The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-rsa-algorithm-state-any-key-for-6d45

stable pending witness
2026-05-29 06:06:04 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the RSA algorithm. State any key formula.
67 chars

Generation

RSA is a public-key cryptography algorithm that uses two keys: a public key for encryption and a private key for decryption. It relies on the mathematical difficulty of factoring large numbers that are products of two prime numbers. The key formulas are: - Choose primes p and q, compute n = pq and φ(n) = (p-1)(q-1) - Encryption: C = M^e mod n - Decryption: M = C^d mod n, where ed ≡ 1 (mod φ(n)) The security comes from the fact that while encryption with e is easy, finding d requires knowing the prime factors of n, which is computationally infeasible for sufficiently large primes.
26 tokens in · 170 tokens out · 4493 ms · $0.0026

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
4499.8 ms
Base LLM
4492.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0026

Trail

06:06:04 received prompt_chars=67 verifiers=['scripture_anchors', 'theology_doctrine']
06:06:04 red_gate decision=pass reason=no disqualifying input patterns detected
06:06:09 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=170 latency_ms=4492.6 cost_usd=0.0026
06:06:09 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:06:09 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:06:09 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:06:09 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:06:09 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:06:09 signed hash_algo=sha256 hash=sha256:c066f6cd39ad8dc1a5d073a9a3a8495debdd712e34623093930e2ba6d50b6738

Content hash

sha256:c066f6cd39ad8dc1a5d073a9a3a8495debdd712e34623093930e2ba6d50b6738

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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