briancapleton.com/papers/s-p-hierarchy

VGF Analysis

The Self-Producing Hierarchy of Closure

A VGF account of prebiotic and biological evolution can be organised around a single recursive principle: lower-level reopening generates higher-level closure, while the resulting higher-level closure becomes the host within which further reopening can occur.

1. Closure and reopening as a reciprocal process

In VGF analysis, closure and reopening are not simply alternating opposites. A closure can create the conditions for further reopening, and reopening within a closure can in turn maintain, modify, or generate closure at a higher level.

lower-level reopening → higher-level closure → new conditions for lower-level reopening

Let A₁, A₂, …, A_n denote lower-level attractors or processes. Their interaction can generate a higher-order attractor 𝒜:

{A₁, A₂, …, A_n} → 𝒜

Once established, however, 𝒜 is not merely an outcome. It changes the conditions under which its own constituents can subsequently vary and reopen:

{A_i} ↔ 𝒜

This should not be interpreted as backwards causation. It is reciprocal constraint across scales. Lower-level processes constitute higher-level organisation, while that higher-level organisation alters the later possibility spaces of the processes from which it arose.

2. Eight nested closure regimes

Relational chemical closurePersistent patterns arise from mutually constraining chemical relations.
Autocatalytic closureReaction networks become mutually sustaining and persist as higher-order process forms.
Compartmental closureA boundary generated by internal processes becomes a host for new internal chemical possibilities.
Self-maintaining protocellular closureBoundary, chemistry, exchange, and repair become reciprocally organised.
Replicative and population closureReplication creates heritable variation and population-level filtering.
Lineage closureIdentity becomes temporally extended across changing generations.
Species closureA broad evolutionary basin stabilises variation while remaining capable of bifurcation.
Ecological and evolutionary closureInteracting species generate a higher-order host that in turn conditions their further evolution.

1. Relational chemical closure

The earliest case need not involve an organism, a cell, or even a self-replicating system. It is enough that chemical processes begin to constrain one another so that a persistent relational configuration forms. If reactions r₁, r₂, …, r_n mutually stabilise some configurations more strongly than others, a higher-order relational attractor may emerge:

{r₁, r₂, …, r_n} → ℛ

ℛ is not identical with any one reaction. Its identity lies in the organisation of relations between them. Once the relational closure exists, it alters the conditions under which its constituent reactions occur.

relations generate closure; closure reorganises relations

2. Autocatalytic closure

A stronger form appears when reactions become mutually sustaining. Schematically:

A → B, B → C, C → A

The relevant closure is no longer any individual molecule. It is the continuing organisation of the network. Molecules may be produced and destroyed while the relational pattern persists. The network is therefore already a process closure: its stability lies in an organised transformation rather than microscopic sameness.

𝒩₁ → β_𝒩 → 𝒩₂

A new pathway can therefore be incorporated through reopening without necessarily destroying the higher-order network.

3. Compartmental closure

A decisive transition occurs when internal chemistry becomes coupled to a boundary. The internal system may contribute to producing or maintaining a membrane-like compartment:

β_internal → γ_boundary

The boundary then alters the chemistry within it:

γ_boundary → β_internal

It retains reactants, modifies concentrations, restricts diffusion, establishes an inside and an outside, and makes new reaction pathways viable. The higher-order closure is therefore generated by the processes it contains, but once generated it becomes a host for their further reopening.

β_internal ↔ γ_compartment

4. Self-maintaining protocellular closure

When compartment, metabolism-like reaction networks, resource exchange, and internal maintenance become sufficiently coupled, the system begins to maintain its own continued existence. The relevant closure is no longer the membrane or the chemistry separately, but their reciprocal organisation.

𝒞 = Γ(γ_boundary, β_chemistry, R_exchange, R_maintenance)

Microscopic components can change continuously while the higher-order organisation persists. Indeed, continued change may be necessary for persistence.

stability through organised change

The protocellular closure is therefore simultaneously a product of its internal dynamics and a host for those dynamics.

5. Replicative and population closure

Replication introduces another level of recursion. A replicating system does not merely maintain one closure; it generates related closures:

P → {P₁, P₂, …, P_n}

Because replication is imperfect, the resulting systems differ. This opens a population-level beta domain:

β_𝒫 = {P₁, P₂, …, P_n}

Differential persistence stabilises some configurations more strongly than others, generating a population closure 𝒫. The population is not reducible to any one individual replicator, and it subsequently conditions which further variants can survive.

{P_i} ↔ 𝒫

6. Lineage closure

Persistent replication across generations produces lineages. A lineage is a temporally extended closure:

L = {P(t₁), P(t₂), P(t₃), …}

Its identity cannot reside in any single organism or generation. The stable element is the continuity of transformation itself.

P(t₁) → P(t₂) → P(t₃) → …

Extensive change can therefore occur while the succession remains within a larger lineage attractor:

{P(t_i)} ⊂ 𝓛

The lineage is consequently a clear example of a reopening closure: it persists by generating descendants that differ from those that preceded them.

