NITI

NITI: Non-custodial Interlinked Tokenization Infrastructure
A Protocol for Bitcoin-Backed Synthetic Assets
WHITEPAPER 0.6
Publication Date: July 14, 2025
Authors: Pedro Martins Rodrigues Novaes Contact: nitidev@proton.me

Abstract
NITI presents a cryptographically secure and economically sound protocol for creating synthetic derivatives on Bitcoin through the Lightning Network. Using Cascading Discreet Log Contracts (CDLCs) with enhanced security properties, participants can create diverse financial instruments including stablecoins, futures, options, and loans while maintaining non-custodial control. This protocol implements a modernized version of Hayek's competing currencies framework with rigorous mathematical foundations, comprehensive risk management, and formal security guarantees. NITI's mission is to implement the free monetary system proposed by Hayek using bitcoin as the sole backing, enabling synthetics that act as private currencies in free competition, backed by layered monetary structures on Bitcoin.

Keywords: Bitcoin, Lightning Network, Discreet Log Contracts, Synthetic Assets, Competing Currencies, Cryptographic Protocols

1. Introduction
   1.1 Problem Statement
   The cryptocurrency ecosystem faces a fundamental tension between Bitcoin's superior monetary properties and the practical need for diverse financial instruments. While Bitcoin excels as a store of value, its volatility limits its utility as a unit of account and medium of exchange for specific use cases. Existing solutions suffer from:

• Centralized stablecoins: Counterparty risk and regulatory vulnerability
• Algorithmic stablecoins: Insufficient collateralization and complex failure modes
• DeFi protocols: Smart contract risk and limited Bitcoin integration

Derived from Gresham's Law, the "Paradox of Money" arises: ceteris paribus, rational agents prefer to spend first currencies with lower potential as a store of value while accumulating currencies with higher potential as a store of value for future exchanges. As the least inflationary currency in existence and the one with the most potential as a long-term store of value, bitcoin tends to be accumulated and not spent. According to Mankiw in "Macroeconomics," money has three functions: Store of Value (transfer purchasing power from present to future), Medium of Exchange (facilitate exchanges), and Unit of Account (determine relative prices). Bitcoin in its raw form maximizes the Store of Value function, while other layers seek to fulfill the remaining functions, each with different attributes and distinct focuses.

The "Non-custodial Interlinked Tokenization Infrastructure" (NITI) is a proposal to create an interlinked and non-custodial tokenization infrastructure, allowing the issuance of stablecoins called "Synthetics." These Synthetics are satoshi balances that simulate the price of other assets, acting as private currencies in free competition. NITI's mission is the monetary system proposed by Hayek in 1976, in “Denationalisation of Money,” creating a protocol so that currencies with stable relative prices can compete freely, using a single backing: bitcoin.

1.2 Money in Layers
Elaborated extensively in Alan Schramm’s article “Bitcoin, the final settlement system,” the concept of Money in Layers states that money has a base layer from which others can be built. Gold, for example, was not used in its raw form for the three main monetary functions but from specialized layers:

• Nuggets: metal after extraction in its original form.
• Bars: standardization of purity, format, measures, and weighing.
• Certificates: ownership documents for divisibility and transport.
• Notes: paper backed by certificates used to price assets.

The view that bitcoin in its raw form maximizes all money functions does not match the history of money. To use bitcoin as a medium of exchange and unit of account, we must recognize the Paradox of Money and Money in Layers. Our proposal divides Bitcoin into layers:

• Bitcoin: native token focused on Store of Value.
• Lightning Network: "certificates" of bitcoin used as Medium of Exchange.
• NITI: synthetics backed by certificates for Unit of Account.

1.3 The Monetary Systems of Hayek and Mises
Hayek, in "The Denationalisation of Money" (1976), proposed private institutions issuing currencies that circulate freely, with users choosing stable ones. This competition leads to better currencies, as issuers maintain value for reputation. Mises, in "The Theory of Money and Credit" (1912), noted humanity tends toward a single money as a natural monopoly, rejecting less suitable goods until one remains. NITI integrates these: a system of private currencies, all backed by bitcoin, facilitating efficiency without added exchanges.

2. Current Solutions and NITI's Differentiation
   Renato Amoedo's article, "Bank stables, Algorithmic and Synthetics," classifies stablecoins into three categories:

2.1 Centralized Stablecoins (IOU)
These derive value from fiat reserves held centrally (e.g., USDT, USDC). They carry counterparty risk, as users lose custody and trust issuers for reserves. Lack of transparency has led to scams and depegging. Subject to regulation and censorship, yet widely used (USDT is the third-largest cryptocurrency).

2.2 Algorithmic Stablecoins
Backed by digital assets via smart contracts (e.g., MakerDAO, TerraUSD), they avoid centralization but require overcollateralization (e.g., 2:1 ratio), increasing costs. Users need technical knowledge of unique algorithms and backing assets. High perceived risk led to collapses like TerraUSD. They focus on fiat replication, competing ineffectively with IOUs.

