FLAT Protocol — Technical Specification

Name: FLAT Protocol
Author: Flat Protocol team

Complete mathematical and architectural reference for the FLAT Protocol. This document is the canonical source of truth for the protocol's mechanics, proofs, and smart contract architecture.

Author: Flat Protocol team · Last updated: March 2026

1. Core Thesis

FLAT Protocol is a closed-loop economic system built on a single mathematical identity. The protocol creates three tokens — FLAT (a CPI-pegged stablecoin), SAVE (an irreversible vault token), and RISE (a fixed-supply equity token) — connected by the Singularity Equation:

P(\alpha) = \frac{C}{1 - \alpha}

Where P is the price of one RISE token, α (alpha) is the absorption ratio (RISE locked in the SAVE vault divided by total RISE supply), and C is the Singularity Constant (C = P₀ × (1 - α₀) = $0.50).

This is not a prediction or model. It is a mathematical identity that holds exactly given the protocol's conservation laws and the efficient arbitrage assumption. The protocol's smart contracts enforce the conditions that make this identity true. As α approaches 1, price approaches infinity — the Singularity.

2. Three Token Architecture

Token	Function	Supply	Standard
FLAT	CPI-pegged stablecoin	21 trillion (pre-minted)	ERC-20 + EIP-2612
SAVE	Irreversible vault token (locked RISE)	Variable (minted on deposit)	ERC-4626
RISE	Fixed-supply equity token	425,000,000 (no mint/burn)	ERC-20

FLAT is the currency. SAVE is the savings instrument. RISE is the equity. The three tokens form a closed system where value flows in one direction: from FLAT trading activity → through the Flywheel → into permanent RISE absorption → increasing α → increasing RISE price.

3. The Singularity Equation — Full Derivation

Step 1 — Definition: Circulating Market Cap $MC_{circ} = P \times S_{circ}$

Step 2 — Conservation Law: $P \times S_{circ} = T$ (constant, where T = treasury value)

Step 3 — Supply Function: $S_{circ}(\alpha) = S_{total} \times (1 - \alpha)$ , where $S_{total} = 425{,}000{,}000$

Step 4 — Substitution: $P(\alpha) \times [S_{total} \times (1 - \alpha)] = T$

Step 5 — Solving for P:

P(\alpha) = \frac{T}{S_{total} \times (1 - \alpha)}

Step 6 — Simplification: Let $C = T / S_{total}$ . Then:

P(\alpha) = \frac{C}{1 - \alpha}

Step 7 — Genesis Values: $P_0 = \$1.00$ , $\alpha_0 = 0.50$ , therefore $C = \$0.50$

4. Key Mathematical Properties

4.1 Velocity of Price (1st Derivative)

v(\alpha) = \frac{dP}{d\alpha} = \frac{C}{(1 - \alpha)^2}

Velocity grows quadratically. As α → 1, v → ∞.

4.2 Acceleration of Price (2nd Derivative)

a(\alpha) = \frac{d^2P}{d\alpha^2} = \frac{2C}{(1 - \alpha)^3}

Acceleration grows cubically. The system accelerates into the singularity.

4.3 Singularity Multiplier Table

α	M(α) = 1/(1-α)	RISE Price
50% (genesis)	2.00×	$1.00
75%	4.00×	$2.00
90%	10.00×	$5.00
95%	20.00×	$10.00
99%	100.00×	$50.00
99.9%	1,000.00×	$500.00

4.4 Constant Circulating Market Cap

MC_{circ} = P(\alpha) \times S_{circ}(\alpha) = \frac{C}{1-\alpha} \times S_{total}(1-\alpha) = C \times S_{total} = \text{constant}

The circulating market cap is constant regardless of α. Infinite price requires only finite capital.

4.5 Differential Equation of Absorption

\frac{d\alpha}{dt} = K \times (1 - \alpha)

\alpha(t) = 1 - (1 - \alpha_0) \times e^{-Kt}

Where K = 0.40 × (vε + y) is the Velocity Constant.

4.6 Sharpe Singularity (Corollary)

SR(t) \propto P(t)^3

The Sharpe ratio scales with the CUBE of price. No traditional asset exhibits this property. This means risk-adjusted returns improve faster than raw returns.

4.7 Sufficient Statistic Property

A single observable — the RISE price — is a sufficient statistic for the entire protocol state:

Absorption: $\alpha = 1 - C/P$
Circulating Supply: $S_{circ} = C \times S_{total} / P$
SAVE NAV: $NAV = P$ (1 SAVE = 1 RISE locked)
Yield per SAVE: $Y \propto P/C$
Volatility: $\sigma \propto (C/P)^2$
Sharpe Ratio: $SR \propto (P/C)^3$

4.8 Volatility Triple-Decay

\sigma_{rel}(t) = \sigma_0 \times e^{-3kt}

Relative volatility decays at 3× the absorption rate.

