Conditional Independence as Fairness

The No-Priors Theorem and the Inevitability of the Markovian Protocol

Further to the previous post

The Control Centroid and the Lunarpunk

Created with Deepseek.

The Anchor and the Liminal Tide: A Defense Forged in Harsh Mathematics

The fundamental asymmetry between the male steward and the female lunarpunk creates a mathematical battlefield where traditional notions of trust and cooperation become lethal vulnerabilities. The steward, bound by his duty to prove, operates in a transparent prison where his freedom asymptotically approaches zero:

Steward_Freedom = Ability_to_Prove / Requirement_for_Transparency → 0

Meanwhile, the lunarpunk follows what we might call the liminal creative gradient—a vector field that pulls her toward optimal self-interest through dark forests and cryptographic enclaves. Her trajectory follows:

dX_lunarpunk/dt = -∇V_creative(X) + η_opportunistic(t)

Where V_creative represents the potential landscape of innovation opportunities, and η_opportunistic(t) represents stochastic alliances and partnerships formed along her path.

The Control Centroid’s Inevitable Pull

The system’s teleoplexic nature means both actors are subject to Bayesian convergence toward the control centroid:

Control_Centroid = [Privacy_Asymmetry→0.95, Regulatory_Treatment→0.90, Funding_Sovereignty→0.10, Evidence_Integration→0.05, Platform_Capturability→0.85]

The Bayesian updating process ensures rational actors converge:

P(Control|Signals) ∝ P(Signals|System_Dynamics) × P(System_Dynamics)

Where P(System_Dynamics) approaches 1 because we observe the institutional physics directly. The steward’s position makes him inherently more vulnerable to this pull due to his mandatory transparency, while the lunarpunk’s ability to hide gives her temporary evasion capabilities.

The Markov Boundary Defense

The steward’s only mathematically viable defense is to instantiate rigorous Markov boundaries without assuming any priors about the lunarpunk’s intentions or alignment. This means enforcing:

S_steward ⊥ E_environment | B_boundary

And critically:

S_steward ⊥ S_lunarpunk | B_transactional

The boundary conditions must be absolute and unforgiving. For any interaction, the steward’s defense requires:

Zero Priors Assumption:

P(Alignment) = 0.5 (maximum uncertainty)P(Trust) = 0 (no assumed trust)

Transactional Proof Requirements:
For any data request or interaction, the lunarpunk must provide:

ZK_Proof(Statement) ∧ DLWE_Verification(Proof) ∧ Boundary_Consistency_Check

Information-Theoretic Security:
The mutual information between steward internal states and lunarpunk enclaves must satisfy:

I(S_steward; S_lunarpunk) ≤ ε for arbitrarily small ε

The Hamiltonian of Interaction

We can model their interaction using Hamiltonian mechanics:

H_total = H_steward + H_lunarpunk + H_interaction

Where the interaction Hamiltonian must be minimized through boundary enforcement:

H_interaction = α·ZK_Verification + β·Boundary_Maintenance + γ·Proof_Generation

The steward’s strategy is to make H_interaction as costly and formalized as possible, ensuring that:

∂H_interaction/∂t → 0 (stationary, predictable interaction protocol)

While the lunarpunk’s natural tendency is toward:

dH_lunarpunk/dt = -∇V_opportunity(X) (following gradients of creative opportunity)

The Necessity of Harshness

The mathematical inevitability of this harsh stance emerges from several irreducible facts:

Asymmetric Vulnerability:
The steward’s position in the control system gives him:

Vulnerability_steward = f(Transparency, Accountability, Physical_Constraints)

While the lunarpunk operates with:
Vulnerability_lunarpunk = f(Privacy, Mobility, Digital_Constraints)

The gradient is stark:

∇Vulnerability_steward ≫ ∇Vulnerability_lunarpunk

No Priors Theorem:
Given the lunarpunk’s utility function:
And the steward’s:

U_steward = α·Safety + β·Compliance + γ·Accountability

Their inner product reveals fundamental misalignment:

⟨U_lunarpunk | U_steward⟩ ≈ 0

Liminal Path Integral:
The lunarpunk’s trajectory follows a path integral through opportunity space:

Path_Lunarpunk = ∫[Creative_Opportunities + Self_Interest_Alliances] dt

This path is inherently unpredictable and self-optimizing, making prior assumptions mathematically invalid.

The Fairness of the Markovian Playing Field

Despite its apparent harshness, this approach creates the only truly fair interaction framework because:

Mathematical Impartiality:
The boundary conditions apply equally to all interactions:

Boundary_Rules = {ZK_Proofs, DLWE_Verification, Atomic_Transactions}

No special exceptions, no preferential treatment.

Transparent Rules:
The interaction protocol is publicly verifiable:

Protocol = {Request→Proof_Spec→ZK_Generation→Verification→Response}

Each step is cryptographically enforced.

Symmetric Accountability:
While their positions are asymmetric, the rules are symmetric:
Accountability_steward = Verifiable_Proofs(Operations)
Accountability_lunarpunk = Verifiable_Proofs(Claims)

The Inevitable Conclusion

The steward’s defense reduces to maintaining:

S_steward ⊥ E_hostile | B_Markov

Where the hostile environment includes not just the control system but also the lunarpunk’s potentially misaligned utility function. The harshness of this stance is not a choice but a mathematical necessity emerging from:

1. The fundamental asymmetry of their positions

2. The zero-priors requirement for security

3. The lunarpunk’s liminal, self-optimizing nature

4. The control centroid’s relentless pull

The only way to create a level playing field in this fundamentally uneven landscape is to make the rules so mathematically rigorous, so boundary-enforced, and so prior-free that both parties can interact without either being able to exploit the other’s inherent vulnerabilities.

This isn’t merely a security protocol—it’s the mathematical instantiation of fairness in a system designed to be unfair. The steward’s harsh Markov boundaries represent not distrust of the lunarpunk specifically, but respect for the mathematical reality that in a teleoplexic battlefield, only rigorously enforced conditional independence provides any hope of maintaining sovereign operation.

The future belongs to those who understand that in asymmetric systems, the only fair defense is one that acknowledges and formalizes the harshness of the underlying mathematics.

Until next time, TTFN.