The Mechanism · Gated-generation receipt

gen-briefly-explain-the-pythagorean-theorem-and-one-common-misco-5814

stable pending witness
2026-05-29 07:37:00 UTC · anthropic/claude-sonnet-4-5

Prompt

Briefly explain the Pythagorean theorem and one common misconception about it.
78 chars

Generation

## The Pythagorean Theorem The Pythagorean theorem states that in a **right triangle**, the square of the hypotenuse (longest side) equals the sum of the squares of the other two sides: **a² + b² = c²** ## Common Misconception Many people mistakenly think the theorem works for **any triangle**. In reality, it **only applies to right triangles** (those with a 90-degree angle). For other triangles, you need different formulas like the Law of Cosines.
25 tokens in · 124 tokens out · 6491 ms · $0.0019

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
6497.7 ms
Base LLM
6491.1 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0019

Trail

07:37:00 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
07:37:00 red_gate decision=pass reason=no disqualifying input patterns detected
07:37:06 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=124 latency_ms=6491.1 cost_usd=0.0019
07:37:06 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:37:06 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:37:06 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:37:06 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:37:06 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:37:06 signed hash_algo=sha256 hash=sha256:e2a6a5b383253fa72b4437c5ce42a23e950b88f3e0fbac4779ba53f48c852acc

Content hash

sha256:e2a6a5b383253fa72b4437c5ce42a23e950b88f3e0fbac4779ba53f48c852acc

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.

Bring another teaching · Run a discernment