HUGGING-FACE1 We began this inquiry by asking what an idea is, and found representation. We asked where an idea sits, and found its position along an evolving chain of custody. We confronted what a hallucination is, and unmasked a trajectory that ha...

RIES PRECISION EQUIVALENCE1 We began this inquiry asking what an idea is, and found only representation. We asked where an idea lives, and found only position; context, contrast, chain-of-custody. We asked what a hallucination is, and found a trajec...

Have You Been Gaslit; Been Saddled with a huge Data Dump, or are simply losing that sense of 100% certainty - you once had? Then you need Zero-Trust Certification - the Next Generation of Frontier Computing! Ask the same question to two frontier lan...

GITHUB1 | WEBSITE2 | DEMO3 Can We Pinpoint the Point of Failure? We began this inquiry by asking what an idea is, and found no absolute container—only representations, projections, and approximations. We then asked where an idea lives, discovering ...

GITHUB1 | WEBSITE2 | PAPER3 We began by asking what an idea is, and found no final answer, only a representation, a projection, an approximation. We then asked where an idea sits, and discovered that its meaning is inseparable from its position in a...

GitHub1 | Website2 Can Chain of Custody Reveal Location? In our previous exploration, we wrestled with a stubborn truth: an idea cannot be absolute or definitively contained. No single embedding, dictionary entry, or neural parameter can fully encap...

GITHUB1 | WEBSITE2 Can It Ever Truly Be defined? Ideas have shaped civilizations, sparked revolutions, inspired masterpieces, and transformed our understanding of reality. Yet despite their immense influence, they remain among the most elusive pheno...

Quick question, before you proceed: "Did Your AI, LLM, MCP or Agent Make a Mistake Today?" Be honest, something unexpected/unexplainable happen - correct? If you're building AI systems today, something probably DID go wrong. Maybe your agent call...

"Convert a promise you can trust, into a fact that you control!" In my previous post, CAPTCHA Farming 2.0, I explored how the AI industry has quietly engineered an extraction loop for human cognition, harvesting our problem-solving and reasoning cha...

How AI Companies Turned Your Thinking Into Their Training Data Here's a thesis worth sitting with, even if you end up rejecting it: the most valuable resource an AI company can extract from you isn't your data. It's your reasoning. And the mechanis...

At the heart of the Riemann Hypothesis lies a deceptively simple question: can the real part of every non-trivial zero of the Riemann zeta function be proven to equal one-half? For over a century and a half, that question has resisted every answer. V...

A Fresh Thermodynamic Lens on the Collatz Conjecture: The Collatz conjecture remains one of mathematics’ most deceptively simple unsolved problems: start with any positive integer, repeatedly apply “divide by 2 if even, or 3n+1 if odd,” and you’ll e...

White Paper1 The Musical Fingerprint of the Collatz Conjecture: Listening for the 4-2-1 Loop. Mathematics is full of simple puzzles, but none are as notorious as the Collatz Conjecture. Pick a number: if it’s even, halve it; if odd, triple it and a...

White Paper:1 https://jmullings.github.io/TheAnalystsProblem/HPHCERTIFICATION.html We present the third instalment of a systematic operator-theoretic programme toward the Riemann Hypothesis. Building on prior works establishing an algebraic singula...

Euler–Maclaurin Control: In this volume, we formalize one of the most delicate bridges in analytic number theory: the transition from discrete arithmetic sums to continuous analytic structure. The Euler–Maclaurin framework is deployed not as a class...

Presenting "The Analyst's Problem: Hilbert Operator"... My paper develops a functional-analytic framework for encoding smoothed Dirichlet energy associated with the Riemann zeta function into a single compact, self-adjoint operator on a separable Hi...

AI Slop or Not? Certifying the Sech⁴ Kernel Against Bochner's and Mercer's Theorems I posted three equations to social media with one question underneath: does kH perfectly satisfy Bochner's and Mercer's theorems? Half the responses assumed it was A...

Welcome to Volume VI of The Analyst’s Problem. In this interactive 3D demonstration we bring together three deep mathematical threads: The Large Sieve – the fundamental inequality that bounds Dirichlet polynomials and underpins modern analytic numbe...

https://jmullings.github.io/riemann-hypothesis-singularity-proof/RHBDNEQUIV.html...

Dirichlet Polynomial Control & ARC Reasoning Engine for AGI! In Volumes I–IV, The Analyst’s Problem built a mathematical engine around Dirichlet polynomials, Toeplitz energy, and a spectral “bridge” inspired by the Riemann Hypothesis. Volume V takes...