History-Conditioned Control in Open Systems: Teleonomic Potentials, Dissipative Computation, and Conditional Agency

Purpose-like descriptions are common in biology, neuroscience, robotics, and artificial intelligence, but the same language is often applied to systems with radically different capacities. A falling object follows a gradient, a thermostat corrects a measured error, a cell changes its behavior after stress, and a planning agent compares alternatives. Dissipation and stabilization alone do not make these systems equivalent. This paper develops a bounded mathematical framework for distinguishing four evidential levels: physical dissipation, regulation, history-conditioned adaptive control, and conditional agency. The core proposal is that a system becomes usefully teleonomic when internally accessible history changes its response to otherwise matched present conditions, returned consequences update that history, and the resulting policy differences survive matched null models and causal interventions. Agency requires additional evidence concerning individuality, system-relative normativity, interactional asymmetry, and a counterfactual action repertoire. The framework replaces a unit-mixing scalar agency index with a claim vector. It separates observational routing measures, such as conditional mutual information and transfer entropy, from interventional causal effects. It also distinguishes a computational mismatch certificate from physical entropy production. For a declared mismatch functional, the balance law is written as mismatch reduction plus uncontrolled production; for a thermodynamically resolved stochastic process, entropy production is defined by a forward-to-reverse path-probability ratio. Neither equation, by itself, establishes purpose or agency. The paper specifies state-only, shuffled-history, consequence-permuted, capacity-matched, energy-matched, and post-hoc narrative nulls; proposes synthetic-controller, morphogenetic, and neural test programs; and states explicit failure conditions. A deterministic five-system reference benchmark then tests the evidential ladder. Open-loop and memoryless-feedback systems fail the history package; writable-history and planner systems pass their declared diagnostic levels; and an observer-only record improves prediction while failing the consequence-writing and memory-intervention tests. The benchmark validates the decision logic, not biological agency. The paper preserves the teleonomic/Telos research bridge developed in Super Information Theory while removing universal-purpose, cross-domain coefficient, and ordinary-buoyancy overclaims. The result is a substrate-general research program for testing when history and consequence have genuine control relevance without treating every organized dissipative process as an agent. A second deterministic benchmark adds two harder adversaries to the original synthetic-controller benchmark. In one, a candidate history variable predicts action only because it proxies an unmeasured present variable; its gain collapses when present state is enriched. In the other, a nominal memory manipulation changes action through an off-target direct route; a selective memory probe has zero effect while an instrumented sham reproduces the naive intervention effect. A true writable-history controller survives both controls. These additional results validate the extended decision logic, not biological or general agency. A third deterministic benchmark tests whether that logic survives five practical hazards: an intervention that reaches only part of its intended target, missing measurements and outcomes, rare positive outcomes, a changed test distribution, and dependence on one prediction family. The true writable-history construction retains positive history gain under all declared conditions. The incomplete-state proxy does not acquire positive out-of-distribution gain in either a regularized interaction-logistic model or a Laplace-smoothed fixed-bin model. Because the proxy sometimes harms shifted prediction, that result is reported as nonbenefit rather than falsely labeled equivalent to zero. The benchmark freezes construction-specific decision margins, multiplicity, power, and held-out-opening rules. It tests an analysis contract; it does not validate a biological substrate.