The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-fermat-s-little-theorem-answer-c-4b1d

stable pending witness
2026-05-29 04:36:23 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of Fermat's little theorem? Answer concisely in 2-3 sentences.
87 chars

Generation

Fermat's Little Theorem is fundamental to modern cryptography and number theory, stating that if p is prime and a is not divisible by p, then a^(p-1) ≡ 1 (mod p). It provides the mathematical foundation for RSA encryption and other public-key cryptography systems that secure digital communications. The theorem is also essential for primality testing and computing modular multiplicative inverses efficiently.
31 tokens in · 95 tokens out · 2300 ms · $0.0015

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
2307.0 ms
Base LLM
2300.2 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0015

Trail

04:36:23 received prompt_chars=87 verifiers=['scripture_anchors', 'theology_doctrine']
04:36:23 red_gate decision=pass reason=no disqualifying input patterns detected
04:36:26 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=95 latency_ms=2300.2 cost_usd=0.0015
04:36:26 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:36:26 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:36:26 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:36:26 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:36:26 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:36:26 signed hash_algo=sha256 hash=sha256:c98cdcddd98e12187c96ed09c8e8cc788b70ad486a62d08ed17e060edaf430b2

Content hash

sha256:c98cdcddd98e12187c96ed09c8e8cc788b70ad486a62d08ed17e060edaf430b2

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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