The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-determinant-state-any-key-formu-8209

stable pending witness
2026-05-29 06:30:32 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the determinant. State any key formula.
65 chars

Generation

The determinant is a scalar value computed from a square matrix that provides important information about the matrix's properties. For a 2×2 matrix, the formula is **det(A) = ad - bc** where A = [[a,b],[c,d]]. A non-zero determinant indicates the matrix is invertible and its column vectors are linearly independent, while a zero determinant means the matrix is singular (non-invertible). Geometrically, the absolute value of the determinant represents the scaling factor of the linear transformation's effect on area (2D) or volume (3D).
25 tokens in · 131 tokens out · 5085 ms · $0.002

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
5094.3 ms
Base LLM
5085.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.002

Trail

06:30:32 received prompt_chars=65 verifiers=['scripture_anchors', 'theology_doctrine']
06:30:32 red_gate decision=pass reason=no disqualifying input patterns detected
06:30:37 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=131 latency_ms=5085.2 cost_usd=0.002
06:30:37 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:30:37 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:30:37 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:30:37 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:30:37 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:30:37 signed hash_algo=sha256 hash=sha256:88ee2fa928f3f3916d2510e104eed46b52d74f213a08eb9142dc03aa4691de99

Content hash

sha256:88ee2fa928f3f3916d2510e104eed46b52d74f213a08eb9142dc03aa4691de99

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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