The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-cross-product-answer-concise-f1b1

stable pending witness
2026-05-29 02:45:35 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the cross product? Answer concisely in 2-3 sentences.
81 chars

Generation

The cross product produces a vector perpendicular to two given vectors, with magnitude equal to the area of the parallelogram they span. This makes it essential for calculating torque, angular momentum, and finding normal vectors to surfaces in physics and engineering. It's fundamentally a 3D operation that captures rotational and orientational relationships between vectors.
28 tokens in · 74 tokens out · 2383 ms · $0.0012

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
2392.3 ms
Base LLM
2382.9 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0012

Trail

02:45:35 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
02:45:35 red_gate decision=pass reason=no disqualifying input patterns detected
02:45:38 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=74 latency_ms=2382.9 cost_usd=0.0012
02:45:38 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:45:38 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:45:38 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:45:38 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:45:38 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:45:38 signed hash_algo=sha256 hash=sha256:6417c1140eed3992c46923c76632710b6caa1ddf22099c11e3fde07222179157

Content hash

sha256:6417c1140eed3992c46923c76632710b6caa1ddf22099c11e3fde07222179157

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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