The Mechanism · Gated-generation receipt

gen-verify-the-pythagorean-relationship-for-a-3-4-5-triangle-ca4e

stable pending witness
2026-05-29 02:10:55 UTC · anthropic/claude-sonnet-4-5

Prompt

Verify the Pythagorean relationship for a 3-4-5 triangle.
57 chars

Generation

# Verifying the Pythagorean Relationship for a 3-4-5 Triangle The Pythagorean theorem states that for a right triangle: **a² + b² = c²** where *c* is the hypotenuse (longest side) and *a* and *b* are the two legs. ## For a 3-4-5 Triangle: Let me identify the sides: - a = 3 - b = 4 - c = 5 (hypotenuse) ## Verification: **Left side of equation:** - a² + b² = 3² + 4² - = 9 + 16 - = **25** **Right side of equation:** - c² = 5² - = **25** ## Conclusion: Since **25 = 25**, the Pythagorean relationship is verified! ✓ The 3-4-5 triangle is indeed a right triangle and is one of the most common **Pythagorean triples** (sets of three positive integers that satisfy the Pythagorean theorem).
27 tokens in · 262 tokens out · 4587 ms · $0.004

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
4595.4 ms
Base LLM
4587.2 ms
Verifiers
0.4 ms
Gates
0.1 ms
Cost
$0.004

Trail

02:10:55 received prompt_chars=57 verifiers=['scripture_anchors', 'theology_doctrine']
02:10:55 red_gate decision=pass reason=no disqualifying input patterns detected
02:11:00 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=262 latency_ms=4587.2 cost_usd=0.004
02:11:00 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:11:00 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:11:00 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:11:00 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:11:00 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:11:00 signed hash_algo=sha256 hash=sha256:74d99d14ca67b001099df31412d95fa7d9a2b61e4c9b2517e39e2faf773b99eb

Content hash

sha256:74d99d14ca67b001099df31412d95fa7d9a2b61e4c9b2517e39e2faf773b99eb

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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