7. Species closure

A species represents a still higher-order stabilisation. Populations, organisms, genotypes, phenotypes, and ecological relations may change substantially while remaining within a species-level attractor:

{A₁, A₂, A₃, …} ⊂ 𝒜_species

The species closure is therefore not a frozen form. It is a structured region of evolutionary possibility within which variation can occur without destroying continuity. Yet the species closure can itself undergo deep reopening. At a branching point:

𝒜 → {𝒜₁, 𝒜₂}

At the species level, this is a bifurcation. At a higher level, it may be the normal continuation of a larger evolutionary attractor.

closure bifurcation at one level = reopening dynamics at another

8. Ecological and evolutionary closure

Once many species interact, their relations generate still larger structures. Predation, symbiosis, competition, resource cycles, environmental modification, reproduction, and niche construction create a continually evolving relational field.

{𝒜_i, R_ij} → ℰ

Once ℰ exists, it becomes part of the conditions under which every 𝒜_i evolves:

{𝒜_i} ↔ ℰ

The higher-order attractor is therefore generated by species and their relations, modified by their reopening, and at the same time the host within which further reopening occurs.

3. Closure as the production of a new possibility space

Across all eight regimes, the same structural principle recurs. A closure does not simply reduce possibility. It stabilises some possibilities and, by doing so, becomes the structured environment of a new beta domain.

β_n → γ_n → β_n+1

Closure therefore does not terminate generativity. It transforms the conditions under which generativity continues.

Compartment

A membrane removes possibilities available to unconstrained chemistry, while making possible a protected internal chemistry.

Replication

Replicative constraint stabilises inherited organisation while opening population-level variation.

Species

Species closure stabilises a lineage while preserving the possibility of variation and eventual branching.

Ecosystem

Ecological constraints limit species in some directions while creating niches and opportunities in others.

constraint at level n generates possibility at level n + 1

4. The hierarchy is nested, but not merely stacked

The eight regimes should not be treated as a simple ladder in which one completed level is placed on top of another. Each new closure remains dependent on processes beneath it, while each higher level feeds constraints back into those lower levels.

C₁ ⊂ C₂ ⊂ C₃ ⊂ … ⊂ C_n

C₁ ↔ C₂ ↔ C₃ ↔ … ↔ C_n

Every level is simultaneously:

a closure at its own scale;
constituted by processes and reopenings occurring within it;
nested inside a larger closure;
and potentially a host for reopening at lower scales.

The hierarchy is therefore not merely one of containment. It is a hierarchy of reciprocal production.

5. The VGF reopening mechanism

The general mechanism can now be expressed as:

closure → internal reopening → relational reorganisation → higher-order closure → expanded reopening capacity

The central point is that reopening does not require the destruction of all stability. Because closures are nested, one level can remain stable while another undergoes extensive reorganisation.

deep reopening at level n can be hosted by closure at level n + 1

But the relation is reciprocal. Reopening at level n may alter the closure at level n + 1:

C_n → C_n′ ⟹ C_n+1 → C_n+1′

The host therefore evolves through the reopening it hosts.

6. Evolution as recursively hosted reopening

On this analysis, biological evolution does not begin with species. Species evolution is a comparatively late expression of a deeper organisational principle already present whenever interacting processes generate a closure that then modifies the possibility space of those processes.

Initially, relational structures merely stabilise one another. Later, compartments provide protected domains of chemical exploration. Self-maintaining systems regulate internal change. Replication opens hereditary possibility spaces. Populations stabilise variation across generations. Lineages stabilise temporally extended transformation. Species maintain broad but bounded evolutionary basins. Ecological and evolutionary systems then become higher-order hosts within which whole species can emerge, transform, branch, and disappear.

what survives becomes the host of what can happen next

Yet what happens next can alter the host:

what survives is continually rewritten by the reopening it makes possible

This is the sense in which the eight closure regimes form a self-producing hierarchy. The hierarchy is not built from fixed layers. Each layer is produced through the activity of the levels nested within it, and each subsequently changes the conditions of activity below it.

7. From closure to the regulation of reopening

At sufficiently developed levels, the deepest form of closure is no longer a structure that merely resists change. It is a structure whose identity consists in organising the processes by which it can change while continuing to exist.

closures that host reopening → closures maintained by reopening → closures that regulate reopening → closures capable of modifying the rules of their own reopening

This final transition provides the conceptual bridge from biological evolution toward the evolution of intelligence. In VGF terms, intelligence can then be approached not as the mere accumulation of more stable structure, but as the emergence of closures increasingly capable of regulating, directing, and eventually reopening the rules governing their own possibility spaces.

Central VGF proposition. Evolution can be analysed as a recursively self-producing hierarchy in which lower-level reopening generates higher-order closure, higher-order closure becomes the host for further reopening, and that reopening in turn modifies the host. Stability and generativity are therefore not opposing endpoints of the process. They are mutually producing aspects of the same nested evolutionary architecture.

Brian Capleton