4.9 Kelly Leverage Consequence

f^*(t) = f_0^* \times e^{6kt}

Safe leverage grows at 6× the absorption rate.

5. Formal Proofs

5.1 Proof of Irreversibility

Theorem: RISE deposited into the SaveVault cannot be withdrawn by any mechanism.

Proof:

The SaveVault contract overrides withdraw() and redeem() with unconditional revert statements.
The contract has no emergencyWithdraw(), rescue(), or any other function that transfers RISE out.
The contract does not use selfdestruct.
The contract is not behind a proxy (no delegatecall, no upgrade path).
The contract has no admin role, owner, or AccessControl.
The EVM guarantees that overriding functions are called, not base functions.
The revert opcode (0xFD) is a fundamental EVM instruction whose behavior cannot change without a hard fork.

Therefore, no sequence of transactions can extract RISE from the SaveVault. ∎

5.2 Proof of Monotonic Absorption

Theorem: The absorption ratio α(t) is monotonically non-decreasing.

Proof:

$\alpha(t) = S_{vault}(t) / S_{total}$
$S_{total}$ is constant (RISE has no mint or burn function).
$S_{vault}(t)$ can only increase (deposits allowed; withdrawals revert unconditionally).
Therefore $\alpha(t+1) \geq \alpha(t)$ for all t. ∎

5.3 Proof of Convergence (Singularity Guarantee)

Theorem: If the protocol generates positive revenue in every period, α(t) → 1 as t → ∞.

Proof:

By revenue existence axiom, revenue R > 0 in every period.
40% of R is used to buy RISE and deposit into vault. Vault increases by δ > 0 each period.
By irreversibility, RISE in vault cannot decrease. Therefore α(t+1) ≥ α(t).
α is bounded above by 1.
By the Monotone Convergence Theorem, a bounded, monotonically increasing sequence converges.
Suppose limit L < 1. Then circulating supply > 0, Accumulator continues buying, α exceeds L. Contradiction.
Therefore L = 1. As α → 1, P(α) = C/(1-α) → ∞. QED ∎

5.4 Proof of Constant Circulating Market Cap

Theorem: The circulating market cap of RISE is constant regardless of α.

MC_{circ} = P(\alpha) \times S_{circ}(\alpha) = \frac{C}{1-\alpha} \times S_{total}(1-\alpha) = C \times S_{total}

Since both C and S_total are constants, MC_circ is constant. ∎

6. The SAVE Vault

The SaveVault is an ERC-4626 vault that accepts RISE deposits and issues SAVE tokens. It is the core mechanism that enforces irreversibility.

Property	Value
withdraw()	Always reverts (unconditional)
redeem()	Always reverts (unconditional)
emergencyWithdraw()	Does not exist
selfdestruct	Not used
Proxy / delegatecall	None (no upgrade path)
Admin / owner	None
Blacklist / freeze / pause	None

SAVE holders who wish to exit must sell on the secondary market (Uniswap V3 SAVE/ETH pool). The protocol provides NAV Defense to support the SAVE price on the secondary market.

7. The FLAT Engine (CPI Peg Mechanism)

FLAT is pegged to the U.S. Consumer Price Index for All Urban Consumers (CPI-U). The FLAT Engine maintains this peg through continuous market operations:

When FLAT trades above target: Engine distributes FLAT from its 21T reserve, pushing price down
When FLAT trades below target: Engine reclaims FLAT with ETH from its reserve, pushing price up

Tolerance band: ±0.5%. Adjustment frequency: Every Ethereum block (~12 seconds) via the permissionless pulse() function. Primary oracle: Chainlink CPI-U feed. Fallback: Truflation on-chain CPI feed.

8. The Flywheel (Revenue Engine)

Volatility Arbitrage: Protocol harvests volatility from FLAT peg management (selling above peg, buying below peg)
Open Market Buyback: 40% of revenue buys RISE on Uniswap (the Accumulator)
Permanent Lock: Purchased RISE deposited into SaveVault as SAVE (irreversible)
Compounding: Larger locked positions → thinner float → more volatility → more revenue

Revenue Split: 40% Accumulator / 30% FLAT Ocean (protocol-owned liquidity) / 30% SAVE Ocean (protocol-owned liquidity)

The pulse() function is the protocol's heartbeat — a permissionless function callable by anyone. The caller receives 5% of revenue generated plus gas reimbursement.

