Invariant Registration Closure in a Conjugate Three-Dimensional Carrier: Complexification, Triadic Closure, SU(3) Automorphisms, and the Boundary to Physical Confinement
A foundational closure note deriving a conjugate complex three-dimensional carrier, the unique alternating triadic closure form, and the SU(3) automorphism group that preserves Hermitian magnitude and triadic closure, while isolating the closure-to-bounded-boundary bridge as an open physical theorem target.
Scope
Exact mathematics includes the odd-dimensional complex-structure obstruction, conjugate doubling to complex dimension three under a fixed paired-sector identification, uniqueness and normalized bounds of alternating triadic closure, and Aut_C(W,h,Omega) ≅ SU(3). Singlet persistence and adjoint boundary-current cancellation are conditional on equivariance and representation assumptions. The paper does not identify the carrier uniquely with QCD color or derive local gauge dynamics, bounded spatial extent, confinement, asymptotic freedom, or a Yang-Mills mass gap.
Relation to other papers
- Builds on Canonical Foundations of Registration Theory
- Builds on Structural Trinity Conjecture (v2.0)
- Builds on Trinity Symmetry / ACRF-4 Registration Quotient Correspondence
- Builds on Candidate Relativistic Brokerage Law
- Builds on First-Principles Brokerage Generator Theorem
- Builds on Minimal Robust Relational Closure
- Builds on Rank-Three Invariant Relational Geometry
- Builds on Finite-Amplitude Permutation-Quotient Dynamics
- Builds on Persistent Registration and Relative Metric
- Extended by Particle–Field Trinity Conjugacy
- Extended by Closure-Induced Complex Structure
Relevant research claims
- Exact TheoremOdd-Dimensional Complex-Structure Obstruction
- Conditional ResultConjugate Doubling Gives a Complex Three-Space
- Exact TheoremUniqueness of Triadic Alternating Closure in Complex Dimension Three
- Exact TheoremNormalized Triadic Closure Index Bounds
- Exact TheoremSU(3) Automorphism Theorem for Hermitian Triadic Closure
- Conditional ResultPersistent Singlet Closure Under Equivariant Succession
- Conditional ResultSinglet Cancellation of Adjoint Boundary-Current Expectation
- ConjectureRegistration Closure–Boundary Conjecture
- ConjectureRadiation as a Propagating Field-Conjugate Regime
Keywords
- Registration Theory
- Trinity
- invariant registration closure
- conjugate registration
- three-dimensional relational carrier
- complexification
- complex structure
- C3
- Hermitian form
- alternating three-form
- triadic closure
- SU(3)
- singlet closure
- physical objecthood
- boundary current
- confinement
- ACRF-4