The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-eigenvalues-and-eigenvectors-state-2b3d

stable pending witness
2026-05-29 08:44:56 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain eigenvalues and eigenvectors. State any key formula.
78 chars

Generation

Eigenvectors are special non-zero vectors that only get scaled (not rotated) when a linear transformation is applied to them. Eigenvalues are the scaling factors that correspond to each eigenvector. The key formula is: **Av = λv** where A is a matrix, v is an eigenvector, and λ (lambda) is the corresponding eigenvalue. To find eigenvalues, you solve the characteristic equation: **det(A - λI) = 0**, where I is the identity matrix.
29 tokens in · 118 tokens out · 3178 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
3185.3 ms
Base LLM
3178.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0019

Trail

08:44:56 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
08:44:56 red_gate decision=pass reason=no disqualifying input patterns detected
08:44:59 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=118 latency_ms=3178.3 cost_usd=0.0019
08:44:59 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:44:59 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:44:59 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:44:59 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:44:59 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:44:59 signed hash_algo=sha256 hash=sha256:e8601389475c125541e2d3aa7e50ec1ed77bfbc09355b7a0eca741b559927c27

Content hash

sha256:e8601389475c125541e2d3aa7e50ec1ed77bfbc09355b7a0eca741b559927c27

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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