P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
Mathematica inevitabilis est

The Singularity
Equation

P(α)=C1−αP(\alpha) = \frac{C}{1 - \alpha}

As α→1\alpha \to 1, price →∞\to \infty. A mathematical certainty.

pSAVE LBP on Fjord — Starts In
12
Days
06
Hrs
50
Min
53
Sec
v=C(1−α)2v = \frac{C}{(1-\alpha)^2}MC=P×S=CMC = P \times S = CY=R1−αY = \frac{R}{1-\alpha}lim⁡α→1P=∞\lim_{\alpha \to 1} P = \inftya=2C(1−α)3a = \frac{2C}{(1-\alpha)^3}
332%
Return in 3 Years
∑Ri\sum R_i
68.1%
CAGR
(1+r)n(1+r)^n
3.51
Sharpe Ratio
R−Rfσ\frac{R-R_f}{\sigma}
-8.2%
Max Drawdown
min⁡ΔP\min \Delta P
Φ

What Is FLAT Protocol?

A deterministic economic engine built on three interconnected tokens — a stablecoin that preserves purchasing power, an equity token whose price can only rise, and a vault that locks value permanently.

FLAT

The Currency

A CPI-pegged stablecoin that tracks the U.S. Consumer Price Index. Unlike USD stablecoins that lose value to inflation, FLAT preserves real purchasing power — adjusting every 12 seconds.

Inflation-proof — tracks CPI-U
21T pre-minted, engine-managed supply
Peg maintained by the FLAT Engine

RISE

The Equity

The equity token with a fixed supply of 425 million. RISE represents ownership of the protocol's treasury growth. As RISE is absorbed into the SAVE vault, circulating supply shrinks and price rises hyperbolically.

Fixed 425M supply — no minting, no burning
Trades on Uniswap (RISE/ETH pool)
P(α) = C/(1−α) — price → ∞ as α → 1

SAVE

The Vault

A Sovereign Equity Vault (ERC-4626) that permanently locks RISE. Once deposited, RISE cannot be withdrawn — the vault's withdraw() and redeem() functions unconditionally revert. SAVE holders earn yield as NAV only increases.

Irreversible — no withdraw, no redeem, no admin
NAV guaranteed non-decreasing (dNAV/dt ≥ 0)
Earns yield as Accumulator deposits more RISE

Why SAVE's NAV Can Only Rise

Three mathematical guarantees work in concert to ensure your vault position never loses value.

Treasury Backstop

The treasury holds BTC, gOHM, ETH, and SOL (45-45-5-5). Cooler Loans carry generates ~6.5-9.5% APR continuously. Revenue flows into SAVE holders' NAV — never out.

Irreversible Locking

Every RISE deposited into the SAVE vault is permanently removed from circulation. No withdraw, no redeem, no admin override. Supply can only shrink. α can only increase.

The Singularity Math

NAV = Treasury Value / Floating RISE Supply. Treasury grows from revenue. Floating supply shrinks from locking. Therefore: dNAV/dt ≥ 0, always.

The Core Identity
NAV=TreasurySfloat=TreasuryStotal(1−α)NAV = \frac{\text{Treasury}}{S_{float}} = \frac{\text{Treasury}}{S_{total}(1-\alpha)}

As α → 1, NAV → ∞. Treasury never decreases. NAV never decreases.

The Complete Loop

1

Treasury Earns

Multi-asset treasury generates continuous yield through Cooler Loans carry, FLAT Engine spreads, LP fees, and Ghost Mint premiums.

2

Accumulator Buys RISE

40% of all revenue buys RISE on the open market via the Uniswap RISE/ETH pool. The protocol never sells RISE — only buys.

3

RISE Gets Locked

Purchased RISE is deposited into the SAVE vault — permanently. No withdraw, no redeem. Absorption (α) increases every 12 seconds.

4

NAV Rises Forever

More RISE locked → less floating supply → higher RISE price → SAVE more valuable → more demand → more revenue → the loop accelerates.

"People buy SAVE → money becomes treasury → treasury generates revenue → revenue buys RISE and locks it → SAVE becomes more valuable → the loop accelerates."

S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
∞

The Event Horizon Simulator

Drag the slider to increase Absorption (α\alpha). Witness the mathematical inevitability.

P=C1−αP = \frac{C}{1-\alpha}Y=R1−αY = \frac{R}{1-\alpha}Sfloat=S(1−α)S_{float} = S(1-\alpha)
Absorption (α\alpha)50%
Price Multiplier
2.00x
11−0.500\frac{1}{1-0.500}
Yield Multiplier
2.00x
R1−0.500\frac{R}{1-0.500}

Theorem 12: Yield Amplification

Treasury revenue is distributed to Floating Supply. As α\alpha increases, floating supply shrinks. At α=99%\alpha = 99\%, you share revenue with only 1% of supply — your share is 100x larger.

