The Banking Butterfly: Decimal Precision Asymmetry in Interest Rate Settlement as a Systematic Wealth Transfer Mechanism — Evidence from Sovereign Custody, Global Custodians, Commercial Lending, and the USD Repo Market

Zenodo Deposit — #33 DOI: 10. 5281/zenodo. 20779418 Title The Banking Butterfly: Decimal Precision Asymmetry in Interest Rate Settlement as a Systematic Wealth Transfer Mechanism — Evidence from Sovereign Custody, Global Custodians, Commercial Lending, and the USD Repo Market Description This paper identifies, names, and quantifies a structural mechanism — decimal precision asymmetry — operating across five channels of the US and global financial system. Financial institutions and global custodians systematically compute interest charges at higher decimal precision than interest payments. The mechanism has two distinct layers. Layer 1 — Day-count convention asymmetry. Charges are computed on an Act/360 basis while client statements and reference rates assume Act/365 or stated annual rates, inflating effective charges by a factor of 365/360 ≈ 1. 013889. At a stated rate of 5%, the effective charge is 5. 0694% — a premium of 6. 94 basis points that applies to every instrument on this basis, every settlement cycle, every year. Layer 2 — Precision truncation asymmetry. Bank settlement systems compute the charge leg (amounts owed to the institution) at six to eight decimal places; the pay leg (amounts owed by the institution) is truncated to two or three decimal places before delivery to the client. The agreed rate is identical on both sides; the precision applied is not. The sign of this gap is always the same: positive for the institution, negative for the client. It is not random rounding noise. It is a directional, configurable property of settlement systems that has never been disclosed or named in the academic literature. Five channels are identified: USD repo market — 4–6T daily outstanding; Act/360 is the universal convention; annual cost 2. 8–4. 2B. US commercial loans (C Act/360 industry standard; annual cost 4. 7B. Global custody cash accounts — ~3. 2T cash within a 160T assets-under-custody base (Big Four: BNY Mellon 52. 1T, State Street 46. 6T, JPMorgan 38T, Citi 24T) ; annual cost 0. 6–3. 0B. Securities lending cash collateral — ~2. 85T; annual cost 0. 3–1. 5B. US domestic deposit base — ~12T interest-bearing; annual cost 1. 2–6. 0B; affects 153 million US deposit holders. Combined annual cost (US market): 9. 6–19. 4 billion. Estimated cumulative cost since computerised settlement standardised these configurations (mid-1980s): 150–350 billion. LATAM Central Bank Exposure Latin American central banks represent the highest-concentration sovereign exposure to this mechanism outside the major Asian reserve accumulators. The largest reserve holder in the region is Banco Central do Brasil (BCB) at approximately 355 billion — not Banco de México (215B) as sometimes assumed. Combined LATAM reserves (BCB, Banxico, BCCh, BCRP, BanRep, BCU, BCRB) total approximately 826 billion. Annual unreconciled interest gap for LATAM central banks: 82M (conservative, 1bp) — 411M (adverse, 5bp) per year. Twenty-five-year cumulative estimate: 3–10 billion. Brazilian Case: The Dual Market Supplement The Brazilian banking system presents the mechanism in its most extreme form. The same institution that arranges dollar-denominated syndicated loans for Petrobras and the Brazilian state at approximately 3% per year — routed through the New York branch of Banco do Brasil, the dollar window for all of Brazil's international capital needs — charges retail customers 8% per month (Act/Monthly) on cheque especial overdraft, equivalent to 321. 1% per year (CNM, 2026; BCB historical series, record as of 2026). The credit card revolving rate (cartão rotativo) reached 443. 3% per year in April 2025 before a 2026 regulation capped cumulative charges at twice the original invoice. This differential — 3% for Petrobras's African platform infrastructure, 321% for a teacher in overdraft — is not risk-priced. It is captivity-priced: large borrowers with alternatives (bond markets, international banks, equity) are competed for; retail borrowers with none are extracted from. The same bank holds both books. The 1988 Brazilian Constitution originally included a 12% interest rate ceiling (Article 192) ; it was struck through constitutional amendment in 2003, following sustained banking lobby pressure. Before 1988, Lei da Usura (Decreto 22. 