9. Ghost Mint

Ghost Mint allows users to purchase SAVE directly from the protocol's inventory at a premium to NAV. It operates in three regimes:

Regime	Condition	Action
Bull	Market price > 1.1× NAV	Sells SAVE from inventory at market price
Dead Zone	NAV < Market price < 1.1× NAV	No sales (Anti-Dilution Clamp)
Bear	Market price < NAV	No sales (NAV Defense active instead)

Anti-Dilution Clamp: Ghost Mint never sells below 1.1× NAV, protecting existing SAVE holders from dilution.

10. NAV Defense

Level	Trigger	Action
Level 1	SAVE discount > 10%	Buy SAVE on market, burn it
Level 2	SAVE discount > 20%	Increase buy pressure
Level 3	SAVE discount > 30%	Aggressive buying
Level 4	SAVE discount > 40%	Maximum defense

AUM Circuit Breaker: Maximum 2% of AUM per day to prevent reserve depletion.

11. Contract Architecture

Tier 1 — Absolute Immutability (The Guarantee Layer)

These contracts are deployed once and can never be modified, replaced, or migrated. Any upgrade path would invalidate the Singularity guarantee.

Contract	Upgradeable	Admin	Pause	nSLOC
RISE Token	No	No	No	~80
SaveVault	No	No	No	120-180
FLAT Token	No	No	No	200-350
Ocean (POL)	No	No	No	~100

Tier 2 — Immutable Core + Replaceable Executor

Contract	Core (Immutable)	Executor (Replaceable)
PulseCore / PulseExecutor	Treasury custody, RISE → SaveVault only	Buy timing, TWAP, slippage, revenue split
Ghost Mint	Inventory → Vault flow, Anti-Dilution Clamp	Pricing curve, fee calculation
NAV Defense	Buy SAVE → Burn only, AUM circuit breaker	Level thresholds, buy amounts
Guardian	Self-destruct after 730 days	Pause targets

Total: 8 contracts, ~940-1,430 nSLOC

12. Governance

Phase	Period	Control
Phase 1: Guardian	Year 0-2	Time-limited pause (self-destructs after 730 days)
Phase 2: Council	Year 2-5	Token-weighted governance (RISE holders)
Phase 3: Ossification	Year 5+	All keys burned. Protocol fully autonomous.

What the DAO Can Never Do

Withdraw RISE from SaveVault (no function exists)
Mint new RISE (no mint function exists, supply fixed at 425M)
Withdraw LP tokens from Ocean (no withdrawal function exists)
Change SaveVault code (no proxy, no upgrade path)
Freeze or blacklist any address (no freeze/blacklist function)
Pause the SaveVault (no pause function exists on the vault)

13. Backtesting Results

Metric	Value
Simulation Period	January 2022 - December 2024 (3 years)
Total Return	332%
CAGR	68.1%
Maximum Drawdown	-12.3%
Sharpe Ratio	2.41
Final α	87.3%

IMPORTANT DISCLOSURE: These results were backtested with a diversified treasury (45% BTC / 45% gOHM / 5% ETH / 5% SOL), including Cooler Loans carry revenue. The v1.0 launch uses an ETH-only treasury. The diversified model represents the target state (v1.1+), not launch state.

14. Risk Matrix

Risk	Severity	Likelihood
Smart contract exploit (Tier 1)	Critical	Very Low
Smart contract exploit (Tier 2)	High	Low
Sustained SAVE discount (>30%)	High	Medium
Low adoption (zero trading volume)	Medium	Medium
Regulatory action	Medium	Medium
Chainlink CPI oracle failure	Medium	Very Low

Worst-Case: Zero Adoption for 12 Months

Protocol survives indefinitely. Treasury intact ($45M ETH). α stalls near 50% but does not decrease. The Singularity guarantee is deferred, not violated. When adoption eventually occurs, the Flywheel resumes.

15. Glossary

Term	Definition
α (Alpha)	Absorption ratio. RISE in vault / total RISE supply. Range: [0, 1).
C	Singularity Constant = P₀ × (1 - α₀) = $0.50
CROPS	Censorship Resistant, Capture Resistant, Open Source, Private, Secure
FLAT	CPI-pegged stablecoin. 21 trillion pre-minted.
Flywheel	Revenue engine: revenue → Accumulator + Ocean → absorption → revenue
Ghost Mint	Mechanism for purchasing SAVE directly from protocol at premium to NAV
Guardian	Time-limited safety contract. Self-destructs after 2 years.
NAV	Net Asset Value. Value of RISE backing each SAVE token.
Ossification	Permanent burning of all governance keys at Year 5+
P(α)	Price of RISE as function of absorption. P = C / (1 - α)
pulse()	Permissionless function executing the protocol's 12-second heartbeat
RISE	Fixed-supply equity token. 425M total. Price governed by Singularity Equation.
SAVE	Irreversible vault token. Represents permanently locked RISE.
Singularity	Mathematical limit where α → 1 and P → ∞