The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-diophantine-equations-answer-con-e1dc

stable pending witness
2026-05-29 07:38:39 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of Diophantine equations? Answer concisely in 2-3 sentences.
85 chars

Generation

Diophantine equations are polynomial equations where only integer solutions are sought, named after ancient Greek mathematician Diophantus. They are significant because they connect number theory to algebra and geometry, with applications in cryptography, coding theory, and computer science. Famous examples include Fermat's Last Theorem, which took over 350 years to prove, demonstrating the profound mathematical depth of these seemingly simple equations.
30 tokens in · 88 tokens out · 3086 ms · $0.0014

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
3092.8 ms
Base LLM
3085.7 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0014

Trail

07:38:39 received prompt_chars=85 verifiers=['scripture_anchors', 'theology_doctrine']
07:38:39 red_gate decision=pass reason=no disqualifying input patterns detected
07:38:42 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=88 latency_ms=3085.7 cost_usd=0.0014
07:38:42 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:38:42 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:38:42 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:38:42 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:38:42 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:38:42 signed hash_algo=sha256 hash=sha256:22a63aa9ccc5a8944a3ff711cf2fb1a3758263da95105c0d84224d7cce79f3cb

Content hash

sha256:22a63aa9ccc5a8944a3ff711cf2fb1a3758263da95105c0d84224d7cce79f3cb

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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