The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-partitions-of-an-integer-answer-328c

stable pending witness
2026-05-29 04:44:00 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of partitions of an integer? Answer concisely in 2-3 sentences.
88 chars

Generation

Partitions of an integer represent all the ways to write a number as a sum of positive integers, where order doesn't matter. They are fundamental in number theory, combinatorics, and mathematical physics, appearing in problems ranging from counting solutions to equations to understanding quantum states and modular forms. The partition function p(n), which counts these partitions, has deep connections to topics like Ramanujan's congruences and the theory of q-series.
30 tokens in · 98 tokens out · 2888 ms · $0.0016

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
2896.6 ms
Base LLM
2888.3 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0016

Trail

04:44:00 received prompt_chars=88 verifiers=['scripture_anchors', 'theology_doctrine']
04:44:00 red_gate decision=pass reason=no disqualifying input patterns detected
04:44:02 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=98 latency_ms=2888.3 cost_usd=0.0016
04:44:02 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:44:02 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:44:02 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:44:02 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:44:02 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:44:02 signed hash_algo=sha256 hash=sha256:b25647f112d889cc9e54b19b82db1bfb3c1c3787fcaeb3028d260920cf95b602

Content hash

sha256:b25647f112d889cc9e54b19b82db1bfb3c1c3787fcaeb3028d260920cf95b602

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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