# The Lupi Program

## Research what you get when you treat companies as if it's a software problem, enabled by AI and abstract math

Endgame: I believe we can enormously increase the efficiency of large organizations, reduce the waste of hundreds of thousand of employee-years spent in coordination, to the point that CxO and VP can get answers to what-if questions in matters of hours, not months.

I am not blind to the terrifying social implications of treating organizations as mechanisms, but unfortunately I think we're headed there in the not so distant future. It's better to think about them in advance and consciously, rather than proceed unaware and consider risks post-hoc.

I think it's worth pursuing and I'd like to research it, so I use the term **Lupi Program** for my research project in honor of the famous Langlands program in mathematics. I do not have any pretension to compare myself to Langlands, but I want to highlight how what follows is the program for a multi-year research program with long-range links between disciplines, and not a ready-made solution that can be implemented tomorrow.

In a few bullet points:

"SRE is what you get when you treat operations as if itâ€™s a software problem." ==> My Program is what you get when you treat companies as if it's a software problem.

Companies are complex hierarchical systems that achieve goals.

They are computational systems. We can "program" and describe their properties. That's what we do, in a very imprecise way, using diagrams and docs and tons of meetings... but they are very imprecise, and lead to constant mis-alignments and very expensive errors.

but, we could do much better! If we bake into a flexible formalism some basic properties, that come from abstract algebra (abstraction, structure determines semantics and dynamics) and physics (symmetries and conservation laws), we can solve the mis-alignment problems at least for the technical parts of orgs.

what is different now? AI can turn a step paradigm shift into a smooth slope of complexity, so that it becomes progressively more precise and quantifiable. Apply it as a recursive process, keep the rest of the company aligned, and it turns a lot of separate islands into a monorepo of up-to-date company behavior, a full organization turned into a differentiable program parametrized by its KPIs or SLOs.

*At this level of abstraction,* with the right formalism and approach, it's possible to connect the dots (think of it as higher-order functional programming for an organization value streams and dynamics):

define and align the value streams, in a formal way that ensures hierarchical composition and prevents unaccountable waste products;

that can be mechanically (algebraically) applied to all business phases

using a method that is flexible enough not to hinder discussion, with tuneable complexity and formalism...

...at its simplest, it will require only pen&paper and a napkin (much in the same a Feynman diagram encodes a very complex differential equation in a drawing)...

...but can be smoothly (in simple cases, automatically with AI; in more complex ones, with CoPilot-style assistants) transformed into full formal specifications.

It will enable:

formal proofs (e.g. TLA+, MITL, CEGAR) that avoid design errors as business processes evolve

probabilistic conformance checking

coarse simulations, including continuous qualitative or quantitative estimations of connected risks, as current situation or what-if scenarios are updated

traceability, observability, and debugging of the whole objectives graph of a company

high-level business thinking and leaders are hobbled by the same "one-mind-barrier" problem that plagues mathematics: the very few at the top only have a vague idea of what is going on, so they have to test their hypotheses for business change and what-if scenarios through a painful and long process of indirection.

While we can't eliminate that, we can surely short-circuit it. We should learn from AI: solving a simpler and more general problem is often more fruitful than solving many tiny detailed instances;

It requires a long detour into abstract mathematics, many parts of compute science and physics, but at the end much of the complexity can be removed (very few write programs in lean4, but many do write in Rust):

the dynamics of complex organizations depend on the interactions among their parts, not on the low-level details (Software in the natural world, Computational mechanics): with a crude parallel to SRE terms, horizontal coarse-graining are SLI and and vertical coarse-graining are SLO.

mathematical proofs, mathematical spaces, dependent type systems are deeply connected and equivalent (HoTT, Cubic homotopy theory)

The mathematical structure of the organizations (space) and their evolution (time) can help us understand what discipline of math can be used to describe their stochastic behavior, or if this is possible at all (DMDU, differential geometry, stochastic physics and QFD, deterministic chaos, complexity, actuarial sciences, agent-based dynamical systems, are all inspirations and tools we can look at);

we should take a unified look at how companies and systems take decisions, study them with the lens of category theory, geometry and topology, to understand the invariants and the commonality;

these ideas are not new, but we haven't put them together in a coherent way in a business setting, nor we could automate choice and implementation until AI progressed to the current point;

Our own language and concepts (written or visual) are of the same nature:

my conjecture is that we can find analogous mathematical spaces if we train LLMs (or a new class of them) on these problems;

that we can find smooth transformations (categorical sheaves) from fuzzy representation (it can be done at the meta-level) on a napkin to dependent typed formal languages (using the properties we want in these processes as desirable "boundary conditions").