The Mechanism · Gated-generation receipt

gen-state-the-rank-of-a-matrix-precisely-and-explain-why-it-matt-99fd

stable pending witness
2026-05-29 03:29:26 UTC · anthropic/claude-sonnet-4-5

Prompt

State the rank of a matrix precisely and explain why it matters in 2-3 sentences.
81 chars

Generation

# Rank of a Matrix The **rank** of a matrix is the maximum number of linearly independent rows (or columns) in the matrix, equivalently the dimension of the vector space spanned by its rows or columns. The rank matters because it determines the dimension of the solution space for linear systems: it tells us whether a system has a unique solution, infinitely many solutions, or no solution. Additionally, rank reveals fundamental properties like invertibility (a square matrix is invertible if and only if it has full rank) and the dimension of the image of a linear transformation.
27 tokens in · 123 tokens out · 3138 ms · $0.0019

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
3144.9 ms
Base LLM
3137.7 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0019

Trail

03:29:26 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
03:29:26 red_gate decision=pass reason=no disqualifying input patterns detected
03:29:30 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=123 latency_ms=3137.7 cost_usd=0.0019
03:29:30 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:29:30 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:29:30 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:29:30 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:29:30 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:29:30 signed hash_algo=sha256 hash=sha256:268d3a6968b1852b87644345918c57b4e642fdf6d283092bcf21c6dbe53c7c6a

Content hash

sha256:268d3a6968b1852b87644345918c57b4e642fdf6d283092bcf21c6dbe53c7c6a

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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