The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-inscribed-angle-theorem-state-a-98d5

stable pending witness
2026-05-29 03:43:55 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the inscribed angle theorem. State any key formula.
77 chars

Generation

The inscribed angle theorem states that an angle inscribed in a circle (formed by two chords with a common endpoint on the circle) is half the measure of the central angle that subtends the same arc. In other words, if an inscribed angle and a central angle intercept the same arc, the inscribed angle measures half of the central angle. **Key formula:** inscribed angle = ½ × central angle, or equivalently, inscribed angle = ½ × (measure of intercepted arc) A useful corollary is that all inscribed angles that intercept the same arc are equal to each other.
27 tokens in · 135 tokens out · 2968 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
2975.1 ms
Base LLM
2967.8 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

03:43:55 received prompt_chars=77 verifiers=['scripture_anchors', 'theology_doctrine']
03:43:55 red_gate decision=pass reason=no disqualifying input patterns detected
03:43:58 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=135 latency_ms=2967.8 cost_usd=0.0021
03:43:58 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:43:58 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:43:58 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:43:58 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:43:58 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:43:58 signed hash_algo=sha256 hash=sha256:d2df4f6541405c8c12d663e24d33667215d425e157671718d0cd6e310779a321

Content hash

sha256:d2df4f6541405c8c12d663e24d33667215d425e157671718d0cd6e310779a321

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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