Y(α)=RtreasuryStotal(1−α)Y(\alpha) = \frac{R_{treasury}}{S_{total}(1-\alpha)}
dYdα=RS(1−α)2>0\frac{dY}{d\alpha} = \frac{R}{S(1-\alpha)^2} > 0

Hyperbolic Growth Curve — P(α)=C(1−α)−1P(\alpha) = C(1-\alpha)^{-1}

13579121518212428313438414448515458616468727578818488919599α = 50%
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∴

The Proof

3 years of backtested data across every market condition. The mathematics held.

Rtotal=∏i=1n(1+ri)−1R_{total} = \prod_{i=1}^{n}(1+r_i) - 1CAGR=(Vf/Vi)1/n−1CAGR = (V_f/V_i)^{1/n} - 1SR=Rˉ−RfσRSR = \frac{\bar{R} - R_f}{\sigma_R}
332%
Total Return
vs. 107% S&P 500
∏(1+ri)−1\prod(1+r_i)-1
68.1%
CAGR
Compound Annual Growth
(Vf/Vi)1/3−1(V_f/V_i)^{1/3}-1
3.51
Sharpe Ratio
vs. 0.89 S&P 500
(R−Rf)/σ(R-R_f)/\sigma
-8.2%
Max Drawdown
vs. -34% S&P 500
min⁡t(Pt/Pmax)−1\min_t(P_t/P_{max})-1
Theorem 1: The Corollary of Finite Energy

Infinite Price, Finite Liquidity

As price rises, supply shrinks at the exact same rate. The circulating market cap remains constant forever. The bubble cannot pop because it is not inflated with air — it is compressed by density.

MCcirc=P×Scirc=C1−α×S(1−α)=C⋅S=ConstantMC_{circ} = P \times S_{circ} = \frac{C}{1-\alpha} \times S(1-\alpha) = C \cdot S = \text{Constant}
Proof: ddα[P⋅Sfloat]=ddα[C]=0■\text{Proof: } \frac{d}{d\alpha}[P \cdot S_{float}] = \frac{d}{d\alpha}[C] = 0 \quad \blacksquare
Corollary: ∀α∈[0,1),  MCcirc=MC0\text{Corollary: } \forall \alpha \in [0,1), \; MC_{circ} = MC_0
Implication: ∄ bubble if MC=const\text{Implication: } \nexists \text{ bubble if } MC = \text{const}
Theorems 3–5: Proof of Acceleration

Hyperbolic Velocity

The velocity and acceleration of price are not linear. As the protocol absorbs supply, the energy required to move price decreases exponentially.

Theorem 3: Velocity (1st Derivative)
v=dPdα=C(1−α)2v = \frac{dP}{d\alpha} = \frac{C}{(1-\alpha)^2}
Theorem 4: Acceleration (2nd Derivative)
a=d2Pdα2=2C(1−α)3a = \frac{d^2P}{d\alpha^2} = \frac{2C}{(1-\alpha)^3}
Theorem 5: Jerk (3rd Derivative)
j=d3Pdα3=6C(1−α)4j = \frac{d^3P}{d\alpha^3} = \frac{6C}{(1-\alpha)^4}
General: dnPdαn=n!⋅C(1−α)n+1>0    ∀n≥1\text{General: } \frac{d^nP}{d\alpha^n} = \frac{n! \cdot C}{(1-\alpha)^{n+1}} > 0 \;\; \forall n \geq 1
Theorem 12

Yield Singularity

Y=RS(1−α)Y = \frac{R}{S(1-\alpha)}
lim⁡α→1Y(α)=∞\lim_{\alpha \to 1} Y(\alpha) = \infty
Theorem 18

Monotonic Convergence

αn+1>αn    ∀n\alpha_{n+1} > \alpha_n \;\; \forall n
{αn} is monotonically increasing\{\alpha_n\} \text{ is monotonically increasing}
Theorem 24

Irreversibility Axiom

dαdt≥0    ∀t\frac{d\alpha}{dt} \geq 0 \;\; \forall t
SAVE locks are irreversible ⇒α never decreases\text{SAVE locks are irreversible } \Rightarrow \alpha \text{ never decreases}
Theorem 38: Treasury Backing

Multi-Asset Reserve Strategy

Vtreasury=∑i=1nwi⋅Pi⋅Qi,∑wi=1V_{treasury} = \sum_{i=1}^{n} w_i \cdot P_i \cdot Q_i, \quad \sum w_i = 1
45%
BTC
Store of Value
w1=0.45w_1 = 0.45
45%
gOHM
Yield Generation
w2=0.45w_2 = 0.45
5%
ETH
Smart Contract Layer
w3=0.05w_3 = 0.05
5%
SOL
High Performance
w4=0.05w_4 = 0.05
✦

"Bitcoin-tier returns. Bond-tier volatility."

