Persistence Architectures: Continuous Realization, Re-instantiation, and Inheritance

"Things persist in different ways" turns out to be a precise, consequential claim — this paper builds the formal vocabulary for it.

The core move is simple but clarifying. Prior work (the companion paper "Pattern, Persist!") defined what it means for a pattern to persist: a compressed description of some system retains enough algorithmic identity over time to remain reusable. This paper asks the next question — how does that happen, mechanically? The answer is a taxonomy of "persistence architectures." At any declared grain of observation, a pattern either persists through continuous realization (one causally connected history, even as the underlying material churns) or through successive re-instantiation (the pattern must be reconstructed across a declared boundary). A brain and a biological lineage are both persistent, but they sit in different branches of this taxonomy. A diamond sits in yet another. The key insight is that reproduction, repair, learning, and selection are mechanisms within these modes — not alternative definitions of persistence itself. This ordering matters: it stops you from accidentally building reproduction into the definition of life, or agency into the definition of persistence.

The paper then narrows to the inheritance branch and asks how acquired information — things an organism learned or experienced — can cross a generational boundary. Two parallel causal routes exist. The selection-mediated route lets acquired state influence which programs leave descendants, but nothing learned gets directly written into the next generation's heritable program. The direct write-back route encodes acquired structure into the transmitted program itself. These are not endpoints of a Darwinian-to-Lamarckian slider; they are independent channels that can both operate simultaneously. The paper formalizes this as a factorization of the transmission operator, and defines the effective write-back bandwidth as the bits of the descendant's program that the transmitted message accounts for, after conditioning out the parent program and the selection signal.

The formal results then bound what write-back can do. The key proposition is that no total computable encoder can invert an arbitrary developmental map while also reliably recognizing when a given acquired state is outside its domain. This is a computability result (the achievable set of a computable developmental map can be undecidable), but the paper is careful about what it actually rules out: not write-back in general, not approximate inversion, not domain-restricted encoders — just a universal, exact, self-certifying inverse. The practical conclusion is that every real write-back channel requires a domain-specific credit-assignment mechanism, and its bandwidth is capped by what its transmitted message can express. A lineage with a trivial encoder transmits nothing acquired, regardless of how much was learned.

Finally, the paper asks how long a written-back message should persist across generations. This is a separate question from whether the pattern persists. Under a linear payoff — retained information is worth what it still predicts about the environment, minus a carrying cost — the optimal retention kernel is a threshold rule: keep the message until its predictive value drops below the cost, then drop it. For exponentially decaying environmental correlations, the optimal retention span is proportional to the feature's correlation time. This is stated as a hypothesis about real channels: mechanisms like epigenetic marks or cultural transmission should have retention spans matched to the timescale of what they encode. The paper is explicit that this is a conjecture, not a theorem, and suggests tagging experiments to test it.