REHAN THEORY LAB

Rehan Muhammad
Independent Researcher

I work on two hard problems at once: making exact computation faster — NP-complete search, kernel-level memory management — and making it safe for AI agents to operate real machines, through bridges with an explicit consent model.

RESEARCH

1

EXACT SEARCH

NP-complete instances solved exactly, faster — by racing independent engines against each other instead of trusting one.

2

KERNEL MEMORY

Allocators and page management inside a real RISC-V kernel — lock-free, arena, and slab, integrated into an existing subsystem.

3

AGENT ACCESS

Letting an AI agent operate the user's own machine, with consent as a first-class constraint rather than an afterthought.

SELECTED WORK

Z++ — exact subset-sum solver

Races 49 engines — published baselines and original work — and reports which one won. You get the answer, plus evidence for why that technique solved that instance.

baselines:  Schroeppel–Shamir · MITM · BCJ · HGJ
original:   GDEP · adaptive partitioning · BigUint
measured:   n=60 → 524 s (i3-2100) = 1,649× vs BCJ
projected:  n=60 → 24.3 s (Ryzen 9) = 35,556×
memory:     ~12 GB floor at n=60
RustPythonMIT

browser-bridge-for-muse

Gives an AI agent access to the user's own browser and desktop — the sessions they already have — instead of a sterile browser that hits a login wall everywhere.

engines:    Chrome profile · CDP · patched driver
interface:  MCP server
consent:    per-session opt-in, visible, scoped
never:      credential export, silent operation
PythonMCPApache-2.0

MAIK — Multi-Agent Intelligence Kernel

An agent system organised as a company: identities, managers, notebooks, scoped permissions, and prompts generated at runtime from each node's own context.

structure:  CEO → manager → agent → sub-agent
routing:    domain → model, chosen from grades
execution:  mouse, keyboard, screen, browser
status:     research prototype — graders internal
PythonagentsMIT

ZPP Unix — RISC-V kernel

A RISC-V kernel extended with lock-free, arena, and slab allocators integrated into an existing memory subsystem. A fork of caffeinix, credited as such in the first line.

upstream:   caffeinix · Troy Mitchell · GPL-3.0
added:      lock_free.c · arena.c · slab.c · palloc.c
scope:      ~390 lines into a ~7,500-line kernel
CRISC-VGPL-3.0

TIMELINE

MAY 2026
Z++ solver
Zenodo DOI archived
JUL 2026
RISC-V allocators
lock-free · arena · slab
AUG 2026
MAIK
multi-agent kernel
SEP 2026
KiloChat
gateway client
OCT 2026
Agent bridge
consent model

RECORD

ArtifactEvidence
Z++ — 49 engines, MIT licencerepository
n=60 → 524 s on i3-2100, 1,649× vs BCJmeasured, not projected
n=60 → 24.3 s on Ryzen 9projection — not yet measured
caffeinix fork: 3 allocators, +391 / −164 linescommit 329116b
DOI archived10.5281/zenodo.20399806
ORCID0009-0003-8748-6524

HOW I WORK

Measure, then claim.Every number carries the machine it ran on and whether it was measured or projected. A ratio computed from two estimates is labelled an estimate.

Credit upstream.A fork says what it is forked from in the first line. Attribution is a licence obligation under GPL, and a credibility requirement under everything else.

State the limit.If it isn't tested, the README says so before the reader finds out. Limitations sections are cheaper than retractions.