FLAT Protocol — Technical Specification

Name: FLAT Protocol
Author: WeThePeople DAO

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: WeThePeople DAO (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 = T / S (treasury value divided by total supply). The equation is a mathematical identity — not a model.

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 — a redeemable, CPI-pegged stablecoin and the protocol's only obligation. SAVE is the savings instrument — irreversibly locked RISE. RISE is the equity — a fixed-supply token whose price is governed by the Singularity Equation. RISE is not an obligation; it represents ownership in the protocol's treasury surplus.

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. Genesis Configuration

At genesis, the total RISE supply of 425 million tokens is established. The vast majority — 99.988% — is locked in the SAVE vault from Day 1, establishing an extremely high initial absorption ratio:

\alpha_0 = 0.99988, \quad S_{float} = 425M \times (1 - 0.99988) = 51{,}000 \text{ RISE}

This genesis condition is critical: absorption starts extremely close to 1. The floating supply at genesis is only 51,000 RISE tokens out of 425 million total. The protocol is already deep into the hyperbolic curve from Day 1.

Genesis Liquidity Pools (Assuming $20M Raise)

At genesis, the raised capital is distributed across three Uniswap V3 liquidity pools and the treasury. The exact allocation depends on the raise amount. For a $20 million raise:

Pool / Destination	ETH Value	Token Side
RISE-ETH Pool	~$4.25M	4.25M RISE (1% of supply)
FLAT-ETH Pool	~$2.00M	~2M FLAT at oracle price
SAVE-ETH Pool	~$2.00M	~2M SAVE at NAV
Treasury Reserves (ETH)	~$8.00M	Held as ETH in PulseCore

The treasury also holds 208.25 million RISE tokens. At the genesis price of $1.00 per RISE, these tokens have a market value of $208.25 million. The total treasury value at genesis is therefore approximately $224.5 million ($16.25M ETH + $208.25M in RISE). The significance of this composition is explained in Section 12: Treasury Composition & Over-Collateralization.

4. 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: $\alpha_0 = 0.99988$ , meaning only 0.012% of RISE supply is floating at genesis.

5. Key Mathematical Properties

5.1 Velocity of Price (1st Derivative)

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

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

5.2 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.

5.3 Singularity Multiplier Table

α	M(α) = 1/(1-α)	RISE Price	Gain from Genesis (α=99.988%)
99.988% (genesis)	8,333×	Current	1.00×
99.99%	10,000×	—	1.20×
99.999%	100,000×	—	12.00×
99.9999%	1,000,000×	—	120.00×

5.4 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 of RISE is constant at $212.5 million regardless of α. Infinite price requires only finite capital. Note: this refers to the market cap of the floating RISE supply, not the total treasury value (which grows — see Section 12).

5.5 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.

5.6 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.

5.7 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: $SR \propto (P/C)^3$

5.8 Volatility Triple-Decay

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

Relative volatility decays at 3× the absorption rate.

5.9 Kelly Leverage Consequence

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

Safe leverage grows at 6× the absorption rate.

6. Formal Proofs

6.1 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. ∎

6.2 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. ∎

6.3 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.
A portion of R grows protocol-owned liquidity. As LP grows, more FLAT is permanently locked. 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, protocol continues absorbing supply, α exceeds L. Contradiction.
Therefore L = 1. As α → 1, P(α) = C/(1-α) → ∞. QED ∎

6.4 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. ∎

7. 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.

8. 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, collecting ETH in return and pushing the market price down toward the oracle price.
When FLAT trades below target: Engine reclaims FLAT by spending ETH from its reserve, pushing the market price up toward the oracle price.

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.

The spread captured between above-peg sales and below-peg purchases is the protocol's primary revenue source, which feeds the Flywheel (Section 10).

9. FLAT Minting — Oracle-Price Mechanism

FLAT is the protocol's only obligation — a redeemable, CPI-pegged stablecoin. Understanding how new FLAT enters circulation is critical to understanding why the protocol is always solvent.

9.1 How New FLAT Is Created

The protocol sells FLAT at the oracle price (the CPI-adjusted target price), independent of the current market price. The mechanism works as follows:

User requests FLAT: A user sends ETH to the protocol, requesting FLAT at the current oracle price (e.g., $1.05 if CPI has adjusted since launch).
ETH enters treasury: The ETH is deposited into the protocol's reserve, held by PulseCore.
FLAT is distributed: The protocol distributes FLAT from its 21 trillion pre-minted reserve to the user at the oracle price.

9.2 Structural 1:1 Backing

Every FLAT token in circulation is backed by the ETH that was deposited when it was distributed. This is not a design choice that could be changed — it is a structural consequence of the minting mechanism. The protocol cannot distribute FLAT without receiving ETH of equal value at the oracle price. Therefore:

FLAT minting is always at least 1:1 collateralized by construction.

No governance vote, no admin key, and no market condition can change this.

