This document proposes a core model for anarchist systems — a hub of invariant constraints from which all voluntary societies (spokes) may be built.

This series aims to operationalize the definition of Anarchism.

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When defining a stateless system structurally, the first question is: what qualifies as one?

Not the common meaning.
Not emotional ideologies.
Not economic systems.
Not political preference.

But the structural essence of what a stateless system is.

That is where this series begins.

At zero, and building upward.

The purpose of this article is to derive the structural base — the invariant — required for any system to qualify as stateless.

The method is simple:

Minimal premises.
Follow logical necessity.

No normative claims.
No ideological references.
No moral assertions.

Structure.
Nothing more.

Key Terms

The following definitions serve as the structural base of the theorem.

Stateless System
A coordination system in which no agent or rule-structure possesses structural authority over others.

Structural authority refers to the capacity, embedded in the rules of the system, to impose binding outcomes on an agent without that agent’s agreement.

“Unilateral” in this context does not refer to the number of actors exercising authority. It refers to the absence of the bound party’s agreement. A rule binding dissenters is unilateral with respect to those dissenters, regardless of whether one person, many persons, or a rotating majority invokes it.

Agent
An entity capable of intentional action, entering or refusing agreement, and sustaining accountable continuity over time.
Agency in this context refers only to structural participation in coordination — not biological, metaphysical, or moral status.

Autonomy
An agent’s capacity to act without external imposition of binding obligation.

Ruler
Any agent or rule-structure possessing structural authority to impose binding outcomes on others without their agreement.

Order
Persistent coordination among agents over time.

The Multi-Agent Condition

At least two agents exist.
Agents interact.
Interaction creates the possibility of conflict.
Persistent coordination among agents requires mechanisms for resolving conflict.

No system of order can avoid this condition.

Any theory of stateless coordination must therefore answer the structural problem of conflict resolution among autonomous agents.

Resolution Mechanisms

Any conflict resolution mechanism must answer a single structural question:

Can one agent or rule-structure impose a binding outcome on another who does not agree?

All mechanisms reduce to one of two structural forms.

A. Binding Without Agreement

One party, or rule-structure, imposes a binding outcome on another who does not agree.
The bound party is obligated regardless of dissent.

B. Binding With Agreement

A binding outcome arises only when affected parties participate in its formation.
Participation is voluntary. Refusal results in non-participation, not obligation.

Clarification:

If a dissenting party is bound against their will, binding without agreement has occurred.

If a party retains the ability to refuse participation without being bound, binding with agreement has occurred.

Any binding outcome either obligates a dissenting party or it does not.
If it does, binding without agreement has occurred.
If it does not, binding depends on agreement.

There is no intermediate state: either dissenters are bound or they are not.

There is no third structural category.

This distinction precedes any moral framing.

Structural Consequences of Binding Without Agreement

If binding without agreement is permitted:

Authority asymmetry emerges.
A binding hierarchy is created.
The bound party no longer operates autonomously.

Structural authority resides in the rule permitting such binding, not in the identity of the actor applying it. Rotation of office, majority vote, or temporary delegation does not eliminate authority; it merely redistributes access to it.

A rule that binds dissenters without their agreement constitutes structural authority, even if no single agent permanently holds that authority.

Structural authority is itself a form of strategic advantage.

Strategic advantage creates asymmetric capability; those who possess access to the binding mechanism face structural pressure to use it or be displaced by others who will.

Restraint is not structurally enforced – it depends on discretion, which is itself an expression of authority.

Authority scope tends to expand.
Power concentration becomes self-reinforcing.

Therefore:
Binding without agreement produces rulers.

A ruler is not defined by title, scale, duration, or permanence — but by structural authority embedded in the rule-system to impose binding outcomes without agreement.

Incompatibility

If a system permits binding without agreement:

It contains structural authority.
Structural authority constitutes rulership.

It is not stateless.

If binding occurs without agreement:
Participation is not autonomous.

Persistent autonomous coordination and binding without agreement are structurally incompatible.

A system cannot simultaneously preserve autonomy and permit structural authority over dissent.

This remains true even in systems with rotating decision-makers or majority rule. If dissenters are bound without their agreement, the rule binding them functions as authority independent of their consent. The authority resides in the rule-form itself.

Stability Requirement

A coordination system must remain stable under recursion.

Stability in this context does not mean mere persistence. Hierarchical systems can persist.

Stability here refers specifically to the persistence of a stateless condition under repeated interaction.

If structural authority to bind without agreement exists:

The binding rule can be invoked repeatedly.
Repeated invocation produces persistent override capability.
Persistent override capability constitutes durable structural authority.

A stateless system permitting binding without agreement contains a mechanism capable of negating its own stateless classification.

Structural validity requires that classification remain invariant under iteration.

If binding without agreement is allowed, classification does not remain invariant.

Stability therefore structurally requires prohibition of binding without agreement.

Stress Testing the Structure

The derived structure must remain internally consistent under edge cases.

Self-Defense

Halting a prior imposed binding does not create new structural authority.
It removes an existing override.
Responsive force aimed at restoring autonomy does not constitute new binding without agreement.
It is not new binding because the prior binding already violated autonomy; responsive force merely removes that violation.

Delegation

Authority may be delegated through agreement.
Delegation must remain scope-bound and revocable.
If delegation becomes irrevocable, it becomes structural authority.
Irrevocable delegation recreates rulership.

Emergency Authority

Temporary structural authority remains authority regardless of duration.
Time does not alter structure.
If binding occurs without agreement, structural authority exists — whether exercised briefly, cyclically, or permanently.

Contract Enforcement

Enforcement consistent with prior agreement does not create new binding without agreement.
Enforcement beyond prior scope does.
Scope defines obligation.
Expansion beyond scope constitutes new binding.

Collective Decision-Making

Collective procedures do not alter structure.

If dissenters are bound without agreement, structural authority exists.
If participation is voluntary and exit remains available, autonomy remains intact.

The number of decision-makers does not change the structural condition.
Only agreement alters structure.

The structure remains internally consistent.

Emergence of the Invariant

To preserve autonomous coordination among multiple agents:

No rule-structure may embed the authority to bind agents without their agreement.
Binding must arise from agreement, not imposition.

Agreement thus emerges as the primitive mechanism preserving autonomy.

This prohibition is structurally necessary for stateless qualification.

The invariant:
Voluntary Order Without Rulers

Identification

The structural invariant derived above is commonly referred to as:
Anarchism.

The term follows the structure — not the reverse.

Classification Claim

This result is not a moral preference.
It is a necessary condition for any system qualifying as stateless.

If structural authority to bind without agreement exists, the system fails qualification.

If autonomous coordination persists without rulers, the system satisfies the invariant.

If structural authority to bind without agreement is permitted in any managed, temporary, rotating, collective, or conditional form, the system contains a ruler at the moment of its exercise.

A structure cannot both contain rulership and qualify as stateless.

Binding without agreement violates invariance.

Its prohibition is therefore necessary for a system to qualify as stateless.

What This Derivation Does Not Do

This derivation establishes only the minimal invariant required for stateless qualification.

It does not:

Define property norms.
Prescribe economic systems.
Specify governance mechanisms.
Resolve historical injustice.

Those are implementation-level problems.

Each implementation of stateless society must satisfy the invariant derived here in order to qualify as stateless.