Pattern, Persist! [LONG Monograph]

Agency is what happens when a pattern fights to stay a pattern — and this paper builds that intuition into a precise, substrate-independent theory.

The core move is to start from persistence rather than from goals or behavior. A pattern persists when its compressed description at time t still describes it at time t+τ — when the "identity program" survives the filter of time. The paper formalizes this as a normalized mutual algorithmic information score between the pattern's earlier and later submodels. High score: the pattern persists. Low score: it dissolved. This is observer-relative (you need a projection and a modeling agent to define the pattern at all), but not arbitrary — most candidate patterns fail to compress, predict, or support action under further observation.

Persistence under perturbation immediately forces a regulator into existence somewhere in the pattern-world system. Something must absorb, cancel, or export the complexity that interaction keeps injecting. The Algorithmic Regulator Theorem (ART, from a companion paper) makes this precise: a sustained reduction in the readout's description length is strong evidence — under the universal Solomonoff prior — that the regulator shares mutual algorithmic information with what it regulates. In plain terms: a successful regulator must carry a model of its world. This is the algorithmic sharpening of Conant and Ashby's 1970 "Good Regulator" theorem. From that model, a scalar objective (the complexity gap itself) and a planner (minimize predicted description length) follow as natural readings, not added machinery. Together these three roles — Modeling Engine, Objective Function, Planning Engine — define the algorithmic agent.

The crucial distinction the paper draws is where the regulator sits. A room held at 21°C by a thermostat is a persistent regulated pattern, but the agent is the thermostat, not the room. A cell is different: the regulatory work is localized inside the pattern itself. The paper operationalizes this with a directional ablation test — null the pattern's action on the world versus null the world's forcing on the pattern, and see which ablation destroys persistence. A Game-of-Life "eater" cell pattern works out the example computably: killing the eater's outward action destroys it; sealing it from incoming gliders does not. That asymmetry certifies self-regulation. A passive "blinker" pattern, which mounts no defense, marks the contrast.

Macroscopic regulation is irreversible — it acts on coarse-grained, many-to-one variables and cannot retain the full microstate fiber it discards. By Landauer's principle, each irreversibly discarded bit costs at least k_BT ln2 in heat. So the thermodynamic price of persistence scales with the irreversible discard rate, not the size of the model. A proton relaxing after a photon hit pays almost nothing (near-equilibrium, reversible export); a cell continuously pays to maintain its identity (far-from-equilibrium, constitutive dissipation). The paper's thesis is that a macroscopic agent is precisely a pattern conserving its own bounded code through a thin, thermodynamically costly boundary, inside a world that — when closed and reversible — conserves algorithmic information globally. Agency is the local form of that global conservation.

The final payoff is a reframing of alignment and evolution. In a collective of agents, the parts need not share an objective — and Arrow's impossibility theorem means they cannot in general be aggregated into one. Instead, alignment is an objective-distribution problem: design the local objectives and the constraints bounding them so the collective as a whole persists, without requiring any single shared reward. Whether a persistent collective counts as one agent or many is then read from the landscape of its regulation — where the load-bearing regulatory structure is localized — not from an intrinsic integration scalar.