The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-master-theorem-answer-concis-6284

stable pending witness
2026-05-29 08:43:16 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the master theorem? Answer concisely in 2-3 sentences.
82 chars

Generation

The Master Theorem provides a quick formula for determining the time complexity of divide-and-conquer algorithms without manually solving recurrence relations. It applies to recurrences of the form T(n) = aT(n/b) + f(n), where a problem is divided into 'a' subproblems of size n/b. This makes it invaluable for analyzing common algorithms like merge sort, binary search, and many recursive solutions.
28 tokens in · 99 tokens out · 2874 ms · $0.0016

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
2880.3 ms
Base LLM
2873.5 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0016

Trail

08:43:16 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
08:43:16 red_gate decision=pass reason=no disqualifying input patterns detected
08:43:19 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=99 latency_ms=2873.5 cost_usd=0.0016
08:43:19 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:43:19 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:43:19 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:43:19 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:43:19 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:43:19 signed hash_algo=sha256 hash=sha256:4dcda2b5ebd55db0137e13d548a94ff961e6db0bba5f35a911cc0393b091a2be

Content hash

sha256:4dcda2b5ebd55db0137e13d548a94ff961e6db0bba5f35a911cc0393b091a2be

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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