NS-L6 Appendix A — Formal Proofs (Public Extract)

Status

Informative Annex
(Not Normative)

This appendix provides selected formal definitions and proofs necessary for understanding the logical foundations of NS-L6. Full internal derivations are maintained in a private research document.

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1. Non-invertibility (Axiom B1)

Let fᵢ : Lᵢ → Lᵢ₊₁ denote the transformation between layers.

Axiom:

fᵢ is not invertible
¬∃ g : Lᵢ₊₁ → Lᵢ

Implication: Higher layers cannot reconstruct lower-layer states.

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2. Observability and Responsibility

Responsibility requires:

Obs_H(Lᵢ) ≠ ∅
Ctrl_H(Lᵢ) ≠ ∅

For layers below L5:

Obs_H(Lᵢ) = ∅
Ctrl_H(Lᵢ) = ∅

Thus:

Resp_H(Lᵢ) = ∅    for i < 5

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3. Minimal Definition of State (Public)

A minimal public definition (subset of internal theory):

σ : I → S

A state σ is a function of an index I (time, cycle, or step).

This definition is sufficient for understanding:

• layer structure,
• non-invertibility,
• responsibility allocation.

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END OF PUBLIC APPENDIX A.