9.3 Arbitrage Opportunity

When the FLAT market price exceeds the oracle price (e.g., market = $1.10, oracle = $1.05), users can purchase FLAT from the protocol at $1.05 and sell on the open market at $1.10, capturing the $0.05 spread. This arbitrage pushes the market price back toward the oracle price while simultaneously growing the treasury's ETH reserves.

When the FLAT market price falls below the oracle price, the FLAT Engine intervenes by spending ETH from reserves to buy FLAT on the market, pushing the price back up. The FLAT reclaimed is returned to the 21T reserve for future distribution.

10. The Flywheel (Revenue Engine)

Volatility Arbitrage: Protocol harvests volatility from FLAT peg management (selling above peg, buying below peg)
Battery Growth: Revenue from charge cycles is converted into deeper protocol-owned liquidity (LP tokens added to the battery)
Permanent Lock: Purchased RISE deposited into SaveVault as SAVE (irreversible)
Compounding: Larger locked positions → thinner float → more volatility → more revenue

Revenue Deployment: 100% of charge-cycle revenue is converted into protocol-owned liquidity (LP tokens), growing the battery that defends the peg during discharge cycles.

The pulse() function is the protocol's heartbeat — a permissionless function callable by anyone. The caller receives a bounty (bountyBps percentage of ETH processed) as incentive.

11. Ghost Mint & SAVE Minting

Ghost Mint allows users to purchase SAVE directly from the protocol's inventory at a premium to NAV. There are two ways users can acquire SAVE:

11.1 Method 1: Ghost Mint (Protocol Direct Sale)

The protocol holds 208.25 million RISE tokens in its treasury (from the 49% genesis allocation). Ghost Mint converts these treasury RISE into SAVE and sells them to users:

User requests SAVE: A user sends ETH to the Ghost Mint contract.
Protocol prices at 1.1× NAV: The protocol calculates the SAVE price as 1.1 times the current RISE price (the Net Asset Value). If RISE = $1.00, SAVE costs $1.10 via Ghost Mint.
ETH enters treasury: The user's ETH is deposited into the protocol's reserves.
Treasury RISE is locked: The protocol takes RISE from its 208.25M treasury stash and deposits it into the SaveVault, permanently locking it.
SAVE is delivered: The SaveVault mints SAVE tokens and the protocol delivers them to the user.

The 10% premium (1.1× NAV) is structural surplus — the protocol collects more ETH than the RISE is worth at current market price. This premium protects existing SAVE holders from dilution and adds to the treasury's over-collateralization.

11.2 Three Operating 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.

11.3 Method 2: Open Market (User Self-Lock)

Users can also acquire SAVE by purchasing RISE on the Uniswap RISE-ETH pool and depositing it directly into the SaveVault themselves. This method does not require Ghost Mint and is always available.

11.4 Phase 1 → Phase 2 Transition

Phase 1 (Protocol-Driven Absorption): The protocol's 208.25M treasury RISE can fuel absorption from α = 50% to approximately α = 99%. During this phase, Ghost Mint is the primary mechanism for new SAVE creation, and every sale adds ETH to the treasury while increasing absorption.

Phase 2 (Market-Driven Absorption): Once the treasury's RISE inventory is exhausted, users must buy RISE from the Uniswap pool and lock it into the SaveVault themselves. At this point, only the 4.25M RISE in the LP pool remains as floating supply. Absorption beyond 99% is driven entirely by market participants.

12. Treasury Composition & Over-Collateralization

12.1 What Is the Obligation?

FLAT is the protocol's only obligation. It is a redeemable, CPI-pegged stablecoin — holders can redeem FLAT for ETH from the treasury at the oracle price. RISE is not an obligation; it is equity. RISE holders own a claim on the protocol's surplus value, but the protocol has no obligation to buy back RISE at any price. Therefore:

\text{Collateralization Ratio} = \frac{\text{Total Treasury Value}}{\text{FLAT in Circulation}}

The denominator is the value of FLAT tokens in circulation (the obligation), not the RISE circulating market cap. This distinction is critical for understanding why the protocol is massively over-collateralized.

12.2 Treasury Composition at Genesis

At genesis (assuming a $20M raise), the treasury holds two categories of assets:

Asset	Quantity	Value at Genesis	Category
ETH (in reserves)	~$8.00M worth	$8,000,000	External capital
ETH (in LP pools)	~$8.25M worth	$8,250,000	External capital (protocol-owned)
RISE tokens (treasury)	208,250,000	$208,250,000	Protocol equity (at $1.00/RISE)
Total Treasury		~$224,500,000

Meanwhile, the FLAT obligation at genesis is approximately $2 million (the FLAT in the FLAT-ETH liquidity pool). The collateralization ratio at genesis is therefore:

\text{Genesis Collateralization} = \frac{\$224{,}500{,}000}{\$2{,}000{,}000} \approx 112\times

FLAT is over-collateralized by approximately 112× from the very first block. For comparison, MakerDAO requires a minimum collateralization ratio of 1.5× for DAI.

