The Mechanism · Gated-generation receipt

gen-explain-the-inscribed-angle-theorem-as-you-would-to-a-capabl-db81

stable pending witness
2026-05-29 08:09:01 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the inscribed angle theorem as you would to a capable student, in 3-4 sentences.
88 chars

Generation

The inscribed angle theorem states that an angle formed by two chords meeting at a point on a circle is always half the measure of the central angle that subtends the same arc. In other words, if you pick any point on a circle and draw two lines to the endpoints of an arc, that angle will be exactly half of what you'd get if you drew lines from the center to those same endpoints. A powerful consequence is that all inscribed angles subtending the same arc are equal to each other, no matter where on the circle you place the vertex. This also means any angle inscribed in a semicircle is always a right angle, since it's half of the 180° central angle.
30 tokens in · 147 tokens out · 4874 ms · $0.0023

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
4880.3 ms
Base LLM
4873.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0023

Trail

08:09:01 received prompt_chars=88 verifiers=['scripture_anchors', 'theology_doctrine']
08:09:01 red_gate decision=pass reason=no disqualifying input patterns detected
08:09:06 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=147 latency_ms=4873.7 cost_usd=0.0023
08:09:06 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:09:06 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:09:06 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:09:06 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:09:06 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:09:06 signed hash_algo=sha256 hash=sha256:202ee98707c8f4a96e745a6f47f38f57787ca2f7fde7a797da237738e6d54fcd

Content hash

sha256:202ee98707c8f4a96e745a6f47f38f57787ca2f7fde7a797da237738e6d54fcd

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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