The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-continued-fractions-answer-conci-d709

stable pending witness
2026-05-29 07:34:20 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of continued fractions? Answer concisely in 2-3 sentences.
83 chars

Generation

Continued fractions provide the best rational approximations to irrational numbers, making them invaluable for approximation theory and number theory. They reveal deep mathematical properties, such as whether a number is rational (finite continued fraction) or has special structure like quadratic irrationals (periodic continued fractions). They also have practical applications in fields like calendar design, gear ratios, and solving Diophantine equations.
28 tokens in · 89 tokens out · 3713 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
3718.3 ms
Base LLM
3712.9 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0014

Trail

07:34:20 received prompt_chars=83 verifiers=['scripture_anchors', 'theology_doctrine']
07:34:20 red_gate decision=pass reason=no disqualifying input patterns detected
07:34:24 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=89 latency_ms=3712.9 cost_usd=0.0014
07:34:24 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:34:24 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:34:24 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:34:24 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:34:24 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:34:24 signed hash_algo=sha256 hash=sha256:90ac28abb9b52857dfa25a62d39a45c2e6f0d443a025db0ced0b17d41d20319c

Content hash

sha256:90ac28abb9b52857dfa25a62d39a45c2e6f0d443a025db0ced0b17d41d20319c

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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