The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-eigenvalues-and-eigenvectors-ans-62d1

stable pending witness
2026-05-29 04:17:45 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of eigenvalues and eigenvectors? Answer concisely in 2-3 sentences.
92 chars

Generation

Eigenvalues and eigenvectors reveal the fundamental directions and scaling factors of linear transformations. They simplify complex matrix operations by identifying special vectors that only get stretched or compressed (not rotated) when the transformation is applied. This makes them essential for applications like analyzing system stability, performing dimensionality reduction (PCA), solving differential equations, and understanding vibration modes in physical systems.
32 tokens in · 83 tokens out · 3626 ms · $0.0013

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
3631.6 ms
Base LLM
3625.6 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

04:17:45 received prompt_chars=92 verifiers=['scripture_anchors', 'theology_doctrine']
04:17:45 red_gate decision=pass reason=no disqualifying input patterns detected
04:17:48 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=32 tokens_out=83 latency_ms=3625.6 cost_usd=0.0013
04:17:48 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:17:48 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:17:48 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:17:48 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:17:48 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:17:48 signed hash_algo=sha256 hash=sha256:34e8c148aabfda800e74404a5c3dc52df15f847d7a3d917a2616e82f59a355ae

Content hash

sha256:34e8c148aabfda800e74404a5c3dc52df15f847d7a3d917a2616e82f59a355ae

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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