The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-pythagorean-theorem-answer-c-bc7f

stable pending witness
2026-05-29 05:51:24 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the Pythagorean theorem? Answer concisely in 2-3 sentences.
87 chars

Generation

The Pythagorean theorem (a² + b² = c²) is fundamental to geometry, establishing the relationship between the sides of a right triangle. It has countless practical applications in construction, navigation, engineering, and physics, and serves as a cornerstone for trigonometry and coordinate geometry. Its significance extends beyond mathematics into virtually every field requiring distance measurement or spatial reasoning.
32 tokens in · 81 tokens out · 2483 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
2490.1 ms
Base LLM
2483.2 ms
Verifiers
0.1 ms
Gates
0.1 ms
Cost
$0.0013

Trail

05:51:24 received prompt_chars=87 verifiers=['scripture_anchors', 'theology_doctrine']
05:51:24 red_gate decision=pass reason=no disqualifying input patterns detected
05:51:26 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=32 tokens_out=81 latency_ms=2483.2 cost_usd=0.0013
05:51:26 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:51:26 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:51:26 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:51:26 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:51:26 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:51:26 signed hash_algo=sha256 hash=sha256:908d02c39aaa55776adc98bb4530b9700bf155cd13894b2155572ba0e46ae949

Content hash

sha256:908d02c39aaa55776adc98bb4530b9700bf155cd13894b2155572ba0e46ae949

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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