The Mechanism · Gated-generation receipt

gen-explain-a-recurrence-relation-as-you-would-to-a-capable-stud-10d2

stable pending witness
2026-05-29 08:07:07 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain a recurrence relation as you would to a capable student, in 3-4 sentences.
82 chars

Generation

A recurrence relation is a way of defining a sequence where each term is expressed as a function of previous terms, rather than having a direct formula. For example, the Fibonacci sequence uses the recurrence F(n) = F(n-1) + F(n-2), meaning each number is the sum of the two before it. You need initial conditions (like F(0) = 0, F(1) = 1) to get the sequence started, and then you can compute any term by working your way up from those base cases. Think of it as a "recipe" that tells you how to build each new term from what you've already calculated.
29 tokens in · 143 tokens out · 3705 ms · $0.0022

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
3712.3 ms
Base LLM
3705.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

08:07:07 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
08:07:07 red_gate decision=pass reason=no disqualifying input patterns detected
08:07:10 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=143 latency_ms=3705.4 cost_usd=0.0022
08:07:10 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:07:10 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:07:10 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:07:10 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:07:10 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:07:10 signed hash_algo=sha256 hash=sha256:994f1c1e7e98dcbc03badbae4a3744697ea28571023ee9362e773e1bdb09438a

Content hash

sha256:994f1c1e7e98dcbc03badbae4a3744697ea28571023ee9362e773e1bdb09438a

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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