UNNS Projection Protocols

From Recursive Substrate to Conceptual Physical Analogues
Interpretation Note (2025)

This page does not present a physical theory or predictive model. It documents projection protocols: structured ways in which recursive UNNS constructs may be mapped onto familiar mathematical and physical formalisms for exploratory and diagnostic purposes.

These mappings are non-unique, non-empirical, and non-committal. Their role is to investigate which invariants survive projection from the recursive substrate — not to assert physical reality.

Theoretical Journey Overview

The UNNS Projection Protocols document structured mappings from recursive substrate to mathematical formalisms. This journey progresses through eleven interconnected protocols, each exploring how recursive invariants project onto familiar structures spanning algebraic, variational, superposition, and geometric closure regimes.

Algebraic Projection Layer

Vector & Tensor Protocols

Maps recursive sequences into vector spaces as exploratory coordinate systems.

V(N) = Σ aₖeₖ → T = V₁ ⊗ V₂ ⊗ ... ⊗ Vᵣ

Significance

  • Provides linear algebraic structure to recursion
  • Enables operator composition and superposition
  • Creates bridge to differential geometry
  • Introduces recursion curvature from non-commuting operators

Exploratory Domains

Quantum Computing Signal Processing Network Theory Machine Learning

Variational Projection Layer

Gauge, Lagrangian & Hamiltonian

Explores action principles and conservation laws as organizational constraints.

S[A] = ∫[½⟨F,F⟩ + V(A)]dμ → δS = 0

Structural Features

  • Operators as gauge connections on recursion mesh
  • Curvature from operator commutators
  • Variational principles for recursive evolution
  • Phase space and symplectic structure

Conceptual Analogues

Maxwell Theory Yang-Mills Fields Classical Mechanics Thermodynamics

Superposition Projection Layer

Quantization & Path Integrals

Explores recursion through Hilbert-space formalism and sum-over-histories structure.

|Ψ⟩ = Σ cₙ|n⟩, Z = Σ_γ exp(iS[γ])

Hilbert-Space Structures

  • Zero nest as vacuum state |0⟩
  • Creation/annihilation operators for coefficients
  • Recursive trajectories as quantum paths
  • Wilson loops measuring recursion curvature

Exploratory Domains

Quantum Algorithms Quantum Field Theory Condensed Matter Quantum Gravity

Geometric Closure Projection Layer

Gauge-Gravity, Holography & Black Holes

Investigates emergent geometry from recursive substrate with holographic encoding metaphors.

Boundary Recursion ⟺ Bulk Geometry

Geometric Structures

  • Discrete curvature analogues from gauge holonomies
  • Holographic encoding patterns: I(Bulk) ≤ S(Boundary)
  • Collapse structures as black hole metaphors
  • Exploring information-theoretic repair mechanisms

Conceptual Domains

Dark Matter Dark Energy Quantum Cosmology Information Theory

Why This Matters

The UNNS Projection Protocols represent a methodological contribution to exploring mathematical structures:

1. Discrete Substrate

Recursive structures provide computational tractability for exploring complex dynamics without requiring continuous field assumptions.

2. Multi-Projection Framework

A single substrate capable of hosting multiple theoretical structures enables systematic comparison of how different formalisms emerge from shared foundations.

3. Invariant Discovery

Projection protocols systematically identify which structural properties survive mapping from recursive substrate to familiar mathematical regimes.

4. Constructive Methodology

Every structure arises through explicit recursive construction, making exploration inherently algorithmic and reproducible.

5. Conceptual Mapping Tool

Provides a systematic framework for investigating how familiar physical and mathematical concepts might relate to discrete recursive processes.