The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-graph-coloring-counts-answer-con-0d85

stable pending witness
2026-05-29 06:23:57 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of graph coloring counts? Answer concisely in 2-3 sentences.
85 chars

Generation

Graph coloring counts reveal fundamental structural properties of graphs and have important applications across mathematics and computer science. The chromatic polynomial, which counts the number of valid colorings using k colors, encodes information about the graph's connectivity, symmetries, and complexity. These counts appear in diverse areas including scheduling problems, statistical mechanics (Potts models), and algebraic graph theory.
29 tokens in · 79 tokens out · 2743 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
2753.1 ms
Base LLM
2742.9 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

06:23:57 received prompt_chars=85 verifiers=['scripture_anchors', 'theology_doctrine']
06:23:57 red_gate decision=pass reason=no disqualifying input patterns detected
06:23:59 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=79 latency_ms=2742.9 cost_usd=0.0013
06:23:59 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:23:59 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:23:59 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:23:59 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:23:59 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:23:59 signed hash_algo=sha256 hash=sha256:b2e6cdad14d9836762d5562864bb43fceef65d74d5d5a8a6a78a34912f44fdb2

Content hash

sha256:b2e6cdad14d9836762d5562864bb43fceef65d74d5d5a8a6a78a34912f44fdb2

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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