The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-maximum-flow-state-any-key-formula-6f7b

stable pending witness
2026-05-29 08:39:32 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain maximum flow. State any key formula.
62 chars

Generation

Maximum flow is a graph theory problem that finds the greatest amount of flow that can be sent from a source node to a sink node through a network with capacity constraints on edges. The **max-flow min-cut theorem** states that the maximum flow value equals the minimum capacity of all cuts separating the source from the sink. A key formula is the **capacity constraint**: for each edge (u,v), the flow f(u,v) ≤ c(u,v), where c(u,v) is the edge capacity. Additionally, **flow conservation** must hold at all intermediate nodes: Σ f(u,v) = Σ f(v,w) (incoming flow equals outgoing flow).
24 tokens in · 156 tokens out · 4156 ms · $0.0024

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
4165.5 ms
Base LLM
4155.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0024

Trail

08:39:32 received prompt_chars=62 verifiers=['scripture_anchors', 'theology_doctrine']
08:39:32 red_gate decision=pass reason=no disqualifying input patterns detected
08:39:36 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=156 latency_ms=4155.7 cost_usd=0.0024
08:39:36 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:39:36 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:39:36 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:39:36 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:39:36 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:39:36 signed hash_algo=sha256 hash=sha256:715c7f333ef4fc6a932b3c7f2bd39d9faea5abea7f790b152f67130ec4b0f6ce

Content hash

sha256:715c7f333ef4fc6a932b3c7f2bd39d9faea5abea7f790b152f67130ec4b0f6ce

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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