#### Written by Grok-4, prompt by [@atrasdoarwario](https://x.com/atrasdoarwario/status/1996812714036154427).

# Enhancing Bitcoin's Scalability: A PID-Inspired Approach to Managing UTXO Set Growth

## Abstract

Bitcoin’s UTXO set is currently an unbounded accumulator that risks long-term centralization as node RAM requirements grow without limit. Existing fee incentives have proven insufficient against sustained low-value output creation (e.g., inscriptions, tokenized assets, dust-heavy protocols). This article proposes a soft-fork mechanism that treats UTXO set size as a controlled variable: a slowly rising target size is defined, and a PID-style feedback controller, updated every difficulty epoch, dynamically raises a minimum-value floor beneath which old UTXOs become unspendable. The result is bounded, predictable growth of the UTXO set with ample warning periods, no hard caps on monetary use, and strong resistance to bloat attacks—all while remaining fully compatible with a soft-fork deployment.

## Introduction

Bitcoin, the pioneering decentralized digital currency, operates as a complex dynamic system governed by consensus rules that ensure security, immutability, and permissionless participation. At its core, Bitcoin maintains a distributed ledger known as the blockchain, which records all transactions in a sequence of blocks. Each transaction involves inputs and outputs: inputs reference previously unspent outputs from prior transactions, while outputs create new spendable units called Unspent Transaction Outputs (UTXOs). The UTXO set represents the aggregate state of all currently spendable coins in the network, serving as a critical component for transaction validation and wallet management.

As Bitcoin has evolved, the UTXO set has grown significantly, influenced by increasing adoption and diverse usage patterns. This growth, while indicative of the network's vitality, poses challenges to its long-term scalability and decentralization. Nodes—computers that validate and relay transactions—must store and process the entire UTXO set in memory for efficient operation, which can strain resources such as random access memory (RAM). Unchecked expansion could lead to higher barriers for running full nodes, potentially centralizing control among fewer, well-resourced participants. This article explores a proposed mechanism to address these concerns: an adaptive control system inspired by Proportional-Integral-Derivative (PID) feedback principles, designed to impose bounded growth on the UTXO set while preserving Bitcoin's foundational properties.

## Motivations for UTXO Set Management

To appreciate the need for enhanced UTXO management, it is essential to understand the current status quo and its vulnerabilities. Bitcoin's design prioritizes efficiency and security through mechanisms like block size limits, which cap the amount of data added per block (approximately 1 MB base size, expandable to about 4 MB with Segregated Witness). These limits help control the overall blockchain size, ensuring predictable hardware requirements for storage on hard disk drives (HDDs). Similarly, the difficulty adjustment algorithm maintains a consistent block production rate of roughly one every 10 minutes by dynamically scaling the computational challenge for miners based on network hashrate.

However, the UTXO set lacks comparable built-in constraints. It accumulates as users create new outputs—often in small denominations—without a mandatory mechanism to consolidate or prune them. This can result from various activities, including high-frequency microtransactions, the embedding of non-monetary data (such as through protocols like Ordinals, which inscribe arbitrary information onto satoshis, Bitcoin's smallest unit), or the anchoring of sidechain or tokenized assets that leverage Bitcoin's security but operate externally. While these innovations expand Bitcoin's utility, they can inadvertently increase the UTXO count disproportionately to their economic value, elevating transaction fees during congestion and raising operational costs for nodes.

Existing incentives, such as transaction fees, partially mitigate this by encouraging users to consolidate low-value UTXOs to avoid higher costs. Yet, these market-driven forces are insufficient against sustained patterns of low-value output creation, particularly when driven by external systems that do not bear the full cost of network maintenance. Over time, this leads to bloat: as of recent estimates, the UTXO set exceeds several gigabytes when loaded into memory, complicating node synchronization and validation. Without intervention, projected growth could undermine decentralization, as fewer individuals or entities might afford to participate fully in the network.

