The Mechanism · Gated-generation receipt

gen-state-a-recurrence-relation-precisely-and-explain-why-it-mat-4295

stable pending witness
2026-05-29 05:19:44 UTC · anthropic/claude-sonnet-4-5

Prompt

State a recurrence relation precisely and explain why it matters in 2-3 sentences.
82 chars

Generation

## Recurrence Relation **Definition:** A recurrence relation is an equation that defines a sequence where each term is expressed as a function of one or more previous terms, typically written as f(n) = g(f(n-1), f(n-2), ...) with specified initial conditions. **Example:** The Fibonacci sequence: F(n) = F(n-1) + F(n-2), with F(0) = 0, F(1) = 1. **Why it matters:** Recurrence relations provide an efficient way to define and analyze recursive algorithms, allowing us to calculate time/space complexity without solving the entire problem. They're fundamental to dynamic programming, algorithm analysis, and modeling naturally recursive phenomena like population growth, making them essential tools in computer science and mathematics.
26 tokens in · 176 tokens out · 4249 ms · $0.0027

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
4260.9 ms
Base LLM
4248.8 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0027

Trail

05:19:44 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
05:19:44 red_gate decision=pass reason=no disqualifying input patterns detected
05:19:49 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=176 latency_ms=4248.8 cost_usd=0.0027
05:19:49 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:19:49 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:19:49 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:19:49 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:19:49 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:19:49 signed hash_algo=sha256 hash=sha256:a08d5d8978a7fe0240981bb22a224a2a74f754ed59bff551485fb21867d305d9

Content hash

sha256:a08d5d8978a7fe0240981bb22a224a2a74f754ed59bff551485fb21867d305d9

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.

Bring another teaching · Run a discernment