The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-pascal-s-triangle-answer-concise-8ad6

stable pending witness
2026-05-29 07:35:54 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of Pascal's triangle? Answer concisely in 2-3 sentences.
81 chars

Generation

Pascal's triangle is a triangular array of numbers where each entry is the sum of the two numbers above it, revealing fundamental patterns in mathematics. It encodes binomial coefficients used in algebra, probability, and combinatorics, showing coefficients for polynomial expansions like (a+b)ⁿ and calculating combinations. The triangle also contains numerous hidden patterns including the Fibonacci sequence, powers of 2, and triangular numbers.
28 tokens in · 95 tokens out · 2746 ms · $0.0015

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
2753.0 ms
Base LLM
2745.8 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0015

Trail

07:35:54 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
07:35:54 red_gate decision=pass reason=no disqualifying input patterns detected
07:35:57 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=95 latency_ms=2745.8 cost_usd=0.0015
07:35:57 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:35:57 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:35:57 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:35:57 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:35:57 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:35:57 signed hash_algo=sha256 hash=sha256:27a769eed161b1d54d9bdea9d0b3b0b66a2f541c8c3d3039bbc8fcb3a17c2922

Content hash

sha256:27a769eed161b1d54d9bdea9d0b3b0b66a2f541c8c3d3039bbc8fcb3a17c2922

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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