The Mechanism · Gated-generation receipt

gen-explain-diophantine-equations-as-you-would-to-a-capable-stud-75fb

stable pending witness
2026-05-29 05:22:44 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain Diophantine equations as you would to a capable student, in 3-4 sentences.
82 chars

Generation

A Diophantine equation is any polynomial equation where you're only looking for integer solutions (whole numbers, positive or negative). For example, while 2x + 3y = 7 has infinitely many solutions if x and y can be any real numbers, there are only specific integer pairs that work, like (2,1) or (-1,3). These equations are named after the ancient Greek mathematician Diophantus and range from simple linear equations to extremely difficult problems like Fermat's Last Theorem. What makes them challenging and interesting is that standard algebraic techniques don't always work—you often need number theory and creative reasoning to find which integer solutions exist.
30 tokens in · 145 tokens out · 5154 ms · $0.0023

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
5161.3 ms
Base LLM
5153.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0023

Trail

05:22:44 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
05:22:44 red_gate decision=pass reason=no disqualifying input patterns detected
05:22:49 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=145 latency_ms=5153.9 cost_usd=0.0023
05:22:49 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:22:49 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:22:49 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:22:49 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:22:49 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:22:49 signed hash_algo=sha256 hash=sha256:57ab4c8af64a60e552fe4d06e5cca79add0a0fb43f309c1dcde0d2a04a000f9d

Content hash

sha256:57ab4c8af64a60e552fe4d06e5cca79add0a0fb43f309c1dcde0d2a04a000f9d

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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