The Mechanism · Gated-generation receipt

gen-state-maximum-flow-precisely-and-explain-why-it-matters-in-2-5468

stable pending witness
2026-05-29 05:01:12 UTC · anthropic/claude-sonnet-4-5

Prompt

State maximum flow precisely and explain why it matters in 2-3 sentences.
73 chars

Generation

# Maximum Flow **Definition:** The maximum flow is the greatest amount of flow that can be sent from a source node *s* to a sink node *t* in a flow network, subject to capacity constraints on edges and flow conservation at intermediate nodes. **Why it matters:** Maximum flow problems model critical real-world scenarios like network bandwidth optimization, transportation logistics, and supply chain management. The max-flow min-cut theorem also establishes a fundamental duality in optimization, proving that the maximum flow equals the minimum capacity of cuts separating source from sink, which has wide-ranging applications in network reliability and resource allocation.
24 tokens in · 131 tokens out · 4511 ms · $0.002

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
4518.6 ms
Base LLM
4511.0 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.002

Trail

05:01:12 received prompt_chars=73 verifiers=['scripture_anchors', 'theology_doctrine']
05:01:12 red_gate decision=pass reason=no disqualifying input patterns detected
05:01:17 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=131 latency_ms=4511.0 cost_usd=0.002
05:01:17 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:01:17 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:01:17 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:01:17 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:01:17 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:01:17 signed hash_algo=sha256 hash=sha256:014ce4662346141c7d003228fd3f47d80371bb1018106fcb5ad72147a01d616b

Content hash

sha256:014ce4662346141c7d003228fd3f47d80371bb1018106fcb5ad72147a01d616b

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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