The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-rank-of-a-matrix-answer-conc-341c

stable pending witness
2026-05-29 07:00:20 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the rank of a matrix? Answer concisely in 2-3 sentences.
84 chars

Generation

The rank of a matrix indicates the dimension of the vector space spanned by its columns (or rows), representing the number of linearly independent columns or rows. It determines key properties such as whether a system of linear equations has a unique solution, infinitely many solutions, or no solution. The rank also reveals the maximum number of independent equations in a system and is fundamental to understanding transformations, invertibility, and the null space of the matrix.
30 tokens in · 93 tokens out · 3417 ms · $0.0015

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
3423.8 ms
Base LLM
3416.6 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0015

Trail

07:00:20 received prompt_chars=84 verifiers=['scripture_anchors', 'theology_doctrine']
07:00:20 red_gate decision=pass reason=no disqualifying input patterns detected
07:00:24 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=93 latency_ms=3416.6 cost_usd=0.0015
07:00:24 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:00:24 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:00:24 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:00:24 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:00:24 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:00:24 signed hash_algo=sha256 hash=sha256:bae69ee3d9717336fee0bdc3add0380c39043ed29ad6d48f88aac79244678514

Content hash

sha256:bae69ee3d9717336fee0bdc3add0380c39043ed29ad6d48f88aac79244678514

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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