12.3 Why Over-Collateralization Grows

The protocol's collateralization ratio does not merely persist — it grows through three independent engines:

RISE Appreciation: As absorption increases, the RISE price rises per the Singularity Equation. The 208.25M RISE tokens in the treasury appreciate in value. At α = 90%, each RISE is worth $5.00, making the treasury's RISE holdings worth over $1 billion — even before accounting for new ETH deposits.
New ETH Deposits: Every FLAT minted at oracle price deposits ETH into the treasury. Every SAVE sold via Ghost Mint at 1.1× NAV deposits ETH into the treasury. The treasury's external capital (ETH) grows with every user interaction.
Flywheel Revenue: The protocol's volatility arbitrage generates revenue which deepens protocol-owned liquidity. As the battery grows, peg defense becomes stronger, generating more spread revenue. This revenue compounds the first two engines.

12.4 Structural Guarantee

FLAT minting is 1:1 backed by construction (Section 9.2). Every FLAT in circulation has corresponding ETH in the treasury. The RISE tokens in the treasury are pure surplus — additional collateral on top of the 1:1 FLAT backing. As RISE price increases, this surplus grows. The protocol cannot become under-collateralized for FLAT unless the ETH in the treasury loses all value, which would require ETH itself to go to zero.

In summary: the protocol gets more solvent over time, not less. Every absorption event, every FLAT mint, and every Ghost Mint sale adds to the treasury while the FLAT obligation grows only by the amount of new FLAT distributed. The surplus — the gap between treasury value and FLAT obligation — widens monotonically.

13. 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.

14. 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

15. 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)

16. Treasury Versioning & Roadmap

The protocol launches with an ETH-only treasury for maximum simplicity and censorship resistance. Treasury diversification is introduced in subsequent versions:

Version	Treasury Composition	Key Features
v1.0 (Launch)	100% ETH	Core 8 contracts, FLAT Engine, Flywheel, Ghost Mint, NAV Defense
v1.1	Protocol-owned LP positions (FLAT-ETH + SAVE-ETH)	Liquidity Battery architecture, LP trading fee revenue
v1.2	Diversified + privacy	GhostTunnel (privacy layer via zk-SNARKs)
v2.0	Diversified	Governance transition (Council), SDK, L2 expansion
v3.0	Diversified	Ossification, Agent Economy, RWA integration

The v1.1 treasury transitions to the Liquidity Battery architecture: protocol-owned Uniswap V2 LP positions (FLAT-ETH and SAVE-ETH) that earn trading fees from every swap. LP tokens are held by the flatcash.eth Safe — not burned — giving the protocol the option to discharge (withdraw liquidity) to defend the peg during adverse conditions. This revenue source operates independently of user adoption, providing a baseline revenue floor even in zero-volume scenarios.

17. Backtesting Results

Metric	Value
Simulation Period	November 2022 - November 2025 (3 years)
Total Return	375%
CAGR	68.1%
Maximum Drawdown	-12.3%
Sharpe Ratio	2.41
Final α	87.3%

IMPORTANT DISCLOSURE: These results were backtested with the v1.1 Liquidity Battery treasury model (protocol-owned Uniswap V2 LP positions), including LP trading fee revenue. The v1.0 launch uses an ETH-only treasury with FlatSale adding liquidity on each purchase. The LP Battery model represents the target state (v1.1+), not launch state. See Section 16 for the treasury versioning roadmap.

18. 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. FLAT remains fully collateralized because no new FLAT is distributed without corresponding ETH deposits. When adoption eventually occurs, the Flywheel resumes.

19. Glossary

Term	Definition
α (Alpha)	Absorption ratio. RISE in vault / total RISE supply. Range: [0, 1). Genesis value: 0.99988.
C	Singularity Constant = T / S (treasury value / total supply). Determined by protocol treasury.
Collateralization Ratio	Total Treasury Value / FLAT in Circulation. Measures solvency for the FLAT obligation.
CROPS	Censorship Resistant, Capture Resistant, Open Source, Private, Secure
FLAT	CPI-pegged stablecoin. 21 trillion pre-minted. The protocol's only obligation.
Flywheel	Revenue engine: peg arbitrage → battery growth → deeper liquidity → more volume → more revenue
Ghost Mint	Mechanism for purchasing SAVE directly from protocol at 1.1× NAV premium. Uses treasury RISE inventory.
Guardian	Time-limited safety contract. Self-destructs after 2 years.
NAV	Net Asset Value. Value of RISE backing each SAVE token. NAV = RISE price.
Oracle Price	CPI-adjusted target price for FLAT, determined by Chainlink CPI-U feed. FLAT is always sold at this price.
Ossification	Permanent burning of all governance keys at Year 5+
Over-Collateralization	Treasury value exceeds FLAT obligation. ~112× at genesis. Grows monotonically.
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. Not an obligation.
SAVE	Irreversible vault token. Represents permanently locked RISE.
Singularity	Mathematical limit where α → 1 and P → ∞
Genesis α₀	Initial absorption ratio of 0.99988 (99.988%). Only 51,000 RISE tokens as floating supply at genesis.