The Mechanism · Gated-generation receipt

gen-state-the-cross-product-precisely-and-explain-why-it-matters-0c51

stable pending witness
2026-05-29 02:40:32 UTC · anthropic/claude-sonnet-4-5

Prompt

State the cross product precisely and explain why it matters in 2-3 sentences.
78 chars

Generation

# Cross Product Definition For vectors **a** = (a₁, a₂, a₃) and **b** = (b₁, b₂, b₃) in ℝ³, their cross product is: **a** × **b** = (a₂b₃ - a₃b₂, a₃b₁ - a₁b₃, a₁b₂ - a₂b₁) ## Why It Matters The cross product produces a vector perpendicular to both input vectors with magnitude equal to the area of the parallelogram they span, making it essential for computing torque, rotational motion, and surface normals in physics and computer graphics. It's the fundamental operation for capturing rotational phenomena and orientation in three-dimensional space.
25 tokens in · 186 tokens out · 4237 ms · $0.0029

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
4244.7 ms
Base LLM
4237.0 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0029

Trail

02:40:32 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
02:40:32 red_gate decision=pass reason=no disqualifying input patterns detected
02:40:36 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=186 latency_ms=4237.0 cost_usd=0.0029
02:40:36 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:40:36 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:40:36 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:40:36 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:40:36 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:40:36 signed hash_algo=sha256 hash=sha256:88c3ec74ae8084622d4c91db6ececce8dacaf22d78ad0e6f3e72d46e67538abc

Content hash

sha256:88c3ec74ae8084622d4c91db6ececce8dacaf22d78ad0e6f3e72d46e67538abc

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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