Call notes from 3-31-2026

tx-structure/calls/notes-3-31-2026.md

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+# Call notes 3-31-2026
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+The group is formalizing cost function metrics for transaction graph analysis and reformulating the problem as max-flow. The core insight: every transaction is a bipartite graph, and subset-sum partitions map naturally to edges between input and output clusters. This generalizes the subjective probability matrix from Istvan's model.
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+The central question is how to compute absorber entropy efficiently, and how quickly it diminishes as an adversary gains information. Absorber entropy functions as an anonymity set size -- the number of distinct sources that could plausibly explain a target UTXO.
+Max flow emerges as a more tractable framing than differential privacy. Where differential privacy measures an instantaneous derivative, max flow quantifies a budget of edges an adversary must cut to de-anonymize a target. More privacy = higher max flow.
+For a given transaction graph, can we apply efficient approximation algorithms — specifically Gomory-Hu trees, which store max flow between any source-sink pair in linear space?
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+Recent work shows max flow is solvable in near-linear time using tree decomposition over small connected components. These algorithms decompose the graph into tractable subproblems, which suggests efficient approximation is feasible.
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+Assume the adversary holds prior knowledge (including off-chain information). The entropy under worst-case conditions defines a conservative lower bound on privacy. When the adversary learns enough to identify a min-cut, they can de-anonymize the target. The goal is to quantify how robust the graph is before that cut is reachable(?) -- need more conscise def. Min cut may not be right wording. 
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+Relation to Prior Work
+This framework addresses a shortcoming in Istvan's model: it replaces the probabilistic framing with a worst-case adversarial one. Min-cost flow covers the probabilistic case; max flow covers the conservative case. The two are complementary -- users or implementations can choose which bound to optimize for.
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+Max flow also enables counterfactual reasoning: "If I coinjoin with maker X instead of Y, how does that change the robustness of the resulting graph?" This separates apparent privacy now from worst-case privacy under future adversarial pressure.
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+Implementers may operate with either a local or global view of the transaction graph. The metric should degrade gracefully under partial information .