The Mechanism · Gated-generation receipt

gen-state-eigenvalues-and-eigenvectors-precisely-and-explain-why-b111

stable pending witness
2026-05-29 06:35:19 UTC · anthropic/claude-sonnet-4-5

Prompt

State eigenvalues and eigenvectors precisely and explain why it matters in 2-3 sentences.
89 chars

Generation

# Eigenvalues and Eigenvectors **Definition:** For a square matrix A, an **eigenvector** v is a non-zero vector that only gets scaled (not rotated) when A is applied to it: Av = λv, where the scalar **λ** is the corresponding **eigenvalue**. ## Why It Matters Eigenvalues and eigenvectors reveal the fundamental directions and scaling factors of linear transformations, making them essential for understanding system behavior. They enable solutions to differential equations, dimensionality reduction (PCA), stability analysis of dynamic systems, Google's PageRank algorithm, quantum mechanics, and countless other applications where finding the "natural axes" of a transformation is critical.
29 tokens in · 155 tokens out · 3811 ms · $0.0024

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
3823.5 ms
Base LLM
3810.9 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0024

Trail

06:35:19 received prompt_chars=89 verifiers=['scripture_anchors', 'theology_doctrine']
06:35:19 red_gate decision=pass reason=no disqualifying input patterns detected
06:35:23 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=155 latency_ms=3810.9 cost_usd=0.0024
06:35:23 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:35:23 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:35:23 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:35:23 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:35:23 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:35:23 signed hash_algo=sha256 hash=sha256:0fa519566379747749effa12cb029236e35bf73064fa4eceab32645e43db6222

Content hash

sha256:0fa519566379747749effa12cb029236e35bf73064fa4eceab32645e43db6222

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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