The Mechanism · Gated-generation receipt

gen-briefly-explain-pascal-s-triangle-and-one-common-misconcepti-0045

stable pending witness
2026-05-29 08:08:07 UTC · anthropic/claude-sonnet-4-5

Prompt

Briefly explain Pascal's triangle and one common misconception about it.
72 chars

Generation

# Pascal's Triangle **What it is:** Pascal's triangle is a triangular array of numbers where each row starts and ends with 1, and every interior number is the sum of the two numbers directly above it. The first few rows are: ``` 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 ``` The numbers represent binomial coefficients and appear in combinatorics, probability, and algebra. **Common misconception:** Many people think Pascal's triangle was invented by Blaise Pascal (17th century France). In reality, it was studied centuries earlier by mathematicians in Persia, China, and India. The Chinese mathematician Jia Xian described it around 1050 CE, over 600 years before Pascal. Pascal did significantly advance its mathematical applications, which is why it bears his name in the West, but he wasn't its originator.
21 tokens in · 211 tokens out · 5171 ms · $0.0032

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
5179.9 ms
Base LLM
5170.7 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0032

Trail

08:08:07 received prompt_chars=72 verifiers=['scripture_anchors', 'theology_doctrine']
08:08:07 red_gate decision=pass reason=no disqualifying input patterns detected
08:08:12 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=21 tokens_out=211 latency_ms=5170.7 cost_usd=0.0032
08:08:12 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:08:12 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:08:12 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:08:12 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:08:12 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:08:12 signed hash_algo=sha256 hash=sha256:0f331806e6f5959ad5cb30e647c66471a38c3a492801b77c0be69a14311e3004

Content hash

sha256:0f331806e6f5959ad5cb30e647c66471a38c3a492801b77c0be69a14311e3004

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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