The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-singular-value-decomposition-st-24c5

stable pending witness
2026-05-29 07:53:18 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the singular value decomposition. State any key formula.
82 chars

Generation

The Singular Value Decomposition (SVD) factorizes any m×n matrix **A** into three matrices: **A** = **UΣV**^T, where **U** is an m×m orthogonal matrix of left singular vectors, **Σ** is an m×n diagonal matrix of non-negative singular values (usually ordered from largest to smallest), and **V**^T is the transpose of an n×n orthogonal matrix of right singular vectors. The singular values on the diagonal of **Σ** are the square roots of the eigenvalues of **A**^T**A** (or **AA**^T). SVD is fundamental in data analysis, dimensionality reduction, and solving linear systems because it provides a complete orthogonal decomposition of any matrix, revealing its rank, range, and null space.
27 tokens in · 188 tokens out · 4256 ms · $0.0029

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
4262.8 ms
Base LLM
4256.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0029

Trail

07:53:18 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
07:53:18 red_gate decision=pass reason=no disqualifying input patterns detected
07:53:22 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=188 latency_ms=4256.2 cost_usd=0.0029
07:53:22 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:53:22 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:53:22 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:53:22 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:53:22 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:53:22 signed hash_algo=sha256 hash=sha256:b71806d0b0510b0c0d15c08838b20c7c44678550791d50a268590eb874c77640

Content hash

sha256:b71806d0b0510b0c0d15c08838b20c7c44678550791d50a268590eb874c77640

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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