PBX Protocol Documentation

PBX is the first financial instrument where investing in air quality and positioning for outsized upside are structurally the same action. Each listed city has its own token trading against USDC in an AMM pool. A protocol-controlled rebalancing engine monitors real-time PM2.5 data and trades to enforce a single rule: each city's price should reflect its air quality relative to the others.

Cleaner air → price rises. Dirtier air → price falls.

Air quality is the first market built on this infrastructure. The underlying mechanism — real-world signal, continuous pricing, on-chain settlement — generalises to any measurable, locally relevant data stream. Air quality is where it starts.

Every trade funds cleaner air. Fees flow to The Air Fund, Buyback and Burn, and Protocol Treasury automatically. Fees fund impact as a byproduct of trading activity.

Every traditional vehicle for improving air quality — donations, offsets, sensor purchases — consumes your capital on use. In PBX, your capital circulates. Impact is funded as a byproduct of market activity, not instead of it.

PM2.5 concentrations swing 300% daily across multiple cities driven by rush hours, weather fronts, and seasonal shifts. That volatility, continuously priced on-chain for the first time, is what generates the trading volume that powers the mechanism.

The demand to trade on environmental data is not theoretical.

Every number in this document describes how the protocol's AMM computes prices and distributes fees. Constant-product math is deterministic: x × y = k. Given a reserve state, marginal price is defined. Given a trading volume, fee revenue is defined. These are not forecasts of demand, adoption, or returns.

Where this document shows a price at a given reserve level, that is the math — not a prediction that reserves will reach that level. Where this document shows annual fees at a given trading volume, that is the math — not a prediction that volume will be reached. Inflow, turnover, and adoption are inputs, not outputs.

For each city i, the protocol defines two values: P_i (token price) and PM2.5_i (concentration). The efficiency score is computed as:

The goal is to keep efficiency scores aligned across all cities. When a city's efficiency is high — meaning it is underpriced for its air quality — the Engine buys it. When efficiency is low (overpriced), the Engine sells.

A city with clean air does not automatically get bid up — it gets bid up if it is underpriced relative to its air quality compared to the other cities. A city with dirty air does not automatically get sold — it gets sold if it is overpriced relative to its air quality versus the others. The rebalancing engine is not rewarding or punishing air quality in isolation. It is closing mispricings. The air quality data is what defines what "correctly priced" means.

Sensitivity and Square-Root Dampening

The exponent −0.5 (square root) was chosen deliberately. It produces graduated responses without over-reacting to extremes:

• ~50% response for routine 4× daily swings
• ~42% dampening for noise in the clean band (5–15 µg/m³)
• ~68% weight drop for extreme events (10→100+ µg/m³)

PBX uses PM2.5 concentration directly — not the EPA's composite AQI. Raw concentration gives continuous, granular signal; the composite AQI bins readings into a coarser index that loses information at the margins. PurpleAir data is used by U.S. federal agencies including the EPA and the USFS (U.S. Forest Service). It is integrated into the EPA's AirNow Fire and Smoke Map, one of the official public air quality monitoring tools used across the country.

Data Roadmap

PurpleAir is the launch data source. The architecture is designed to incorporate additional feeds over time — including government reference monitors (EPA AirNow, ECCC, state-level networks) and satellite-derived PM2.5 estimates — to improve coverage, redundancy, and geographic expansion beyond the initial three cities.

Two tables illustrate how the rebalancing mechanism works in practice — from a symmetric baseline to a single-city air quality improvement.

Initial State — All Cities Equal

Scenario A — Toronto PM2.5 Drops

Toronto PM2.5 drops from 10 to 8 µg/m³. The Engine detects that Toronto is now underpriced relative to its improved air quality and buys TOR until efficiency scores re-align.

A 20% improvement in PM2.5 translates to an 11.8% price appreciation — the square-root dampening moderates the response proportionally.

The most demanding scenario is a correlated smoke event where all three cities spike simultaneously — but by different amounts. Under linear formula, relative spread would be ~20%. Under square-root dampening, spread compresses to ~9%.

Correlated Smoke Event

The dampening prevents correlated macro events from producing outsized price divergences that would distort the relative signal across cities.

PBX enforces relative efficiency balance. It does not cap absolute price level. If net inflows raise all prices while PM2.5 is stable, all prices rise together — the mechanism only acts when the ratio across cities diverges.

This means early liquidity providers benefit from both macro-level adoption growth (all prices up) and city-level air quality improvement (relative price up). The two return sources are structurally independent.

Fees compress as protocol market cap grows. This creates a competitive schedule that attracts high-volume traders at scale while maintaining impact funding at every tier.

Each city token has a fixed supply of 100,000,000. PBX launches with three cities — Toronto (TOR), New York (NYC), and Chicago (CHI) — for an aggregate protocol supply of 300,000,000 at launch. The schedule below applies identically to every city.

Applied identically to TOR, NYC, and CHI. Aggregate protocol supply at launch: 300,000,000 tokens across all three cities.

PBX has two distinct user groups with different motivations — and both are essential to the flywheel.

The reinforcement loop: utility adopters raise the floor → higher floor means larger price swings on the same PM2.5 move → larger swings attract more speculators → more volume → more contributions to The Air Fund → better air quality → stronger narrative → more utility adopters.

PBX pools use constant-product AMM math: x × y = k, where x and y are the USDC and token reserves. Given any reserve state, the marginal token price is determined. The table shows the token price at various hypothetical reserve states.

These are AMM mechanics. The relationship is deterministic: in a constant-product pool, price is a function of the ratio of reserves.

The table below shows annual fee output as a function of daily turnover at a hypothetical $500M circulating market cap (52 bp fee tier, 18/52 split to The Air Fund). Turnover is daily trading volume as a percentage of market cap.

This table shows fee output as a function of turnover rate. It does not forecast actual turnover.

PBX uses a constant-product AMM (same math as Uniswap) across three city tokens. Each pool starts with $20K USDC and 2M tokens at $0.01. Total supply: 300M tokens, fixed — no inflation. Graduated buy rounds are processed at $25K increments. After each buy, the protocol sells back 30% of tokens, with 70% of sell proceeds re-deposited as liquidity and 30% allocated to treasury.

The Fee Math

Every trade pays a fee, collected as tokens and sold to USDC. At a hypothetical $500M circulating market cap (52 bp tier): 18 bp to The Air Fund, 18 bp to Buyback & Burn, 16 bp to Protocol Treasury. The buyback share buys tokens back and burns them — so the net sell pressure is only 34 bp.

• At 1% daily turnover: $5M daily volume → $26K/day → $9.5M/yr total fees
• At 5% daily turnover: $25M daily volume → $130K/day → $47.5M/yr total fees

Air Fund share at each level = (18/52) × total fees.

Structural Difference

BTC and ETH drain value via inflation that dilutes all holders. PBX drains via trading fees — only traders pay. Holders who don't trade experience zero dilution. The buyback simultaneously creates buy pressure and reduces supply. Fees step down as the protocol scales (60 bp at launch → 10 bp at $100B+ cap), rewarding growth with lower costs.

PBX rests on three observations — each independently validated by existing market data.