2.3 Synthetics and NITI's Approach
NITI synthetics link to commodities, stocks, indices, or any verifiable price, with issuers choosing baskets for niches. All follow a standard DLC model for transparency. Unlike IOUs, NITI enables token diversity (e.g., Diesel hedge, Bitcoin fee rates, weather), impossible for centralized systems due to complexity. Standardization reduces risk perception; users know all synthetics adhere to the protocol, unlike flawed unique systems (e.g., TerraUSD incompatible). NITI fills a market gap by enabling peculiar use cases via private BTC-collateral contracts.

3. Theoretical Foundations
   3.1 Monetary Theory and the Optimization Problem
   We formalize the monetary utility function as a multi-objective optimization problem:

Definition 3.1 (Monetary Utility Function)

( U(m_i, t, \theta) = \alpha(\theta,t) \cdot V(m_i,t) + \beta(\theta,t) \cdot T(m_i,t) + \gamma(\theta,t) \cdot A(m_i,t) + \delta(\theta,t) \cdot S(m_i,t) )

Where:

• ( V(m_i,t) ): Store of value utility at time t
• ( T(m_i,t) ): Transaction utility (speed, cost, finality)
• ( A(m_i,t) ): Accounting utility (price stability, divisibility)
• ( S(m_i,t) ): Security utility (censorship resistance, seizure resistance)
• ( \alpha, \beta, \gamma, \delta ): Time and agent-dependent preference weights
• ( \theta ): Agent preference parameters

Theorem 3.1 (Monetary Specialization Theorem) For any agent ( \theta ) and time period [t₁,t₂], there exists an optimal portfolio allocation across monetary assets that maximizes expected utility subject to budget and liquidity constraints.

Proof Sketch: This follows from standard portfolio optimization theory with the additional constraint that monetary assets must satisfy the medium of exchange property. The formal proof is provided in Appendix A.

3.2 Layered Monetary System
Definition 3.2 (Monetary Layer) A monetary layer L_i consists of:

• Asset Set: A_i = {a₁, a₂, ..., aₙ}
• Transfer Function: f_i: A_i → A_i
• Settlement Function: g_i: A_i → A_{i-1}
• Risk Function: r_i: A_i → ℝ⁺

Theorem 3.2 (Layer Stability Condition) A monetary layer L_i is stable if and only if:

( \forall a \in A_i: \mathbb{E}[r_i(a)] \leq \mathbb{E}[r_{i-1}(g_i(a))] + \phi_i )

where ( \phi_i ) is the convenience yield of layer i. This ensures higher layers provide utility benefits to compensate for risk.

3.3 Hayek's Competing Currencies: A Game-Theoretic Framework
Definition 3.3 (Currency Competition Game) The currency competition game G consists of:

• Players: N = {issuers, users, oracles}
• Strategies: S_i for each player type
• Payoffs: π_i(s₁, s₂, ..., sₙ) for strategy profile s
• Information Structure: I_i for each player

Theorem 3.3 (Existence of Nash Equilibrium) Under mild regularity conditions, the currency competition game has at least one Nash equilibrium.

Corollary 3.3.1 (Stability of Equilibrium) The equilibrium is stable if the Jacobian of the best response functions has all eigenvalues with negative real parts.

4. Cryptographic Architecture
   4.1 Discreet Log Contracts
   Definition 4.1 (Secure DLC) A Secure DLC is a tuple (Setup, Commit, Reveal, Settle) where:

• Setup(1^λ, O, P₁, P₂) → (pp, sk₁, sk₂, pk₁, pk₂, pk_O)
• Commit(pp, sk_i, m, t) → (σ̃_i, R_i)
• Reveal(pp, pk_O, outcome, t) → σ_O
• Settle(pp, σ̃₁, σ̃₂, σ_O, outcome) → (σ₁, σ₂)

DLCs allow private agreements using real-world data, similar to Lightning Network but for conditional payments. Alice and Bob pre-sign transactions, with only the oracle-signed outcome executable.

Theorem 4.1 (DLC Security Properties) The Enhanced DLC construction satisfies: Completeness, Soundness, Privacy, Atomicity. Proof: See Appendix B.

4.2 Cascading Discreet Log Contracts (CDLCs)
Definition 4.2 (CDLC) A Cascading DLC extends the basic DLC with:

• Cascade Function: Cascade(DLC₁, DLC₂, ..., DLCₙ) → CDLC
• Enhanced Security Construction: H_secure(C_k, D_j, nonce, timestamp) = SHA3-256(C_k ⊕ D_j ⊕ nonce ⊕ timestamp)
• Anti-Correlation Mechanism: α'_i = KDF(α_base, i, chain_id); β'_i = KDF(β_base, i, chain_id)

CDLCs interconnect DLCs in sequence, where one result triggers the next. For example, Alice and Bob set a DLC on BTCUS