The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-discrete-logarithm-problem-stat-0fbe

stable pending witness
2026-05-29 07:16:06 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the discrete logarithm problem. State any key formula.
80 chars

Generation

The discrete logarithm problem asks: given a generator **g**, a prime modulus **p**, and a value **h**, find the exponent **x** such that **g^x ≡ h (mod p)**. While computing **h** from **g**, **x**, and **p** (modular exponentiation) is computationally efficient, finding **x** given **g**, **h**, and **p** is believed to be computationally intractable for sufficiently large values. This asymmetry forms the basis for many cryptographic systems, including Diffie-Hellman key exchange and ElGamal encryption.
28 tokens in · 143 tokens out · 4279 ms · $0.0022

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
4288.5 ms
Base LLM
4279.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

07:16:06 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
07:16:06 red_gate decision=pass reason=no disqualifying input patterns detected
07:16:10 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=143 latency_ms=4279.1 cost_usd=0.0022
07:16:10 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:16:10 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:16:10 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:16:10 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:16:10 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:16:10 signed hash_algo=sha256 hash=sha256:cb66f46afc31cee51a028405a7f6ec0b6df9088469a58ae75eb3059b06436e7c

Content hash

sha256:cb66f46afc31cee51a028405a7f6ec0b6df9088469a58ae75eb3059b06436e7c

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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