The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-pythagorean-theorem-state-any-k-5954

stable pending witness
2026-05-29 05:09:27 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the Pythagorean theorem. State any key formula.
73 chars

Generation

The Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse (the longest side opposite the right angle) equals the sum of the squares of the other two sides. The key formula is **a² + b² = c²**, where *c* is the length of the hypotenuse and *a* and *b* are the lengths of the other two sides. This theorem is fundamental in geometry and has countless applications in mathematics, physics, and engineering.
29 tokens in · 115 tokens out · 2879 ms · $0.0018

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
2886.0 ms
Base LLM
2878.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0018

Trail

05:09:27 received prompt_chars=73 verifiers=['scripture_anchors', 'theology_doctrine']
05:09:27 red_gate decision=pass reason=no disqualifying input patterns detected
05:09:29 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=115 latency_ms=2878.6 cost_usd=0.0018
05:09:29 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:09:29 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:09:29 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:09:29 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:09:29 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:09:29 signed hash_algo=sha256 hash=sha256:2002b11aad91f7f132d9d958e6e8305ebd52f9ba33ebbddb4938753346786433

Content hash

sha256:2002b11aad91f7f132d9d958e6e8305ebd52f9ba33ebbddb4938753346786433

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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