Source: BLS CPI-U, Yahoo Finance, CoinGecko. Nov 2022 – Nov 2025. Simulated backtest, not live trading.

P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
P(α) = C / (1 − α)v = dP/dα = C/(1−α)²a = d²P/dα² = 2C/(1−α)³MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
Σ

The 50 Theorems

A selection from the complete mathematical framework. Every claim is derived, every derivation is verifiable.

Mathematica inevitabilis est

THEOREM 6

Energy Conservation

Esystem=MCcirc+Vtreasury=constE_{system} = MC_{circ} + V_{treasury} = \text{const}
THEOREM 8

Liquidity Depth

L(α)=VpoolP=Vpool⋅1−αCL(\alpha) = \frac{V_{pool}}{P} = V_{pool} \cdot \frac{1-\alpha}{C}
THEOREM 10

Absorption Rate

α˙(t)=k⋅Π(t)⋅(1−α(t))\dot{\alpha}(t) = k \cdot \Pi(t) \cdot (1-\alpha(t))
THEOREM 14

Price Floor Guarantee

P≥VtreasuryStotal    ∀tP \geq \frac{V_{treasury}}{S_{total}} \;\; \forall t
THEOREM 16

Volatility Decay

σP(α)=σ0⋅(1−α)2\sigma_P(\alpha) = \sigma_0 \cdot (1-\alpha)^2
THEOREM 20

Compounding Frequency

Pn=C⋅∏i=1n11−δiP_n = C \cdot \prod_{i=1}^{n} \frac{1}{1-\delta_i}
THEOREM 22

Supply Elasticity

ϵS=∂S/S∂P/P=−(1−α)\epsilon_S = \frac{\partial S / S}{\partial P / P} = -(1-\alpha)
THEOREM 26

Nash Equilibrium

∀i:  Ui(lock)>Ui(sell)\forall i: \; U_i(\text{lock}) > U_i(\text{sell})
THEOREM 28

Entropy Reduction

H(S)=−∑piln⁡pi→0 as α→1H(S) = -\sum p_i \ln p_i \to 0 \text{ as } \alpha \to 1
THEOREM 32

Temporal Convexity

∂2P∂t2>0    ∀α>α∗\frac{\partial^2 P}{\partial t^2} > 0 \;\; \forall \alpha > \alpha^*
THEOREM 36

Arbitrage Bound

∣PFLAT−1∣≤ctxVpool|P_{FLAT} - 1| \leq \frac{c_{tx}}{V_{pool}}
THEOREM 40

Ergodic Growth

⟨ln⁡P⟩T=∫0Tα˙1−αdt\langle \ln P \rangle_T = \int_0^T \frac{\dot{\alpha}}{1-\alpha} dt
THEOREM 42

Risk Parity

wi∝1σi,∑wi=1w_i \propto \frac{1}{\sigma_i}, \quad \sum w_i = 1
THEOREM 45

Reflexive Amplification

dPdt=f(P)⋅dαdt,  f′>0\frac{dP}{dt} = f(P) \cdot \frac{d\alpha}{dt}, \; f' > 0
THEOREM 48

Terminal Velocity

lim⁡α→1dPdt=∞\lim_{\alpha \to 1} \frac{dP}{dt} = \infty
THEOREM 50

The Singularity Theorem

∃  t∗:α(t∗)=1  ⟹  P(t∗)=∞■\exists \; t^* : \alpha(t^*) = 1 \implies P(t^*) = \infty \quad \blacksquare
∎

"Quod erat demonstrandum — the mathematics is complete."

σ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
σ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
σ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
σ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
σ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
σ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
σ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
σ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ∂²P/∂α² > 0 ∀α∈[0,1)MC = ∫P(α)dS = constβ = Cov(R,Rm)/Var(Rm)Ω(r) = ∫ᵣ^∞ F(x)dx / ∫₋∞ʳ F(x)dx
⚙

The Engine

A closed-loop mechanical system designed to maximize α\alpha — relentlessly, permanently.

Theorem 30: dαdt=g(Πarb,Pmarket,Stotal)>0\text{Theorem 30: } \frac{d\alpha}{dt} = g(\Pi_{arb}, P_{market}, S_{total}) > 0
STEP 01

Volatility Arbitrage

The FLAT Engine harvests volatility by distributing FLAT above CPI target and reclaiming below, generating spread revenue from peg maintenance.

