Pattern, Persist! Algorithmic Persistence, Telehomeostatic Closure, and the Graded Architecture of Agency

A unified algorithmic theory of what it means for a pattern to persist, and what "agency" really is.

The core move is deceptively simple: instead of asking "is this thing alive or an agent?", ask "does a compact description of this thing remain reusable over time?" A pattern — a cell, a thermostat, a glider in Conway's Game of Life, a human — is defined as a compressed submodel in an observer's world-model. Persistence is then measured by how much of that compressed description survives across time (normalized mutual algorithmic information between earlier and later snapshots). This sidesteps the usual binary debates about agency and life by making everything graded and observer-relative. Crucially, "observer-relative" doesn't mean arbitrary: a candidate pattern has to keep earning its description by compressing new data it wasn't trained on.

The paper's second key insight is about information budgets. Under reversible physics, the total algorithmic complexity of a closed system is conserved. But local complexity — the description length of a subsystem — can grow, shrink, or migrate. A bounded pattern living inside that conserved budget faces a hard constraint: identity-relevant novelty (new information that would change what the pattern is) can't just disappear. It has to go somewhere. The Algorithmic Persistence Balance (APB) is the formal ledger tracking where it goes: into updated internal structure, model updates, retained memory, outward action, or records left in the world. Once internal growth is bounded, the residual novelty must flow through the boundary or stay in the environment. A bounded self-code also can't double as an indefinitely growing memory — these are provably incompatible.

"Telehomeostasis" is the name given to whatever organization is causally load-bearing for a pattern's continued persistence. The paper measures this via directional ablation: suppress the pattern's outward causal influence and see if persistence drops; suppress incoming support and check the same. This gives a two-dimensional causal profile — how much does the pattern do versus how much does it depend on — without requiring a privileged anatomical boundary. A stone, a cell, and a corporation can all be placed in the same descriptive space; they just occupy very different regions of it.

The framework deliberately separates several things that prior theories conflate. An "Algorithmic Agent" is any system with a Modeling Engine, Objective Function, and Planning Engine — its objective need not be self-preservation. Telehomeostatic agency is the special case where that functional organization participates in keeping the focal pattern alive. Self-targeting, internalization, model depth, and delegation are treated as independent coordinates, not synonyms. This lets the framework handle cases like apoptosis (a cell "choosing" death to serve organism-level persistence) or humans using hospitals and institutions as externalized regulatory machinery without breaking the formalism.

The paper is long and technically dense — it's a review article aimed at Physics of Life Reviews — and it explicitly positions itself as a synthesis across cybernetics, autopoiesis, active inference, dissipative adaptation, and information-theoretic individuality rather than a replacement for any of them. The ideal quantities (Kolmogorov complexity) are uncomputable, so the empirical program relies on fixed computable code classes as proxies. Four testable predictions are sketched: that identity-relevant novelty satisfies the persistence balance, that grounded regulation obeys the GART tradeoff, that forgetting costs follow what is erased (Landauer), and that neural irreversibility tracks learnable model updates.