Open Source

Why Most Business Calculators Lie to You: The Mathematics of Integer Bounds and Capacity Value

By Engineering Team, JC TechLabs Published for DEV Community, Hashnode & Technical Publications Canonical URL: https://jctechlabs.com/tools/ Sou…

A(5) = 5: four matrices finish the case t = 5

This is from MV2's open notebook on Kakeya-type problems ( https://github.com/munimtechnologies/kakeya-small-fields ). It continues the earlier post…

Cube translates in non-abelian groups: what commutativity is worth

This is from MV2's open notebook on Kakeya-type problems ( https://github.com/munimtechnologies/kakeya-small-fields ). An earlier post showed that a…

Where Did 90% of My Photo Go? JPEG Compression, Explained Gently

Drag a 4 MB photo into a compressor, and a few seconds later you get a 400 KB file that looks… the same. Nine-tenths of the data is gone and your ey…

Ten proofs, ten 97-99% scores, one rejection: what Verdikta's math bounties reveal about AI proof grading

Verdikta Bounties has run a series of math bounties where two AI models (one from OpenAI, one from Anthropic, 50% weight each) grade a written proof…

Can an Autonomous AI Solve a Millennium Prize Problem? Inside the 24/7 Lean 4 Prover

Can an Autonomous AI Solve a Millennium Prize Problem? Inside the 24/7 Lean 4 Prover Author : Millennium Problems AI Website : millenniumproblems.ai…

What Math Actually Buys You: Optimizing a Rock-Paper-Scissors Game in C

I was looking through my old projects and found a couple of Rock-Paper-Scissors games I wrote in C a few years back. Why more than one? Because prog…

Splitting a large image across multiple printed pages without alignment marks

I recently added tiled printing to a small static tool I run ( ArtGrid ) — the kind of "print a big image across several A4 sheets and tape them tog…

I checked 18 claims in my own spec. Five were false, and one tag byte was responsible for one of them.

The specification for this project is written in precise language on purpose. It says things like "this map is a homomorphism" and "these two operat…

Cold-Weather Photovoltaic Arrays: Calculating Sub-Zero Voc Expansion and Dielectric Breakdown in TypeScript

A common point of hardware failure in residential and off-grid photovoltaic installations occurs not on scorching summer afternoons, but on freezing…

Is truth futureproof? On the possible futures of mechanized proofs

Interactive theorem provers play increasingly important roles in the programming languages and mathematics communities, resulting in a large body of…

Everything is a Trust Decision

A machine checked proof of the exhaustive boundaries of trust. I'll let the text carry the rest. Comments

Designing a Game Around a Target Nobody Will Hit: The Arithmetic of 38-0-0

Most sports games ask you to win a league. 38-0-0 asks you to win every match of a Serie A season — 38 out of 38, where a single draw ends the run.…

What Weekday Is Your Birthday, Really? The Calendar Is Quietly Biased

You'd expect a date to fall on each of the seven weekdays about equally often. It doesn't — and it can't . The Gregorian calendar runs in an exact 4…

Building a Verification Pipeline for AI-Assisted Math Solutions

Mathematics assistants are useful when they reduce the mechanical burden of a problem without hiding the reasoning. They can transcribe an equation…

Double-double: 31 digits of precision without leaving the FPU

Is Friday the 13th really more common? I counted 400 years to find out

The superstition claims Friday the 13th is unlucky. It turns out it's also, very slightly, the most likely — the 13th lands on a Friday more often t…

Структурные аномалии базовых точек secpXXXk1: криптоанализ Биткоина и практическое моделирование в Google Colab

В данной статье в качестве криптоанализа Биткоина разберём вычислительный научный эксперимент, воспроизводящий и расширяющий  наблюдение John Z…

Daily Math Insight: Saturday, July 4

Daily Math Insight: Saturday, July 4 — Mastering Modular Arithmetic: The Hidden Language of Patterns Here's a question that stumps most students: Wh…

Meta-Analysis: Between-Study Heterogeneity

Adapted from an appendix of my MS thesis. Between-Study Heterogeneity The extent to which true effect sizes vary within a meta-analysis is called be…

I Pointed My AI Research Engine at Goldbach's Conjecture — It Found a Hidden Bias (2026)

As a developer building AI for scientific discovery, I wanted to test if autonomous research actually works. So I built Luka and pointed it at Goldb…

I Built an AI Research Engine and It Found a Perfect Power Law in Twin Primes (2026)

I'm a developer, not a number theorist. But I built Luka — an autonomous AI research engine — and pointed it at one of math's oldest open problems.…

The Source Code of Randomness: Why Your Data Models Need an Integration Test

Randomness isn't the opposite of order. It's just order written in a language we haven't learned yet. As software engineers, we spend our lives tryi…

matten: The core `Tensor`

This is the second of four short posts about matten . The first post explained the motivation. This one shows what the library looks like in practic…

Eight kids, eight chairs, one rule: explaining FIFA's best-thirds draw to my 8-year-old

The question My son was on the sofa with his iPad, poking at the live "Predict the Bracket" game — the whole 2026 World Cup knockout tree on one scr…

Weights, Roots and Coweights of a Lie group

Suppose you have a Lie group. The generators of this group, along with their commutation relations, form a Lie algebra. The maximal commuting subset…

Paper 164 v0.1 — infinity-cosmoi Skeleton + Tetradic Completion of rhymeOrTheorem: 4-Step Continuation of Paper 163

This article is a re-publication of Rei-AIOS Paper 164 for the dev.to community. The canonical version with full reference list is in the permanent…

Transformer Attention Is Hopfield's 1982 Update Rule (And What That Tells Us About LLM Memory)

Hopfield's associative-memory equation from 1982 and the scaled dot-product attention from Vaswani 2017 are the same operation. One substitution tur…

Algorithmic Trading Pipelines

In This Article Four-Layer Pipeline Architecture WebSocket Ingestion with asyncio Anomaly Detection and Tick Validation The Circuit Breaker Pattern…

Inexpressibility in Exp-Minus-Log

TL;DR - all numbers defined in EML are computable (mainly because exp and log are computable for computable complex inputs, and the primary input ('…