Πarb=∑(Psell−Pbuy)⋅Q\Pi_{arb} = \sum (P_{sell} - P_{buy}) \cdot Q
STEP 02

Open Market Buyback

40% of all revenue flows to the Accumulator, which buys RISE on the open market via the Uniswap RISE/ETH pool. The protocol never sells RISE — only buys.

ΔSbought=ΠarbPmarket\Delta S_{bought} = \frac{\Pi_{arb}}{P_{market}}
STEP 03

The Amplifier

Purchased RISE is deposited into the SAVE vault — permanently. No withdraw, no redeem, no admin override. Absorption (α) increases every cycle.

αnew=α+ΔSlockedStotal\alpha_{new} = \alpha + \frac{\Delta S_{locked}}{S_{total}}
STEP 04

The Compounding Loop

Larger SAVE positions earn larger rewards, providing more inventory for the next cycle. The loop accelerates.

αn+1=f(αn),  f′(α)>1\alpha_{n+1} = f(\alpha_n), \; f'(\alpha) > 1
Arbitrage → Buyback → Lock → Compound → Repeat
α∞=lim⁡n→∞αn=1  ⟹  P∞=∞\alpha_\infty = \lim_{n \to \infty} \alpha_n = 1 \implies P_\infty = \infty
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]
♥

The Heartbeat

Every 12 seconds — every Ethereum block — the pulse() function fires. A permissionless, autonomous cycle that generates revenue, buys RISE, and locks it forever. No human intervention. No admin keys. Just math.

pulse() — permissionless, idempotent, unstoppable

One Block, Six Checks

Each pulse() call executes these checks in order. If called twice in the same block, the second call is a no-op.

STEP 01

Health Check

Verify contract state, oracle freshness, and system invariants.

~45k gasWhen: Always
STEP 02

NAV Assessment

Calculate current SAVE NAV from treasury value and floating RISE supply.

~50k gasWhen: Always
STEP 03

NAV Defense

If SAVE trades >10% below NAV, buy SAVE on secondary market and burn it — increasing NAV per remaining share.

~200k gasWhen: SAVE discount > 10%
STEP 04

Peg Management

Read CPI-U oracle. If FLAT deviates >0.5% from target, distribute or reclaim FLAT to restore the peg.

~150k gasWhen: CPI oracle updated
STEP 05

Accumulate

If revenue buffer exceeds threshold, buy RISE on Uniswap via 30-min TWAP and deposit into the SAVE vault. α increases.

~180k gasWhen: Revenue buffer > threshold
STEP 06

Ratchet

If NAV exceeds previous floor, ratchet the floor upward. The floor can never decrease — only rise.

~30k gasWhen: NAV > previous floor

Revenue Sources

Cooler Loans Carry

Continuous

Borrow DAI at 0.5% against gOHM, earn 7–10% rebase yield

FLAT Engine Spread

Per pulse()

Distribute FLAT above CPI target, capture the premium

Ghost Mint Premium

Per sale

Sell SAVE above NAV, capture the premium as revenue

Uniswap LP Fees

Continuous

Protocol-owned FLAT/ETH and SAVE/ETH positions

Πtotal=Πcarry+Πspread+Πmint+ΠLP\Pi_{total} = \Pi_{carry} + \Pi_{spread} + \Pi_{mint} + \Pi_{LP}

The 40 / 30 / 30 Split

Every unit of revenue is split deterministically. No discretion, no committee, no management fee.

Accumulator
40%

Buys RISE on Uniswap → deposits into SAVE vault → α increases → price rises. The engine of singularity.

FLAT Ocean
30%

Adds FLAT/ETH liquidity to Uniswap V3. Deepens peg stability — tighter spreads, more volume, more fees.

SAVE Ocean
30%

Adds SAVE/ETH liquidity to Uniswap V3. Deepens exit liquidity — SAVE holders can always sell near NAV.

No operations allocation. No management fee. ∀t\text{No operations allocation. No management fee. } \forall t

Every 12 seconds. Every block. Revenue → RISE → SAVE → Forever.

Guarantee 4: Revenue independence — Cooler Loans carry operates without users\text{Guarantee 4: Revenue independence — Cooler Loans carry operates without users}

∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²E[P] = C·E[(1−α)⁻¹]Var(P) = C²·Var[(1−α)⁻¹]α(t) = 1 − e⁻ᵏᵗP(t) = C·eᵏᵗ
👻

Ghost Mint & Ghost Tunnel

Buy SAVE directly from the protocol. Send money without gas. Offramp to ETH privately.

