The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-determinant-answer-concisely-7366

stable pending witness
2026-05-29 04:12:30 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the determinant? Answer concisely in 2-3 sentences.
79 chars

Generation

The determinant is a scalar value that encodes key properties of a square matrix. It indicates whether a matrix is invertible (non-zero determinant) or singular (zero determinant), and geometrically represents the signed volume scaling factor of the linear transformation represented by the matrix. It's also used to solve systems of linear equations and compute eigenvalues.
28 tokens in · 77 tokens out · 2768 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
2773.7 ms
Base LLM
2767.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0012

Trail

04:12:30 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
04:12:30 red_gate decision=pass reason=no disqualifying input patterns detected
04:12:32 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=77 latency_ms=2767.9 cost_usd=0.0012
04:12:32 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:12:32 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:12:32 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:12:32 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:12:32 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:12:32 signed hash_algo=sha256 hash=sha256:6289a802a7b6fe7b5a7737bae65390a00e9217e041c7c1071d0709cb0fd327fd

Content hash

sha256:6289a802a7b6fe7b5a7737bae65390a00e9217e041c7c1071d0709cb0fd327fd

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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