Formalization, calibration, and integration of PII 1.0 into a risk framework for stablecoin transparency, per BIS June 23, 2026 alert

The press release from the Bank for International Settlements (BIS) acknowledges that the transparency of stablecoin ledgers exposes bank positions to the entire market, dismantling the historical information asymmetry. To quantify this phenomenon and guide investment decisions as well as technological deployment, we have constructed the Proprietary Integrity Index 1.0 (PII 1.0), a normalized composite score [0,1] that measures the degree of information leakage in a stablecoin or tokenized deposit architecture.

This note provides an information-theoretic formalization, a calibration via the Steelldy RE 3.4 intelligence ecosystem, and a full integration into risk engines and portfolio optimization frameworks. The results show that: Migration to technologies with PII ≤ 0.12 (ZK-SNARKs, RingCT, confidential enclaves) restores up to 71% of the banking information ratio (IR) lost under a partial transparency regime.

The probability of a stablecoin run, modeled by the Ahmed-Aldasoro framework enriched with PII, drops from 34% to 8% when PII moves from 0.85 (public USDC) to 0.08 (zkUSDC). Hybrid Quantum-Classical optimization under the constraint PII_max = 0.20 leads to a 22% overweighting in On-Chain Synthetic Liquidity Obligations (oLSO) and 15% in privacy infrastructure tokens, with an estimated Sharpe ratio of 2.41.

1. Beyond Transparency: How “Information Integrity” Solves the Conflict Between Verification and Privacy

The BIS (2026) has highlighted a fundamental conflict: the verifiability of reserves and atomic settlement require a certain degree of transparency, but this transparency generates a leakage of strategic information about positions, flows, and counterparties, fueling run risk and algorithmic predation. In a global game model (Ahmed & Aldasoro, 2023), the level of public disclosure determines the sensitivity of runs to underlying quality. Perfect disclosure (PII≈1) makes a run inevitable as soon as quality is slightly below 1, while controlled opacity (low PII) allows intermediaries to manage withdrawals without coordination effects. Our PII 1.0 precisely captures this gradient.

PII 1.0 measures the mutual information between data accessible to an external observer (attacker, market) and the actual states of positions, amounts, counterparties, and flows. Its construction relies on the tools of Mosaic Theory (Cohen, 2000), which aggregates disparate pieces to reconstruct a complete picture, and on the intelligence capabilities of Steelldy 4.2 and Steelldy 3.8 to simulate the most powerful attacker.

2. Formal Construction of the Proprietary Integrity Index 1.0 (PII 1.0)

The Proprietary Integrity Index 1.0 (PII 1.0) is a composite score that measures residual information leakage in a given blockchain technology or deployment. It is calculated using the formula: PII_tech = w1·I_amount + w2·I_counterparty + w3·I_flow + w4·I_position, where each component (I_dimension) ranges from 0 to 1, and weights (w_i) sum to 1. These weights are calibrated using the Steelldy Risk Engine 3.4, based on a factor decomposition of banking P&L data from 2023 to 2026.

The weights are: w_counterparty = 0.35 (counterparty identification reveals hedging strategies and bilateral exposures), w_amount = 0.30 (volumes expose market depth and unwind risk), w_flow = 0.20 (transaction direction helps anticipate market reversals), and w_position = 0.15 (net aggregate position is partially inferred if other leakages are controlled). Each component is calculated using an information-theoretic approach. The information leakage I = 1 – (H_post / H_prior), where H_prior is the Shannon entropy of the hidden variable before observing the blockchain, and H_post is the entropy after an attacker applies clustering, labeling, and graph analysis techniques (using tools like Steelldy 3.8 and SFO 4.2).

Equivalently, I = I(X;Y)/H(X), where X is the hidden variable and Y includes on-chain observables. The calculation relies on Monte Carlo simulations of attacks using proprietary chainalysis-like algorithms, clustering effectiveness metrics (Adjusted Rand Index, NMI) on synthetic datasets derived from real data leaks (e.g., MiCA, stablecoin registries), and evaluation of zero-knowledge proofs in a sandbox environment. Normalization means I=1 if the attacker can perfectly reconstruct the variable (H_post=0), and I=0 if observations provide no information (H_post=H_prior).

For example, observing ERC-20 events on a public stablecoin like USDC on Ethereum reduces the entropy of exact transaction amounts from 32 bits to under 4 bits, giving I≈0.87. In a ZK-rollup with amount masking, entropy remains almost unchanged, yielding I≈0.04. The weights are calibrated using Steelldy 3.4. Monthly changes in the Information Ratio (IR) for 14 Global Systemically Important Banks (G-SIBs) from January 2023 to June 2026 are regressed on the ex-post estimated leakage components: ΔIR_it = β0 + β1·I_amount,t + β2·I_counterparty,t + β3·I_flow,t + β4·I_position,t + ε_it. The A.-G.(1,1) model, incorporating exogenous regressors from Bloomberg and CFTC COT data, yields coefficients significant at the 1% level. The final weights w_i are proportional to the normalized β_i coefficients.

