The Mechanism · Gated-generation receipt

gen-state-the-pythagorean-theorem-precisely-and-explain-why-it-m-a9f0

stable pending witness
2026-05-29 05:16:54 UTC · anthropic/claude-sonnet-4-5

Prompt

State the Pythagorean theorem precisely and explain why it matters in 2-3 sentences.
84 chars

Generation

## Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides: **a² + b² = c²**, where c is the hypotenuse. This theorem matters because it fundamentally connects geometry and algebra, allowing us to calculate distances and angles in countless practical applications from construction and navigation to computer graphics and physics. It's one of the most useful mathematical relationships ever discovered, forming the basis for trigonometry and appearing everywhere from the Pythagorean distance formula to Einstein's spacetime equations.
29 tokens in · 134 tokens out · 4701 ms · $0.0021

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
4708.1 ms
Base LLM
4700.7 ms
Verifiers
0.1 ms
Gates
0.1 ms
Cost
$0.0021

Trail

05:16:54 received prompt_chars=84 verifiers=['scripture_anchors', 'theology_doctrine']
05:16:54 red_gate decision=pass reason=no disqualifying input patterns detected
05:16:58 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=134 latency_ms=4700.7 cost_usd=0.0021
05:16:58 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:16:58 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:16:58 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:16:58 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:16:58 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:16:58 signed hash_algo=sha256 hash=sha256:f011b0caef7209f55ccbf65c6e9e1d0973321a0d71d92e3f81bfa7edd3e7700a

Content hash

sha256:f011b0caef7209f55ccbf65c6e9e1d0973321a0d71d92e3f81bfa7edd3e7700a

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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