The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-discrete-logarithm-problem-a-eb9f

stable pending witness
2026-05-29 06:11:33 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the discrete logarithm problem? Answer concisely in 2-3 sentences.
94 chars

Generation

The discrete logarithm problem is fundamental to modern cryptography because it's computationally difficult to solve, meaning that while it's easy to compute g^x mod p, finding x given g^x is extremely hard for large numbers. This one-way mathematical property forms the security basis for many encryption systems, including Diffie-Hellman key exchange, ElGamal encryption, and some digital signature schemes. If the discrete logarithm problem were easily solvable, much of today's public-key cryptography would be broken.
31 tokens in · 116 tokens out · 3545 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
3552.0 ms
Base LLM
3545.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0018

Trail

06:11:33 received prompt_chars=94 verifiers=['scripture_anchors', 'theology_doctrine']
06:11:33 red_gate decision=pass reason=no disqualifying input patterns detected
06:11:37 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=116 latency_ms=3545.2 cost_usd=0.0018
06:11:37 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:11:37 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:11:37 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:11:37 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:11:37 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:11:37 signed hash_algo=sha256 hash=sha256:c2570332d45049c0b2f6d6af12b9b7ed3a5e3585726fd730f1e4df622639a56f

Content hash

sha256:c2570332d45049c0b2f6d6af12b9b7ed3a5e3585726fd730f1e4df622639a56f

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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