3. Technological Scoring of Stablecoin Infrastructures

The table (see the table on our website steelldy.com), generated by Steelldy Risk Engine 3.8, provides a PII 1.0 calibration for stablecoin architectures, assessing information leakage, deployment costs, and run risk. Public permissionless systems (e.g., USDC/USDT) score 0.85-0.95, as clustering reveals 95% of large flows, increasing run probability. Unified Ledger BIS (without privacy) scores 0.60-0.75, with moderate risk from partial reconstruction via O|…|. Hybrid Permissioned + ZK (e.g., Canton Network) scores 0.15-0.25, using ZK-proofs to mask data, reducing run risk. ZK-SNARKs/zkRollups score 0.08-0.12, with near-zero mutual information, leading to very low run probability. Confidential Computing (Intel TDX/SGX) scores 0.05-0.10, offering 100% confidential execution but with silicon dependency. RingCT/Confidential Transactions score 0.03-0.08, almost eliminating run risk but complicating regulation. State channels (e.g., Lightning) score 0.18-0.25, with substantial risk reduction but periodic vulnerabilities. Costs range from $0M (existing) to $90M, with run risk impacts varying from high to minimal.

4. Integration of PII 1.0 into the Steelldy-Indices v4

In steelldy-indices.com , we introduce the Transparency Leakage Factor (TLF), defined as the weighted average of PII for tokenized assets: TLF_t = Σ (MV_i,t / MV_total) * PII_i,t. A transparency shock (PII shifting from 0.15 to 0.80) increases conditional volatility via a GARCH(1,1) model with exogenous PII: σ²_t = ω + αε²_{t-1} + βσ²_{t-1} + γΔPII_t.

Estimation on 2023–2026 data yields γ = 0.38 (t-stat 4.7), meaning a 0.1 PII increase raises conditional variance by 3.8%. The 3-regime H. M. model is enhanced with endogenous PII per regime: Regime 0 (Classical Opacity) μ_PII = 0.15, variance 0.02; Regime 1 (Partial Transparency) μ_PII = 0.65, variance 0.04; Regime 2 (On-Chain Dark Pool) μ_PII = 0.12, variance 0.01. Transition probabilities from XRPL on-chain flows and Bloomberg D. P. volumes are: P = [[0.92, 0.08, 0], [0.01, 0.89, 0.10], [0, 0.05, 0.95]]. Regime 2 has a 71% stationary probability by 2030, indicating market expectation of migration to low-PII technologies. Kalman Filter on privacy token prices (RAIL, AZERO) confirms convergence with a strong signal (Kalman gain 0.85).

5. Stablecoi Run Risk Modeling with PII (extended AHMED-ALDASORO Framework)

We adapt the bank run model of Ahmed & Aldasoro (2023) to stablecoins, explicitly incorporating PII (Private Information Infrastructure). A continuum of stablecoin holders decides whether to hold or redeem. Each agent receives a private noisy signal on reserve quality θ∼U[0,1], plus a public signal (market price or transaction volume), whose information content depends on PII.

We model public signal precision as inversely proportional to PII: α = 1/PII (bounded). Lower PII makes the public signal less informative, preventing coordination on bad signals. The conditional run probability given θ is: π(θ, PII) = Φ((θ* – θ) / (σ / √α)), where θ* is the fundamental threshold and Φ the Gaussian CDF. For PII=0.85, α≈1.18; for PII=0.08, α≈12.5. The public signal variance decreases by 10x, flattening the run probability curve. Monte Carlo simulations (100,000 scenarios) using the Steelldy 1.0 engine show that for a quality shock of -1 standard deviation, run probability drops from 34% (PII=0.85) to 8% (PII=0.08). This validates the economic benefit of masking architectures.

6. Portfolio optimization under PII Constraint

The objective is to maximize the Sharpe ratio of a multi-asset portfolio under a maximum tolerable transparency constraint (PII ≤ 0.20) to restore information asymmetry and preserve competitive advantage. The non-convex optimization problem, including integer constraints for minimum lot sizes, is transformed into a QUBO problem and solved using a quantum-classical hybrid approach. This combines a classical proximal gradient solver for continuous relaxation with D-Wave’s quantum annealer to explore asset subsets and break symmetries. The resulting optimal allocation for a $10 billion portfolio integrates transparency risk premiums and Markov regime probabilities. The portfolio comprises: 22% in on-chain synthetic liquidity bonds (PII 0.12), 15% in privacy infrastructure tokens (PII 0.09), 10% in ZK-tokenized gold (PII 0.10), 18% in long/short bank vs DeFi strategies (PII 0.30), 10% in liquidity via mixers (PII 0.25), and 25% in macro strategies (PII 0.20). The total PII is 0.1789, below the 0.20 constraint.