The Mechanism · Gated-generation receipt

gen-explain-the-pythagorean-theorem-as-you-would-to-a-capable-st-ab2d

stable pending witness
2026-05-29 06:44:42 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the Pythagorean theorem as you would to a capable student, in 3-4 sentences.
84 chars

Generation

The Pythagorean theorem tells us that in a right triangle (one with a 90-degree angle), there's a special relationship between the sides. If you square the lengths of the two shorter sides (called legs) and add them together, that sum equals the square of the longest side (called the hypotenuse). We write this as a² + b² = c², where c is always the hypotenuse. This means if you know any two sides of a right triangle, you can always calculate the third side.
32 tokens in · 115 tokens out · 2193 ms · $0.0018

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
2199.6 ms
Base LLM
2192.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0018

Trail

06:44:42 received prompt_chars=84 verifiers=['scripture_anchors', 'theology_doctrine']
06:44:42 red_gate decision=pass reason=no disqualifying input patterns detected
06:44:44 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=32 tokens_out=115 latency_ms=2192.9 cost_usd=0.0018
06:44:44 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:44:44 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:44:44 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:44:44 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:44:44 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:44:44 signed hash_algo=sha256 hash=sha256:043a490850aa4c6f39c3fc73fc75157bdf544ef33d3f41a9b47f8df5c0830c28

Content hash

sha256:043a490850aa4c6f39c3fc73fc75157bdf544ef33d3f41a9b47f8df5c0830c28

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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