The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-counting-with-repetition-answer-eb95

stable pending witness
2026-05-29 07:06:24 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of counting with repetition? Answer concisely in 2-3 sentences.
88 chars

Generation

Counting with repetition is significant because it models real-world scenarios where the same item can be selected multiple times, such as drawing cards with replacement, password generation, or inventory systems with unlimited stock. It uses the formula (n + r - 1) choose (r) for combinations with repetition, which differs fundamentally from counting without repetition and leads to larger possible outcomes.
29 tokens in · 82 tokens out · 3545 ms · $0.0013

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
3552.2 ms
Base LLM
3545.4 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

07:06:24 received prompt_chars=88 verifiers=['scripture_anchors', 'theology_doctrine']
07:06:24 red_gate decision=pass reason=no disqualifying input patterns detected
07:06:28 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=82 latency_ms=3545.4 cost_usd=0.0013
07:06:28 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:06:28 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:06:28 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:06:28 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:06:28 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:06:28 signed hash_algo=sha256 hash=sha256:b6fae38b4b920672bedfb7dd39cd2ba820d98c0e20f5764dc3f8e3ae505a3f5f

Content hash

sha256:b6fae38b4b920672bedfb7dd39cd2ba820d98c0e20f5764dc3f8e3ae505a3f5f

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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