The Mechanism · Gated-generation receipt

gen-explain-eigenvalues-and-eigenvectors-as-you-would-to-a-capab-c960

stable pending witness
2026-05-29 07:37:19 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain eigenvalues and eigenvectors as you would to a capable student, in 3-4 sentences.
89 chars

Generation

When you apply a matrix transformation to most vectors, it changes both their direction and length—but eigenvectors are special vectors that only get stretched or squished, keeping the same direction. The eigenvalue tells you the "stretch factor": how much longer or shorter the eigenvector becomes. For example, if a matrix has an eigenvector **v** with eigenvalue 3, then applying the matrix to **v** just triples its length while pointing the same way. Finding eigenvalues and eigenvectors reveals the fundamental "axes" along which a transformation acts most simply.
32 tokens in · 123 tokens out · 8586 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
8593.0 ms
Base LLM
8586.0 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0019

Trail

07:37:19 received prompt_chars=89 verifiers=['scripture_anchors', 'theology_doctrine']
07:37:19 red_gate decision=pass reason=no disqualifying input patterns detected
07:37:27 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=32 tokens_out=123 latency_ms=8586.0 cost_usd=0.0019
07:37:27 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:37:27 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:37:27 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:37:27 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:37:27 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:37:27 signed hash_algo=sha256 hash=sha256:bd39ec13fb5487d6e44b7fac97b616e287f5372ad02b0851d05578d15071e6ab

Content hash

sha256:bd39ec13fb5487d6e44b7fac97b616e287f5372ad02b0851d05578d15071e6ab

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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