The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-inscribed-angle-theorem-answ-c8c1

stable pending witness
2026-05-29 06:43:37 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the inscribed angle theorem? Answer concisely in 2-3 sentences.
91 chars

Generation

The inscribed angle theorem states that an angle inscribed in a circle is half the measure of the central angle that subtends the same arc. This fundamental relationship is significant because it allows us to calculate unknown angles in circles and proves that all inscribed angles subtending the same arc are equal, which is essential for solving geometric problems involving circles and for understanding cyclic quadrilaterals.
30 tokens in · 81 tokens out · 5146 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
5152.7 ms
Base LLM
5146.0 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

06:43:37 received prompt_chars=91 verifiers=['scripture_anchors', 'theology_doctrine']
06:43:37 red_gate decision=pass reason=no disqualifying input patterns detected
06:43:42 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=81 latency_ms=5146.0 cost_usd=0.0013
06:43:42 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:43:42 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:43:42 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:43:42 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:43:42 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:43:42 signed hash_algo=sha256 hash=sha256:5ef289bd097161768bf7aa9dedeb6849accee1d7f370f4ada7045331ea7058b1

Content hash

sha256:5ef289bd097161768bf7aa9dedeb6849accee1d7f370f4ada7045331ea7058b1

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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