From Antireturn Recurrence to Pauli Exclusion in EAS: The Electron Spin–Statistics Interface

Abstract

This paper is archived as a speculative research work. This paper establishes the Pauli-exclusion consequence of the electron-like bounded-support sector of Entanglement–Algebraic Spacetime (EAS) at the conventional relativistic quantum interface. The construction does not introduce spin, fermionic exchange, canonical anticommutation relations, Fock space, or Hilbert-space antisymmetry as primitive Scalar-Field (SF) ontology. The argument begins from an already-established native result. Exhaustive phase-resolved route analysis of the electron-like bounded support selects exactly one physical antireturn recurrence class, =ABA,BAB/reflection, whose nontrivial recurrence element satisfies r:Φ -Φ, r^2=e. The resulting native recurrence parity is represented faithfully by the central element r -I_2∈ Z(SU(2)_ spin), which supplies the standard physical spin- 12 carrier , J^2= 34 I_2, m_s=± 12. The same physical-spin representation embeds in the conventional massive Dirac carrier , ≤ft( 12,0) ≤ft(0, 12). A separate theorem fixes the electric-charge branch. For a charge-eligible handed bounded support, _H=H_B(1,1,1), Q_b(B)=H_B=±1. Consequently the zero-sum projection of the physical single-support charge report vanishes identically: _H=0. Thus Pauli structure cannot be obtained as a nonzero zero-sum remainder after charge extraction. Charge and spin instead arise through separately typed branches of the same electron-like bounded organization: handedness supplies the charge class, whereas antireturn recurrence supplies the physical-spin representation. Here PEP denotes the Pauli-exclusion theorem stack developed in this paper. The PEP-native SF transition/report algebra is shown below to have exact functional read locality, write locality, remote-candidate independence, no hidden shared resource, explicit pair-local scalar-change provenance, and factorization across independent transition scopes. On Pauli's 1940 relativistically invariant free-particle domain with the positive-energy requirement, the established spin- 12 Dirac sector has Fermi–Dirac statistics; the later L\"uders–Zumino theorem supplies the corresponding interacting-field extension. The Fermi–Dirac classification gives the antisymmetric N-electron state space ^N . For duplicate complete one-electron states, h h=0, which is the Pauli exclusion principle. The result is therefore Pauli's standard half-integral-spin statistics theorem applied to an established EAS antecedent, with a separately stated interacting-field extension, not a theorem conditional on an unproved EAS locality selector. It neither identifies native antireturn parity with particle exchange nor derives quantum-field formalism as primitive SF ontology. Instead it shows that the already-established EAS electron structure supplies the spin- 12 Dirac antecedent and the PEP-relevant native locality properties. The remaining Hilbert-space, relativistic-covariance, spectrum/vacuum, field-domain, and locality structures belong to the conventional theorem domain at the quantum interface; they are not unresolved EAS locality mechanisms.