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10.1 Privacy as a Function of Pool Size

In privacy systems, anonymity is not a binary property. It is a statistical one. The strength of unlinkability increases with the size and diversity of the anonymity set. Fragmentation across multiple pools, denominations, or assets reduces effective anonymity by shrinking the set of plausible counterparties for any given withdrawal. Abyss therefore adopts a single global anonymity pool. All deposits, regardless of origin, asset type, or intended use, converge into the same commitment set after normalization into $V. This ensures that every participant benefits from every other participant’s activity. Privacy scales monotonically with usage. Formally, for a withdrawal ( W ), the adversary’s uncertainty is bounded by: 
Anonymity(W) ∝ |CommitmentSet|
A single pool maximizes this quantity.

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10.2 Avoiding Denomination Fragmentation

Many privacy protocols require users to deposit fixed denominations. While this simplifies accounting, it fragments liquidity and creates identifiable patterns. Unique combinations of denominations can themselves become fingerprints. Abyss deliberately avoids fixed denominations. Deposits may be of arbitrary size, and withdrawals may be arbitrary fractions of a deposit. Balance enforcement is handled entirely inside the ZK circuit. This eliminates denomination-based correlation and allows natural payment behavior.

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10.3 Composability Advantages

A single pool enables seamless composition with other protocols. Applications integrating Abyss do not need to reason about which pool or asset to use. There is one interface, one proof system, and one anonymity set. This is critical for:
  • Merchant payments
  • Exchange settlement
  • Payroll systems
  • Prediction market payouts
Each integration increases privacy for all users, not just its own participants.

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10.4 Economic and UX Implications

From an economic standpoint, a single pool concentrates liquidity, reducing slippage during entry and exit conversions. From a user perspective, it removes decision complexity. There is no need to choose a pool, denomination, or strategy. Correct usage defaults to maximal privacy.

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10.5 Failure Isolation and Risk

A single pool does not imply shared custody or shared failure domains. Each commitment is independent. A compromised secret affects only that commitment. The protocol does not expose global balance state, preventing systemic leakage.

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10.6 Design Trade-Offs

The primary trade-off is circuit complexity. Supporting arbitrary balances and infinite withdrawals increases proof complexity relative to single-use notes. Abyss accepts this cost to achieve stronger privacy and usability guarantees.

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10.7 Summary

The single pool design is not an optimization. It is a foundational choice. It reflects the protocol’s thesis that privacy improves through convergence, not separation.