What question did this study set out to answer?

This research aims to demonstrate how a single 19-bit polynomial can unify multiple physical concepts such as gravity and quantum entanglement.

June 19, 2026Open Access

The GTE Polynomial as Unified Field Theory: One 19-Bit Description for Spatial Dynamics, Gauge Coupling, Gravity, Entanglement, and Baryon Number

Key Points

This research aims to demonstrate how a single 19-bit polynomial can unify multiple physical concepts such as gravity and quantum entanglement.
Developed a polynomial p(L,C,R) that describes various fundamental physical structures.
Analyzed five key elements including gauge coupling, quantum entanglement, and vacuum stability using the polynomial.
Certified foundational results through machine verification in Lean 4 with zero errors.
The polynomial effectively generates gravitational coupling and quantum entanglement, showing values like S = 2.4459 and a vacuum stability fixed point.
It provides a unified description for baryon number as topological charge and SM fermion/boson distinctions without additional specification.
The cosmological constant's value was connected to the halting-weighted MDL residual, yielding = 0.6899.

Abstract

A single polynomial p (L, C, R) = C + R - CR - LCR 7, requiring KCMCA = 19 bits to specify, simultaneously generates five fundamental physical structures: Rule 110 Turing universality (), Standard Model gauge vertex conservation via winding arithmetic (), gravitational coupling via the Poisson equation ² = Gₑff\, p (wₓ, wᵧ, wᵦ) (), quantum entanglement with CHSH parameter S = 2. 4459 (86. 5\% of the Tsirelson bound, ), and the Born rule from Page-Wootters analysis (). The additional specification cost for each role beyond the first is exactly zero. From the same 19-bit description applied to the three-tape architecture (SpivackThreeTapeCMCA): (i) color confinement as an MDL theorem (description-length gap K 3. 17 bits) ; (ii) Nc = 3 from the tape count alone; (iii) baryon number B = 13ⱼ q (wⱼ) as a topological charge; (iv) SM fermion/boson split from the non-primitive roots of ; and (v) lepton-W universality from shared winding sectors. The PMDL variational principle yields gravity as local MDL minimization; the halting-weighted MDL residual from PSC undecidability gives the cosmological constant, whose census-capacity evaluation is the zero-parameter value = 0. 6899 (+0. 18 from Planck 2018). Gravity and the floor are the record and measure sectors of one Gaussian generating functional ZJ. The vacuum w = 0 is the unique fixed point of p (x, x, x) x 7, establishing vacuum stability from first principles. All foundational results are machine-certified in Lean 4 with zero sorry.

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