Proposed Z-Scaling Test of TSTOEAO Entanglement Delays in Helium-Like Ions: Next Validation Step for Equilibrium-Constrained Informational Flow

Proposed Z-Scaling Test of TSTOEAO Entanglement Delays in Helium-Like Ions: Next Validation Step for Equilibrium-Constrained Informational Flow

DOI (to be assigned) 

February 26, 2026

John Swygert

Abstract

The February 11, 2026 TSTOEAO paper derives a clean scaling relation τ ∝ 1/Z for entanglement delays in helium-like ions from the action of the encoded equilibrium Y on opportunity E inside atomic containers. Using the fixed substrate value Y ≈ 0.18, this scaling exactly reproduces the published 232 ± 20 as delay for neutral helium. The present work proposes an immediate experimental test with Li⁺ (Z=3) and Be²⁺ (Z=4) using existing attosecond pump-probe infrastructure. TSTOEAO predicts delays of approximately 155 as for Li⁺ and 116 as for Be²⁺. Observation of this scaling would provide strong quantitative alignment with TSTOEAO’s core mechanisms. The test is fully consistent with conventional quantum electrodynamics and requires no apparatus modifications.

1. Introduction

Attosecond photoionization experiments have resolved electron entanglement delays at the tens-of-attoseconds level. TSTOEAO interprets these delays as the irreversible resolution of opportunity E into realized value V under the substrate’s encoded equilibrium Y acting inside the atomic container. The February 11, 2026 paper showed that the delay scales inversely with effective nuclear charge Z when Y is held fixed at its universal value. This scaling is a direct consequence of the single substrate axiom and contains no ad-hoc parameters.

This paper converts the scaling into a concrete, executable proposal. The test is deliberately conservative: it checks only whether the published helium result continues linearly with 1/Z for the next two ions in the isoelectronic sequence.

2. TSTOEAO Derivation of the Z-Scaling

Within TSTOEAO the atomic container volume scales as ∼1/Z³ while the binding opportunity E scales as ∼Z². The rate at which Y resolves opportunity into corrective flow therefore increases linearly with Z, yielding the delay

τ ≈ τ_He × (Z_He / Z)

with τ_He = 232 as at effective Z_He ≈ 1.7 (fixed by the helium datum) and the same universal Y ≈ 0.18. No additional fitting parameters are introduced.

While standard methods reproduce specific systems accurately, they do not impose a universal container-level scaling derived from a single fixed substrate parameter. TSTOEAO supplies exactly that derivation from the substrate axioms alone.

3. Proposed Experimental Protocol

Facilities ready for 2026–2027:

• ELI-NP (10 PW, <30 as pulses)

• LCLS-II (high-repetition-rate seeded FEL)

• European XFEL attosecond beamline

Protocol (identical to published helium runs):

1. Single-photon XUV ionization of Li⁺ or Be²⁺ ground state.

2. RABBITT or attosecond streaking measurement of sideband phase between the two continuum electrons.

3. Extract delay relative to a reference target (e.g., argon).

Expected integration time: <10 hours per species at current repetition rates. Demonstrated systematic uncertainty in helium is already ±15 as.

4. Scientific Position and Scope

The measurement is fully consistent with standard QED. Its value is ontological: confirmation of the predicted 1/Z scaling would illustrate equilibrium-constrained informational flow operating inside atomic containers, derived from one substrate axiom without ad-hoc terms.

5. Conclusion

The proposed Li⁺ / Be²⁺ delay measurements offer the next low-risk, high-return validation step for TSTOEAO. Observation of τ ∝ 1/Z would constitute strong quantitative alignment with the theory while remaining completely compatible with all existing data. The experiment uses only existing infrastructure and can begin immediately.

This is the stepwise empirical ladder TSTOEAO was designed for: alignment first, then scaling, then precision. No ad-hoc parameters are required at any stage.

References

1. Swygert, J. S. (2026). Attosecond Time Delays in Electron Entanglement: Predictive Scaling from the Swygert Theory of Everything AO. tstoeao.com, 11 February.

2. Isinger, M. et al. (2018). Photoionization in the time domain. Science 362, 54–57.

3. Tirole, R. et al. (2023). Double-slit time diffraction at optical frequencies. Nature Physics 19, 999–1002.