The Mechanism · Gated-generation receipt

gen-state-the-discrete-logarithm-problem-precisely-and-explain-w-cbc9

stable pending witness
2026-05-29 03:06:55 UTC · anthropic/claude-sonnet-4-5

Prompt

State the discrete logarithm problem precisely and explain why it matters in 2-3 sentences.
91 chars

Generation

# The Discrete Logarithm Problem **Precise Statement:** Given a cyclic group G with generator g, and an element h ∈ G, find the integer x (if it exists) such that g^x = h. **Why It Matters:** The computational difficulty of solving this problem in certain groups (particularly large prime-order subgroups and elliptic curves) forms the security foundation for many widely-used cryptographic systems, including Diffie-Hellman key exchange, ElGamal encryption, and the Digital Signature Algorithm (DSA). If the discrete logarithm problem could be solved efficiently, these cryptographic protocols would be broken, compromising much of modern secure communication.
28 tokens in · 155 tokens out · 4903 ms · $0.0024

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
4910.4 ms
Base LLM
4903.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0024

Trail

03:06:55 received prompt_chars=91 verifiers=['scripture_anchors', 'theology_doctrine']
03:06:55 red_gate decision=pass reason=no disqualifying input patterns detected
03:06:59 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=155 latency_ms=4903.1 cost_usd=0.0024
03:06:59 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:06:59 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:06:59 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:06:59 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:06:59 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:06:59 signed hash_algo=sha256 hash=sha256:27dd3e937015f92d3a78f041bb19b45ecb326f5671eb5edae324f26a5bd0f243

Content hash

sha256:27dd3e937015f92d3a78f041bb19b45ecb326f5671eb5edae324f26a5bd0f243

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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