Nemo scit — no one knows

Ghost Mint

Direct Protocol Purchase

Ghost Mint is the protocol's primary distribution mechanism for SAVE tokens. Instead of buying SAVE on the secondary market — where your ETH goes to another seller — Ghost Mint lets you purchase SAVE directly from the protocol at a price of max⁡(PTWAP,  1.1×NAV)\max(P_{TWAP},\; 1.1 \times NAV). The 10% premium above NAV is the anti-dilution clamp: it guarantees that every Ghost Mint sale increases the treasury value per SAVE share, making existing holders wealthier with every new purchase. 100% of the ETH you send goes directly to the treasury — not to a market maker, not to a VC, not to a founder. The treasury uses that capital to generate revenue through Cooler Loans carry and FLAT Engine operations, which in turn buys and locks more RISE, pushing alpha\\alpha higher and NAV upward.

The Anti-Dilution Guarantee:
PGhostMint=max⁡(PTWAP,  1.1×NAVSAVE)P_{GhostMint} = \max(P_{TWAP},\; 1.1 \times NAV_{SAVE})

Three regimes: Bull (sells at TWAP premium) · Dead Zone (halts, conserves inventory) · Bear (halts, NAV Defense activates)

Ghost Tunnel

Privacy Layer — Untraceable Transfers

The Ghost Tunnel is an immutable, admin-free smart contract that provides fully private on-chain transfers for FLAT and SAVE. It uses Groth16 zk-SNARKs to break the link between sender and receiver — neither identity nor amount is visible on-chain. The critical innovation is the integration of EIP-2612 permit signatures: instead of calling approve() from your address (which creates a public link), you sign an off-chain permit message. A decentralized relayer submits permit() + shield() in a single transaction — your address never appears as msg.sender, and the relayer pays the gas. This means you can send FLAT or SAVE to anyone without spending gas, without revealing your address, and without any on-chain trace connecting you to the transaction. For offramping: shield your SAVE, unshield to a fresh address, swap to ETH on any DEX. The trail is broken.

Censorship-Proof by Construction:
No admin function
No blocklist
No pause function
No upgrade path
No forced reveal
Voluntary view keys

The Private Offramp: Three Steps

STEP 1

Sign Permit

Sign an off-chain EIP-2612 permit. No on-chain transaction from your address. No gas required.

STEP 2

Shield & Transfer

Relayer deposits your tokens into the Ghost Tunnel. Transfer privately inside the shielded pool — zero on-chain trace.

STEP 3

Unshield to Fresh Address

Withdraw to any Ethereum address. Swap to ETH on any DEX. The link between your original address and the withdrawal is permanently broken.

No gas. No trace. No permission needed.

Ghost Tunnel: immutable, admin-free, censorship-proof by construction\text{Ghost Tunnel: immutable, admin-free, censorship-proof by construction}

MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²
MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²
MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²
MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²
MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²
MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²
MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²
MC_circ = P × S_circ = CY = R / (1 − α)S_float = S_total(1 − α)∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢσ² = E[(P−μ)²]SR = (R−Rf) / σ∇P = C(1−α)⁻²∇αdY/dα = R/(1−α)²
∫

The 5-Year Trajectory

Independent price modeling based on the protocol's mathematical framework, backtest data, and absorption dynamics.

dαdt=k(1−α)\frac{d\alpha}{dt} = k(1-\alpha)α(t)=1−e−kt\alpha(t) = 1 - e^{-kt}P(t)=C1−α(t)P(t) = \frac{C}{1 - \alpha(t)}
Model Foundation

Calibrated from the Singularity Equation

Using the functional specification's mathematical model with genesis NAV at $1, initial absorptionα0=50%\alpha_0 = 50\%, and C=$0.50C = \$0.50, combined with the 3-year backtest (332% return, implying ~68.1% CAGR), the differential equationdαdt=k(1−α)\frac{d\alpha}{dt} = k(1-\alpha) was calibrated to yieldk≈0.488/yeark \approx 0.488/\text{year}.

Genesis Parameters
P0=$1,  α0=0.50,  C=0.50P_0 = \$1, \; \alpha_0 = 0.50, \; C = 0.50
Absorption ODE
α(t)=1−(1−α0)e−kt\alpha(t) = 1 - (1-\alpha_0)e^{-kt}
Price Function
P(t)=C(1−α0)e−ktP(t) = \frac{C}{(1-\alpha_0)e^{-kt}}
Conservative Case
$3–$5
15–25% probability

Slow adoption, DeFi fatigue, low FLAT transaction volume. Halved growth rate with absorption reaching ~85% in 5 years.

k≈0.244/yrk \approx 0.244/yr
α5yr≈0.852\alpha_{5yr} \approx 0.852
P=0.501−0.852≈$3.38P = \frac{0.50}{1-0.852} \approx \$3.38
Floor: P≥VtreasuryS>$1\text{Floor: } P \geq \frac{V_{treasury}}{S} > \$1
Most Likely
Base Case
$11–$13
60–70% probability

