Scale-Invariant Consensus¶

Core Theorem (Informal)¶

The hypervisor switching law is a universal consensus mechanism that operates identically at every scale of organization:

P(leader = i) = exp(β · f_i) / Σⱼ exp(β · f_j)

The only things that change between scales are: 1. What the agents are (dimensions, neurons, nodes, people) 2. What f_i measures (activation, fitness, reputation, competence) 3. What β is (neural temperature, network responsiveness, social inertia)

Mathematical Properties¶

Convergence¶

The gossip protocol guarantees that all nodes eventually share the same ledger state. From identical ledger state, all nodes compute identical softmax output. Therefore: consensus is a mathematical consequence of data propagation, not a separate protocol.

No voting. No rounds. No quorum. Just math on shared data.

Hysteresis (Stability)¶

The current Agent Zero has inertia (hysteresis parameter h):

f_current += h

This prevents thrashing — the leader does not switch on every minor fluctuation. The same mechanism prevents consciousness from switching hypervisor dimensions on every minor stimulus. Stability is built into the equation.

Threshold (Minimum Competence)¶

Nodes below a threshold θ are excluded from the softmax entirely:

If f_i < θ, then P(leader = i) = 0

This prevents incompetent or malicious nodes from ever becoming Agent Zero, regardless of how few competitors exist. In consciousness: this is why a fully traumatized dimension (f_i ≈ 0) never becomes hypervisor.

Will Override (Emergency)¶

A meta-level override exists for crisis situations:

If emergency(t) = true, then leader = argmax(crisis_competence_i)

In consciousness: the fight-or-flight override that forces Kinesthetic to hypervisor status regardless of what was running. In the network: a protocol-level emergency that forces the most crisis-capable node to lead.

Connection to Least Action¶

The softmax leader election minimizes total system energy: - The most optimized node requires the least energy to lead - Switching only when a clearly better leader emerges (hysteresis) minimizes switching cost - The system naturally settles into the lowest-energy configuration

This IS the principle of least action applied to distributed consensus.

S = ∫ (E_switching + E_leadership - V_coordination) dt → minimize

Source: @B_Niko, session v7, 2026-03-10