The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-polygon-angle-sums-answer-concis-bc27

stable pending witness
2026-05-29 02:35:50 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of polygon angle sums? Answer concisely in 2-3 sentences.
82 chars

Generation

Polygon angle sums reveal a fundamental geometric relationship: the sum of interior angles in any polygon depends only on the number of sides, following the formula (n-2)×180°. This property is essential for solving geometric problems, verifying polygon constructions, and understanding why certain tessellations work. It also demonstrates how complex shapes can be understood by breaking them into simpler triangles.
29 tokens in · 84 tokens out · 4454 ms · $0.0013

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
4463.8 ms
Base LLM
4453.7 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

02:35:50 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
02:35:50 red_gate decision=pass reason=no disqualifying input patterns detected
02:35:54 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=84 latency_ms=4453.7 cost_usd=0.0013
02:35:54 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:35:54 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:35:54 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:35:54 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:35:54 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:35:54 signed hash_algo=sha256 hash=sha256:0a156ddb26dbe3a5881e9f4737968b5b04662eb6be3614d6645a26296fbc8972

Content hash

sha256:0a156ddb26dbe3a5881e9f4737968b5b04662eb6be3614d6645a26296fbc8972

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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