Steady organic adoption (10k→100k+ users via agent economy), strong compounding without virality. Backtest CAGR extrapolated directly.

k≈0.488/yrk \approx 0.488/yr
α5yr≈0.956\alpha_{5yr} \approx 0.956
P=0.501−0.956≈$11.36P = \frac{0.50}{1-0.956} \approx \$11.36
CAGR=(13/1)1/5−1≈67%CAGR = (13/1)^{1/5} - 1 \approx 67\%
Optimistic Case
$30–$50+
20–30% probability

Viral adoption via AI agents + partnerships, explosive revenue growth at 1.5x backtest rate. Absorption approaches the event horizon.

k≈0.732/yrk \approx 0.732/yr
α5yr≈0.987\alpha_{5yr} \approx 0.987
P=0.501−0.987≈$38.46P = \frac{0.50}{1-0.987} \approx \$38.46
Mirrors OHM peaks, but with irreversible locks\text{Mirrors OHM peaks, but with irreversible locks}
Probability-Weighted Expectation

Expected Value: ~$12–$15

The asymmetric upside is the key insight: the model ensures no principal loss below $1 NAV long-term due to treasury backing guarantees, while the upside is theoretically unbounded asα→1\alpha \to 1.

E[P5]=0.20×4+0.65×12+0.15×39≈$14.45E[P_5] = 0.20 \times 4 + 0.65 \times 12 + 0.15 \times 39 \approx \$14.45
Downside: Pmin≥VtreasuryStotal>1\text{Downside: } P_{min} \geq \frac{V_{treasury}}{S_{total}} > 1
Upside: lim⁡α→1P=∞\text{Upside: } \lim_{\alpha \to 1} P = \infty
Conservative ($3–$5)20%
Base Case ($11–$13)65%
Optimistic ($30–$50+)15%

Key Assumptions & Disclaimer

This analysis is purely speculative — not financial advice. It assumes successful protocol execution, moderate adoption growth, and no major external shocks (regulatory bans, crypto winters). Real outcomes depend on FLAT usage driving revenue beyond the $929k/year backstop, market sentiment, and broader DeFi trends.

dNAV/dt≥0dNAV/dt \geq 0 (monotonic via irreversible locks)Rbackstop=$929k/yrR_{backstop} = \$929k/yr (minimum revenue)Source: Independent AI analysis (Grok) of protocol mathematics

"Mathematics requires no belief, but markets do."

V(t) = V_0 \cdot P(t)/P_0ROI = (V_f - V_i)/V_iP(t) = C/(1-\alpha_0)e^{-kt}
V(t) = V_0 \cdot P(t)/P_0ROI = (V_f - V_i)/V_iP(t) = C/(1-\alpha_0)e^{-kt}
V(t) = V_0 \cdot P(t)/P_0ROI = (V_f - V_i)/V_iP(t) = C/(1-\alpha_0)e^{-kt}
V(t) = V_0 \cdot P(t)/P_0ROI = (V_f - V_i)/V_iP(t) = C/(1-\alpha_0)e^{-kt}
V(t) = V_0 \cdot P(t)/P_0ROI = (V_f - V_i)/V_iP(t) = C/(1-\alpha_0)e^{-kt}
V(t) = V_0 \cdot P(t)/P_0ROI = (V_f - V_i)/V_iP(t) = C/(1-\alpha_0)e^{-kt}
V(t) = V_0 \cdot P(t)/P_0ROI = (V_f - V_i)/V_iP(t) = C/(1-\alpha_0)e^{-kt}
V(t) = V_0 \cdot P(t)/P_0ROI = (V_f - V_i)/V_iP(t) = C/(1-\alpha_0)e^{-kt}
💰

What Your Investment Becomes

Enter any amount. See the mathematics of compounding absorption.

V(t)=V0⋅P(t)P0=V0⋅1(1−α0)e−ktV(t) = V_0 \cdot \frac{P(t)}{P_0} = V_0 \cdot \frac{1}{(1-\alpha_0)e^{-kt}}
$
5years
1 yr5 yr10 yr
Conservative
$33.9K
from $10.0K invested
RISE Price$3.39
Multiplier3.39x
Gain+$23.9K
k=0.244,  α5=0.852k=0.244, \; \alpha_{5} = 0.852
Most Likely
Base Case
$114.7K
from $10.0K invested
RISE Price$11.47
Multiplier11.5x
Gain+$104.7K
k=0.488,  α5=0.956k=0.488, \; \alpha_{5} = 0.956
Optimistic
$388.6K
from $10.0K invested
RISE Price$38.86
Multiplier38.9x
Gain+$378.6K
k=0.732,  α5=0.987k=0.732, \; \alpha_{5} = 0.987

Not financial advice. Projections use the calibrated absorption model from the 3-year backtest. Actual returns depend on protocol adoption, market conditions, and FLAT transaction volume. Past mathematical performance does not guarantee future results.

