The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-a-recurrence-relation-answer-con-5a56

stable pending witness
2026-05-29 08:17:54 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of a recurrence relation? Answer concisely in 2-3 sentences.
85 chars

Generation

A recurrence relation defines a sequence where each term is expressed as a function of previous terms, providing a compact way to describe complex patterns and processes. It is fundamental in computer science for analyzing algorithm efficiency (particularly recursive algorithms) and in mathematics for modeling dynamic systems, population growth, and solving counting problems. Recurrence relations can often be solved to find closed-form expressions, enabling direct calculation of any term without computing all previous values.
29 tokens in · 91 tokens out · 4353 ms · $0.0015

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
4360.1 ms
Base LLM
4353.5 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0015

Trail

08:17:54 received prompt_chars=85 verifiers=['scripture_anchors', 'theology_doctrine']
08:17:54 red_gate decision=pass reason=no disqualifying input patterns detected
08:17:58 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=91 latency_ms=4353.5 cost_usd=0.0015
08:17:58 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:17:58 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:17:58 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:17:58 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:17:58 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:17:58 signed hash_algo=sha256 hash=sha256:352333b6a94835c2f5d7141df47930701a599f9743acce9df9f431d42ecd7523

Content hash

sha256:352333b6a94835c2f5d7141df47930701a599f9743acce9df9f431d42ecd7523

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