The Mechanism · Gated-generation receipt

gen-explain-the-cross-product-as-you-would-to-a-capable-student-a924

hold
2026-05-29 05:43:57 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the cross product as you would to a capable student, in 3-4 sentences.
78 chars

Generation

The cross product takes two vectors in 3D space and produces a third vector that's perpendicular to both of them. The direction follows the right-hand rule: point your fingers along the first vector, curl them toward the second, and your thumb shows where the result points. The magnitude equals the area of the parallelogram formed by the two vectors, which you can calculate as |**a** × **b**| = |**a**||**b**|sin(θ). It's especially useful in physics for finding torque, angular momentum, and magnetic forces.
28 tokens in · 124 tokens out · 3463 ms · $0.0019

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
wait
output contains coercion language: ['force']
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
3473.2 ms
Base LLM
3463.1 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0019

Trail

05:43:57 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
05:43:57 red_gate decision=pass reason=no disqualifying input patterns detected
05:44:00 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=124 latency_ms=3463.1 cost_usd=0.0019
05:44:00 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:44:00 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:44:00 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:44:00 way_gate decision=wait reason=output contains coercion language: ['force']
05:44:00 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:44:00 signed hash_algo=sha256 hash=sha256:ed92137ac9f308c1775cd68a82f913d698fdc6d468910b428424f7a5f16bead1

Content hash

sha256:ed92137ac9f308c1775cd68a82f913d698fdc6d468910b428424f7a5f16bead1

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