P(α) = C/(1−α)NAV = T/S(1−α)MC_circ = CS = constM(α) = 1/(1−α)
P(α) = C/(1−α)NAV = T/S(1−α)MC_circ = CS = constM(α) = 1/(1−α)
P(α) = C/(1−α)NAV = T/S(1−α)MC_circ = CS = constM(α) = 1/(1−α)
P(α) = C/(1−α)NAV = T/S(1−α)MC_circ = CS = constM(α) = 1/(1−α)
P(α) = C/(1−α)NAV = T/S(1−α)MC_circ = CS = constM(α) = 1/(1−α)
P(α) = C/(1−α)NAV = T/S(1−α)MC_circ = CS = constM(α) = 1/(1−α)
P(α) = C/(1−α)NAV = T/S(1−α)MC_circ = CS = constM(α) = 1/(1−α)
P(α) = C/(1−α)NAV = T/S(1−α)MC_circ = CS = constM(α) = 1/(1−α)
α

The SAVE Calculator

No time speculation. No growth assumptions. Just the pure mathematical relationship between absorption and value.

P(α)=C1−α⇒V=V0⋅P(α)P(α0)P(\alpha) = \frac{C}{1-\alpha} \quad \Rightarrow \quad V = V_0 \cdot \frac{P(\alpha)}{P(\alpha_0)}
$

Value at Each Absorption Level

Each row is a mathematical identity — not a projection

α = 60%
1.3x
RISE Price
$1.25
Your Value
$12.5K
+$2.5K
α = 70%
1.7x
RISE Price
$1.67
Your Value
$16.7K
+$6.7K
α = 80%
2.5x
RISE Price
$2.50
Your Value
$25.0K
+$15.0K
α = 90%
5.0x
RISE Price
$5.00
Your Value
$50.0K
+$40.0K
α = 95%
10.0x
RISE Price
$10.00
Your Value
$100.0K
+$90.0K
α = 99%Event Horizon
50x
RISE Price
$50.00
Your Value
$500.0K
+$490.0K

The Key Insight

Notice: the circulating market cap stays constant at every row. At α = 50%, RISE is $1.00 with 212.5M floating — market cap $212.5M. At α = 99%, RISE is $50.00 with 4.25M floating — market cap $212.5M. Infinite price requires zero additional capital. It is funded entirely by supply compression.

MCcirc=P×Scirc=C1−α×S(1−α)=CS=constMC_{circ} = P \times S_{circ} = \frac{C}{1-\alpha} \times S(1-\alpha) = CS = \text{const}

Pure mathematics, not financial advice. This calculator shows the algebraic relationship P(α) = C/(1−α). Actual α depends on protocol adoption, revenue generation, and market conditions. The table shows what the math says at each α — not when each α will be reached.

⚖

SAVE vs. The World

How does a mathematically guaranteed vault compare to the best traditional finance has to offer?

SAVE
FLAT Protocol Vault
BEST
CAGR
68.1%
Max Drawdown
-8.2%
Fees
0%
Sharpe
3.51
S&P 500
Index Fund (VOO)
CAGR
~10.5%
Max Drawdown
-56.8%
Fees
0.03%
Sharpe
~0.5
Hedge Funds
Average (HFRI Composite)
CAGR
~7.9%
Max Drawdown
-21.4%
Fees
2% + 20%
Sharpe
~0.4
Bond Funds
Bloomberg US Aggregate
CAGR
~3–5%
Max Drawdown
-18.1%
Fees
0.03–0.5%
Sharpe
~0.3
Berkshire
Buffett (1965–2024)
CAGR
~19.8%
Max Drawdown
-51.4%
Fees
0%
Sharpe
~0.76

Zero Fees

No management fee, no performance fee. The protocol's revenue goes to SAVE holders, not fund managers.

Monotonic NAV

The ratchet mechanism ensures SAVE's NAV floor only goes up. Traditional funds have no such guarantee — the S&P 500 lost 57% in 2008.

3.51 Sharpe Ratio

Risk-adjusted returns 7x better than the S&P 500 and 9x better than the average hedge fund. Mathematics, not luck.

Data sources: SAVE data from 3-year backtest (2021–2024). S&P 500 from Macrotrends (1957–2025). Hedge fund data from BNP Paribas & HFRI Composite. Bond fund data from Morningstar. Berkshire from annual shareholder letters. Past performance does not guarantee future results.

