UNNS Physics Protocols

From Recursive Vectors to Black Holes

The UNNS Physics Journey

The UNNS Physics Protocols establish a comprehensive framework that bridges recursive mathematics with fundamental physics. This journey takes us from basic vector spaces through gauge theory, quantum mechanics, and ultimately to models of gravity and black holes.

Stage 1: Foundations

Vector Protocol → Tensor Protocol

Establish linear and multilinear structures for recursive nests

Stage 2: Classical

Gauge Protocol → Lagrangian → Hamiltonian

Develop action principles and energy conservation

Stage 3: Quantum

Quantization → Path Integral → Gauge Path Integral

Introduce quantum operators and sum-over-histories

Stage 4: Gravity

Gauge-Gravity → Holographic → Black Holes

Emergent geometry from recursive substrates

Vector & Tensor Protocols

The UNNS Vector Protocol (UVP)

The Vector Protocol establishes the linear algebraic foundation by mapping nests into vector spaces.

Key Concept: Nest Vectorization
V(N) = Σ(k≥0) a_k e_k ∈ V
Maps recursive sequences to infinite-dimensional vectors with basis {e_k}.

Vector Visualization

The UNNS Tensor Protocol (UTP)

Extends vectors to tensors for multilinear recursive interactions.

Key Innovation: Tensor products of nests enable interaction modeling
T(N₁,...,Nᵣ) = V(N₁) ⊗ ... ⊗ V(Nᵣ)

The tensor protocol introduces:

  • • Multilinear operator actions
  • • Contraction operations (trace analogs)
  • • Recursion curvature tensors from non-commuting operators

Classical Field Theory Protocols

Gauge Protocol

Treats UNNS operators as connections on a recursion mesh.

Connection: A : V → End(V)
Curvature: F(v,w) = [A(v), A(w)] - A([v,w])

Gauge Field Visualization

Lagrangian Protocol

Defines action principles for recursive dynamics.

S[A] = ∫ [½⟨F,F⟩ + V(A)] dμ

Variational principle yields recursive Euler-Lagrange equations.

Hamiltonian Protocol

Introduces phase space and energy conservation.

Phase Space: P = {(aᵢ, pᵢ) | i ≥ 0}
Hamilton's Equations:
ȧᵢ = ∂H/∂pᵢ, ṗᵢ = -∂H/∂aᵢ

Quantum Protocols

Quantization Protocol

Elevates nests to quantum states in Hilbert space.

Vacuum State: |0⟩ = Zero Nest
Creation/Annihilation: â†ᵢ, âᵢ operators
Commutation: [âᵢ, â†ⱼ] = δᵢⱼ

Quantum State Evolution

Path Integral Protocol

Sum-over-histories formulation for recursive trajectories.

Z = Σ_γ exp(iS[γ])

Each recursive path γ contributes with phase weight from action S[γ].

Gauge Path Integral

Combines gauge theory with path integrals, introducing Wilson loops.

Wilson Loop: ⟨W(C)⟩ = (1/Z) ∫ Daₑ Tr(U(C)) exp(iS_G)
Measures recursion curvature around closed paths.

Gravity & Holographic Protocols

Gauge-Gravity Correspondence

Recursion coefficients on edges define discrete geometry.

Key Principle: Boundary recursion ⟺ Bulk geometry
Discrete Ricci curvature emerges from gauge holonomies.

Emergent Geometry

Holographic Principle

All bulk information is encoded in boundary UNNS sequences.

I(Bulk) ≤ S(Boundary)

This UNNS analog of AdS/CFT suggests reality emerges from boundary recursion data.

Black Hole Model

Recursion collapse generates horizons with entropic boundaries.

Horizon Condition: Recursion coefficients stabilize to fixed point
Entropy Law: S = α · #{boundary nests}
Information Paradox: Resolved via repair operators

Black Hole Formation

References & Resources

Complete documentation for the UNNS Physics Protocols:

Foundation Protocols

📄 The UNNS Vector Protocol (UVP) - Linear structures for recursive nests 📄 The UNNS Tensor Protocol (UTP) - Multilinear extensions and curvature

Classical Field Theory

📄 The UNNS Gauge Protocol (UGP) - Connections and field strengths 📄 The UNNS Lagrangian Protocol (ULP) - Action principles 📄 The UNNS Hamiltonian Protocol (UHP) - Phase space and conservation

Quantum Theory

📄 The UNNS Quantization Protocol (UQP) - Operators and Hilbert space 📄 The UNNS Path Integral Protocol (UPIP) - Sum-over-histories 📄 The UNNS Gauge Path Integral (UGPI) - Wilson loops and holonomy

Gravity & Holography

📄 The UNNS Gauge-Gravity Correspondence (UGGC) - Emergent geometry 📄 The UNNS Holographic Principle (UHP) - Boundary/bulk duality 📄 The UNNS Black Hole Model (UBHM) - Recursion collapse and horizons

These protocols establish UNNS as a comprehensive mathematical substrate capable of modeling phenomena from quantum mechanics to general relativity through the lens of recursive number theory.