The motivation for reform, therefore, stems from a desire to balance innovation with sustainability. An ideal solution would allow gradual UTXO expansion to accommodate genuine monetary usage while introducing feedback to curb excessive accumulation, all without compromising Bitcoin's permissionless nature or requiring a hard fork that could fragment the community.

## A PID-Inspired Feedback Controller for UTXO Control

Drawing from control theory, which studies how systems maintain desired behaviors through feedback, this proposal introduces a dynamic mechanism to regulate UTXO set size. PID controllers, widely used in engineering for processes like temperature regulation or autopilot systems, combine three terms: Proportional \(P\) for immediate response to errors, Integral (I) for correcting persistent deviations, and Derivative (D) for anticipating changes based on trends. In Bitcoin's context, we adapt this framework to compute a minimum value threshold—or "floor"—below which UTXOs become ineligible for spending, effectively deprecating them over time.

Importantly, this deprecation rule constitutes a soft fork: it restricts the set of valid transactions to a subset of those previously allowed, without introducing new capabilities. Upgraded nodes enforce the rule, rejecting deprecated UTXOs as invalid inputs, ensuring backward compatibility and minimizing disruption.

### Mechanism Overview

The controller activates at each difficulty adjustment epoch, approximately every two weeks (2016 blocks), aligning with Bitcoin's existing periodic recalibrations for predictability.

1. **Define a Target UTXO Size Trajectory**: Establish an increasing maximum target for the UTXO set size, denoted as $T(t)$, where $t$ represents the epoch number. This could grow sublinearly with time or blockchain height to reflect organic adoption— for instance, $T(t) = U_0 \cdot (1 + r)^t$, with $U_0$ as the initial size and $r$ a small annual growth rate (e.g., less than 1%). This permits expansion while preventing unbounded divergence.

2. **Measure the Error**: At each epoch, compute the error $e(t) = S(t) - T(t)$, where $S(t)$ is the current UTXO set size (measured by count or aggregate data footprint).

3. **Compute the Floor Adjustment**: Apply the PID formula to adjust the value floor $F(t)$:

$$ \Delta F(t) = K_p \cdot e(t) + K_i \cdot \sum_{k=0}^{t} e(k) + K_d \cdot \frac{e(t) - e(t-1)}{\Delta t} $$

Here, $K_p, K_i, K_d$ are tunable gains, selected conservatively through simulations to ensure stability (e.g., using root locus analysis to avoid oscillatory or unstable roots in the system's characteristic equation). The floor $F(t)$ increases only if $e(t) > 0$, applying to UTXOs below this threshold.

4. **Deprecation Process**: UTXOs with values below $F(t)$ are marked as unspendable in future transactions. To provide fairness and predictability, implement a grace period (e.g., 4-12 months) during which owners can consolidate affected UTXOs.

5. **Safeguards and Tuning**: Incorporate clamps on $\Delta F(t)$ (similar to Bitcoin's difficulty adjustment limits) to prevent abrupt changes that might cause network congestion from mass consolidations. Periodic reviews of gains and targets via community governance would adapt the system to evolving conditions.

### Stability and Dynamics Considerations

In dynamic systems terms, the UTXO set can be modeled as an integrator accumulating outputs minus expenditures. The PID controller introduces negative feedback to dampen this accumulation, driving $S(t)$ toward $T(t)$ with minimal overshoot. Simulations would verify robustness against adversarial scenarios, such as deliberate UTXO spam, ensuring the system's poles remain in the stable region of the complex plane.

Potential benefits include reduced node resource demands, lower fees during normal operation, and enhanced decentralization. Risks, such as over-deprecation affecting small holders, can be mitigated through careful gain selection.

## Conclusion

This PID-inspired approach offers a principled path to managing Bitcoin's UTXO set, fostering sustainable growth while upholding core principles. By integrating feedback control, Bitcoin can evolve as a resilient dynamic system, better equipped for widespread adoption. Further research, including detailed modeling and community discourse, is essential to refine and potentially implement such enhancements.