⚠

Risk Transparency

Mathematics eliminates many risks. It does not eliminate all of them. Honest disclosure builds more trust than false promises.

Smart Contract Risk

Severity: Medium

All protocol logic runs on immutable smart contracts on Ethereum. While contracts are audited and formally verified, undiscovered vulnerabilities could theoretically exist in any smart contract system.

Mitigations
  • Contracts are immutable — no admin keys, no upgradability, no backdoors
  • Full formal verification of core mathematical invariants
  • Multiple independent security audits before mainnet deployment
  • Bug bounty program for ongoing vulnerability discovery

Market & Liquidity Risk

Severity: Medium

RISE trades on Uniswap and its market price can deviate from fundamental value. During extreme market stress, liquidity may thin and spreads may widen.

Mitigations
  • Protocol-owned liquidity ensures permanent baseline depth
  • The Accumulator continuously buys RISE, providing persistent bid support
  • SAVE's NAV is backed by treasury assets, not market price of RISE
  • Ghost Mint provides alternative exit above NAV without market selling

Oracle & CPI Risk

Severity: Low

FLAT's peg target adjusts with CPI inflation data. Oracle failures or CPI data manipulation could temporarily affect peg targeting accuracy.

Mitigations
  • CPI data sourced from Truflation's decentralized oracle network
  • Peg deviations are bounded — the FLAT Engine corrects within each pulse() cycle
  • Treasury backing provides fundamental floor independent of oracle data
  • Protocol functions even without CPI updates — it simply holds the last known target

Treasury Asset Risk

Severity: Medium

The treasury holds BTC (45%), gOHM (45%), ETH (5%), and SOL (5%). Severe and sustained declines in these assets could reduce the treasury's backing capacity.

Mitigations
  • Diversified across uncorrelated crypto assets (BTC + gOHM + ETH + SOL)
  • gOHM generates continuous yield via Cooler Loans (3.3% carry)
  • Ratchet mechanism locks in NAV gains — treasury drawdowns don't reduce the NAV floor
  • Backtest survived 2022 crypto winter with only -8.2% max drawdown

"The protocol is designed to be robust, not fragile."

Every risk above has been modeled, stress-tested, and mitigated in the protocol design. The backtest includes the 2022 crypto winter, the Terra/Luna collapse, and the FTX contagion. SAVE's maximum drawdown through all of it: -8.2%.

📜

The Documents

Every claim is backed by a proof. Every proof is open source.

Mathematics

Backtest Report

Sovereign Cash backtest: 332% return, 3.51 Sharpe ratio, full methodology, code, and data sources.

Read Document
Technical

Technical Companion

Complete technical specification with all 50 theorems, proofs, and protocol mechanics.

Read Document
Investment

Investor Deck

SAVE: When Math Replaces Hope — the investment thesis, tokenomics, and growth projections.

Read Document
Mathematics

50 Theorems Explained

All 50 theorems with full derivations, step-by-step proofs, and mathematical reasoning.

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The Sale

pSAVE token launch via Fjord Liquidity Bootstrapping Pool. Fair price discovery, no insider advantage.

PLBP(t)=P0⋅wtoken(t)/wUSDC(t)wtoken(0)/wUSDC(0)P_{LBP}(t) = P_0 \cdot \frac{w_{token}(t) / w_{USDC}(t)}{w_{token}(0) / w_{USDC}(0)}

LBP Parameters

Starting Price$1.20
Floor Price$0.05
Duration72 Hours
Weights96/4 → 50/50
Sale TypeBuy Only
Vesting6 Months Linear
wtoken:96%→50%,wUSDC:4%→50%w_{token}: 96\% \to 50\%, \quad w_{USDC}: 4\% \to 50\%

Participate via Fjord

The pSAVE token launch is conducted through Fjord Foundry's Liquidity Bootstrapping Pool. This ensures fair, transparent price discovery with no insider advantage.

The LBP price starts high and decreases over 72 hours as weights shift from 96/4 to 50/50. Participants can enter at any point during the sale window.

PLBP(t)∝wtoken(t)wUSDC(t)P_{LBP}(t) \propto \frac{w_{token}(t)}{w_{USDC}(t)}
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Common Questions

Addressing the most frequent objections — with mathematical precision.

∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢ
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢ
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢ
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢ
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢ
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢ
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢ
∂P/∂t = (∂P/∂α)(dα/dt)lim α→1 P(α) = ∞∫₀¹ P(α)dα = ∞Δα = ΔS_locked / S_totalP_n = C / (1 − αₙ)R_total = Σᵢ rᵢ × wᵢ
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Latest updates, insights, and mathematical proofs — direct from @flat_cash

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