Building value through accumulation

Short summary

HOCAI's value = (cbBTC pool × BTC price) / 10M tokens. Returns = BTC growth + cbBTC additions. Math shows: At 50% annual BTC growth, base case yields ~1.8x yearly (vs. BTC's 1.5x), compounding to 18.9x over 5 years (vs. BTC's 7.59x). With investor additions, up to 28.5x in 5 years—leveraged exposure faster than traditional assets.

Lets us explain

Bitcoin's allure lies in its finite supply and decentralized strength, consistently delivering as digital gold. Yet, pure holding misses amplification potential. HOCAI refines this with a treasury model akin to MicroStrategy—aggressively acquiring Bitcoin for value enhancement—but fully on-chain for transparency and inclusivity. Critically, HOCAI is engineered to outperform Bitcoin itself through compounded mechanisms, as we'll demonstrate with math below.

Problem: Volatility and Stagnation in Portfolios

Investors often juggle Bitcoin's stability with altcoins' growth bets, but ETH-paired assets like our initial WETH liquidity expose holders to unnecessary swings, as seen in the past year's dips and recoveries. Early HOCAI adopters endured this, yet held firm, highlighting the need for a Bitcoin-backed pivot to harness consistent growth.

Agitating the Issue: Lost Opportunities in Fragmented Strategies

Without compounding, gains remain linear; bear markets erode confidence, and alt hype fades. What if you could steadily amplify Bitcoin exposure, leveraging AI to trade efficiently, capitalize on spikes, and incorporate investor gifts—all while reusing a battle-tested token with no recent sells and established branding?

Solution: HOCAI's Leveraged Bitcoin Strategy

With 10 million tokens backed by an expanding cbBTC pool on Base starting at 0.1 cbBTC, HOCAI commits to weekly Bitcoin buys. Treasury operations, fueled by AI and trading algorithms on Base pairs, accelerate accumulation with an assumed 20% annual yield. On Bitcoin surges, we sell HOCAI at premiums to rebuy more cbBTC, boosting the ratio per token. Investor-gifted funds—at a base $250 weekly—are directly converted to cbBTC additions, effectively issuing value by enhancing the pool without minting new tokens. Everything's on-chain: balances, trades, and metrics. No opacity—just verifiable growth continuing HOCAI's success from gaming to treasury.

To illustrate why HOCAI grows faster than pure Bitcoin, consider the core dynamics. The HOCAI/cbBTC relationship functions like a liquidity pool with the constant product formula , where a is the HOCAI reserve (fixed supply portion in the effective treasury pool), b is the cbBTC reserve, and k is constant. However, since HOCAI supply is capped at the effective value per token is driven by net asset value (NAV): where is total cbBTC in the pool, and is Bitcoin's price in USD.

Holding pure Bitcoin yields returns solely from . For HOCAI, returns compound from both Bitcoin's price growth and additional cbBTC accumulation: . The extra comes from three sources: (1) weekly investor additions (base $250 USD, or $13,000 annually, converted to cbBTC), (2) AI-trading earnings from preallocated pools yielding 20% annually added as cbBTC, and (3) strategic sales during peaks (not modeled in base case).

Assume Bitcoin grows at an annual rate r = 50% (historical average). In the worst case (no investor additions or engagement), the 20% yield gives HOCAI returns ≈ (1 + r) * (1 + 0.2) = 1.5 * 1.2 = 1.8x annually. Over 5 years: Pure BTC = —more than double.

In the base case with $13,000 annual investor additions, growth compounds further. Starting with

Each year, apply 20% yield

, then grow . After 5 years, HOCAI multipliers reach approximately 28.5x (vs. BTC's 7.59x), as additions front-load growth while yields compound. For example, if initial increases by 0.11 cbBTC from additions in year 1 (at initial ), backing boosts 110% pre-yield, creating amplified exposure independent of . Investor gifts amplify this: A $10,000 contribution buys ~0.00085 cbBTC (at $118,000 BTC), added directly, increasing without dilution.

This math proves HOCAI's edge: It captures Bitcoin's upside plus proactive accumulation, making it a superior long-term bet for amplified returns.