LK Digital Solutions

Research

Research by LK Digital Solutions.

Federal Reserve data is available below. Published work follows.

Consumer Price Index for All Urban Consumers: All Items in U.S. City Average

CPIAUCSL · Monthly · Index 1982-1984=100 · % chg from yr ago

Source: Federal Reserve Bank of St. Louis (FRED). 119 observations shown.

Recent observations

CPIAUCSL
DateValueChange
Aug 1, 20263.35+0.05
Jul 1, 20263.30-0.16
Jun 1, 20263.46-0.70
May 1, 20264.17+0.39
Apr 1, 20263.78+0.49
Mar 1, 20263.29+0.85
Feb 1, 20262.43+0.04
Jan 1, 20262.39-0.26
Dec 1, 20252.65-0.04
Nov 1, 20252.70-0.33
Sep 1, 20253.02+0.08
Aug 1, 20252.94+0.20
Jul 1, 20252.74—

Reports

Published research

The first reports are on the bench now. In the meantime, the live data below doesn't wait.

Papers

Research papers

July 21, 2026 · PDFCoalescence-Class Cardinalities in Finite Grand Couplings Need Not Be Deterministic

The answer to Open Problem 3.11 of Grimmett and Holmes is negative. The proof is computer-assisted and reproducible, made by GPT-5.6 Sol.

probability · mathematics · markov-chains · computer-assisted-proofView PDF →
July 21, 2026 · PDFUniversality of Unboppy Balanced Binary Rotors of Fundamental Period 24

We prove a finite classification theorem for homogeneous rotor-router networks: every fixed-phase balanced primitive unboppy binary rotor of fundamental period 24 is universal. The proof is computer-assisted but fully finite, produced by GPT-5.6 Sol.

mathematics · combinatorics · exhaustive-search · computer-assisted-proof · rotor-routerView PDF →

Research areas

01AI Systems

How AI systems remember context and respond reliably.

02Digital Operations

How small teams replace fragile manual work with software.

03Markets & Infrastructure

How digital demand changes as software and search improve.