626/1933) capped lending rates at 12% per year — rates that would make the current cheque especial a criminal offense under that law. The precision asymmetry mechanism (this paper) and the dual-market credit structure (the Brazilian supplement) are different expressions of the same operator: the financial system applies exact, configurable precision when extracting from captive counterparties, and minimum-required precision when crediting them. Lorenz Analogy and dm³ Reading The compounding divergence between charge-leg precision and pay-leg precision has the structure of a positive Lyapunov exponent in settlement arithmetic — deterministic, monotonically growing, invisible at the transaction level and measurable only over time. This is the Banking Butterfly: the initiating perturbation (δr of order 10⁻⁴ to 10⁻⁵) is below the threshold of single-transaction perception while its cumulative effect on sovereign-scale books is in the tens to hundreds of millions of dollars per year. Within the dm³ contact-geometric framework (Grossi 2026), the mechanism instantiates operator non-commutativity K, F ≠ 0: applying the precision function F before the compounding rule K on the charge leg, and K before F on the pay leg, produces a directional, compounding divergence whose sign is always positive for the institution. Three Diagnostic Tests The paper proposes three tests any central bank can run using data it already holds — incoming and outgoing settlement confirmations, original trade documents, and historical custody statements: Charge-leg vs. pay-leg precision audit — extract 1, 000 settlements, compute δr for each; a Kolmogorov–Smirnov test against zero-mean symmetric δr detects structural asymmetry. Day-count convention reconciliation — compare Act/360 vs. stated basis for every USD position; compute the effective premium. Long-horizon settlement reconciliation — recompute all interest accruals on a position held 3+ years using confirmed rates at confirmed precision; the difference is the cumulative unreconciled gap. A model contract clause and a minimum examination standard for banking supervisors (OCC, Federal Reserve, FDIC) are provided. A CEMLA coordination recommendation for LATAM central banks is included. Author's note. The author is a former employee of the category of institution described in this paper. He managed sovereign custody and treasury relationships with Latin American central banks — BCB, Banxico, BCCh, BanRep, BCRP — at major global banks, including One Chase Manhattan Plaza - JPMorgan's Securities Markets and Finance Division at thier 58th Floor, and at the Corporabe Bank - Madison Avenue Branch of Banco do Brasil New York (BBNY), the dollar-funding window for Brazil's international operations. The mechanism described here was observed in live account reconciliation. The arithmetic does not depend on the author's emotional state. 365 divided by 360 is 1. 013889 whether it is computed by a bitter former employee or by the Treasury of the United States. The data will say. Authors Name Affiliation ORCID Pablo Nogueira Grossi G6 LLC, Newark, New Jersey 07104, USA 0009-0000-6496-2186 Keywords (one per line) interest rate settlement decimal precision asymmetry day count conventions Act/360 global custody assets under custody BNY Mellon State Street JPMorgan Citi repo market securities lending precision truncation wealth transfer central bank risk management LATAM Banco Central do Brasil cheque especial dual credit market Lyapunov exponent Banking Butterfly Lorenz dm³ framework Principia Orthogona operator non-commutativity CEMLA banking regulation deposit rates usury License Creative Commons Attribution 4. 0 International (CC BY 4. 0) Upload type Publication → Working paper / Preprint Related identifiers DOI / URL Relation Resource type 10. 5281/zenodo. 19117399 Is part of Publication (series root) 10. 5281/zenodo. 20682934 References Publication (TOGT / Contact-Geometric Theory) 10. 5281/zenodo. 20710023 References Publication (Alterna) 10. 5281/zenodo. 20719399 References Publication (TEFL preprint) 10. 5281/zenodo. 20779067 References Publication (Enceladus preprint, deposit #32) https: //github. com/TOTOGT/AXLE Is supplemented by Software (AXLE Lean 4 engine) Files to upload File Role banking-butterfly-preprint. html Primary deposit (full preprint with figures) fig1compoundingdivergence. png Figure 1 — compounding divergence fig2ₐct360ₚremium. png Figure 2 — Act/360 premium fig3fivechannels. png Figure 3 — five channels annual cost fig4ₛettlementₐrchitecture. png Figure 4 — settlement architecture fig5ₗatamₑstimates. png Figure 5 — LATAM central bank estimates fig6big4ₐuc. png Figure 6 — Big Four AUC fig7ₕistoricalcumulative. png Figure 7 — cumulative cost 1960–2025 bankingbutterflyₚreface. md Supplementary — Author's statement / preface DOI 10. 5281/zenodo. 20779418