The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-recurrence-relation-state-any-key-5f48

stable pending witness
2026-05-29 08:31:24 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a recurrence relation. State any key formula.
71 chars

Generation

A recurrence relation is an equation that defines a sequence where each term is expressed as a function of previous terms. It provides a recursive way to compute sequence values rather than an explicit formula. **Key formula example:** The Fibonacci sequence follows the recurrence relation **F(n) = F(n-1) + F(n-2)** with initial conditions F(0) = 0 and F(1) = 1. Recurrence relations often require base cases (initial conditions) to uniquely determine the sequence.
26 tokens in · 116 tokens out · 3502 ms · $0.0018

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
3509.3 ms
Base LLM
3502.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0018

Trail

08:31:24 received prompt_chars=71 verifiers=['scripture_anchors', 'theology_doctrine']
08:31:24 red_gate decision=pass reason=no disqualifying input patterns detected
08:31:27 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=116 latency_ms=3502.3 cost_usd=0.0018
08:31:27 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:31:27 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:31:27 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:31:27 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:31:27 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:31:27 signed hash_algo=sha256 hash=sha256:51abefb14da2245712e83d5c6d6bc6f4cffa1a2349038b39a1ce3d3417bf847e

Content hash

sha256:51abefb14da2245712e83d5c6d6bc6f4cffa1a2349038b39a1ce3d3417bf847e

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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