The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-chinese-remainder-theorem-an-7d61

stable pending witness
2026-05-29 06:02:10 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the Chinese remainder theorem? Answer concisely in 2-3 sentences.
93 chars

Generation

The Chinese Remainder Theorem provides a method for solving systems of congruences with coprime moduli, essentially showing that such systems always have a unique solution modulo the product of the moduli. It's significant because it enables breaking down complex modular arithmetic problems into simpler, independent subproblems, with applications ranging from ancient calendar calculations to modern cryptography and computer arithmetic.
29 tokens in · 82 tokens out · 2802 ms · $0.0013

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
2808.7 ms
Base LLM
2801.6 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

06:02:10 received prompt_chars=93 verifiers=['scripture_anchors', 'theology_doctrine']
06:02:10 red_gate decision=pass reason=no disqualifying input patterns detected
06:02:12 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=82 latency_ms=2801.6 cost_usd=0.0013
06:02:12 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:02:12 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:02:12 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:02:12 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:02:12 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:02:12 signed hash_algo=sha256 hash=sha256:e35d32efacf3d6e187b35c5614b64679fa2d033b7decbca70ebbbdcad703cae9

Content hash

sha256:e35d32efacf3d6e187b35c5614b64679fa2d033b7decbca70ebbbdcad703cae9

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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