The Mechanism · Gated-generation receipt

gen-define-the-pythagorean-theorem-and-give-one-short-worked-exa-d100

stable pending witness
2026-05-29 05:42:23 UTC · anthropic/claude-sonnet-4-5

Prompt

Define the Pythagorean theorem and give one short worked example.
65 chars

Generation

# Pythagorean Theorem **Definition:** In a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. **Formula:** a² + b² = c² where *c* is the hypotenuse and *a* and *b* are the other two sides. ## Worked Example Find the hypotenuse of a right triangle with legs of 3 cm and 4 cm. **Solution:** - a = 3 cm, b = 4 cm - a² + b² = c² - 3² + 4² = c² - 9 + 16 = c² - 25 = c² - c = 5 cm The hypotenuse is **5 cm**.
22 tokens in · 195 tokens out · 3114 ms · $0.003

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
3122.1 ms
Base LLM
3113.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.003

Trail

05:42:23 received prompt_chars=65 verifiers=['scripture_anchors', 'theology_doctrine']
05:42:23 red_gate decision=pass reason=no disqualifying input patterns detected
05:42:27 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=22 tokens_out=195 latency_ms=3113.9 cost_usd=0.003
05:42:27 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:42:27 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:42:27 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:42:27 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:42:27 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:42:27 signed hash_algo=sha256 hash=sha256:8e125cde1388b2fbd5e6222a96a84b31c73361cdc0145e00151bf2f3879c7fc4

Content hash

sha256:8e125cde1388b2fbd5e6222a96a84b31c73361cdc0145e00151bf2f3879c7fc4

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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