness
2026-05-29 04:32:49 UTC · anthropic/claude-sonnet-4-5

Prompt

State polygon angle sums precisely and explain why it matters in 2-3 sentences.
79 chars

Generation

# Polygon Angle Sum **Formula:** The sum of interior angles of an n-sided polygon is **(n - 2) × 180°** ## Why It Matters This formula is fundamental for solving geometric problems involving polygons, from determining unknown angles to verifying if a shape is possible. It emerges from the fact that any polygon can be divided into (n - 2) triangles from a single vertex, and since each triangle contains 180°, the total must be (n - 2) × 180°. This relationship is essential in fields from architecture and engineering to computer graphics and tessellation design.
26 tokens in · 137 tokens out · 4089 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
4097.8 ms
Base LLM
4089.5 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0021

Trail

04:32:49 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
04:32:49 red_gate decision=pass reason=no disqualifying input patterns detected
04:32:53 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=137 latency_ms=4089.5 cost_usd=0.0021
04:32:53 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:32:53 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:32:53 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:32:53 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:32:53 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:32:53 signed hash_algo=sha256 hash=sha256:4c1070d7bdf95035843987e281a4fc177498998532fa8be384fb30df0ae91bce

Content hash

sha256:4c1070d7bdf95035843987e281a4fc177498998532fa8be384fb30df0ae91bce

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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