What question did this study set out to answer?

This research aims to establish a positive mass gap for Yang-Mills theory and explore emergent gravitational properties stemming from quantum phenomena.

April 25, 2026Open Access

Yang–Mills Mass Gap, Emergent Newton Constant, and Black-Hole Information from Void Circuit Closure (0≡∞) Main manuscript PRE PRINT

Key Points

This research aims to establish a positive mass gap for Yang-Mills theory and explore emergent gravitational properties stemming from quantum phenomena.
Utilized the Wilson lattice and Osterwalder–Schrader reconstruction for quantum field theoretical proof.
Applied Tomita–Takesaki modular theory to derive the mass gap and emergent Newton constant.
Validated the emergence of black-hole information theorems from Void-boundary ergodic invariance.
Proved a positive mass gap of m_YM ≥ 4 a_OS λ* > 0 for Yang-Mills theory on R^4.
Established an emergent Newton constant G_eff = π²/16, demonstrating its independence from other parameters.
Identified twelve black-hole information theorems, suggesting significant implications for quantum gravity.

Abstract

Main Manuscript (187 pp) — Submitted to Annals of Physics. Supplementary Technical Archive — "SupplementaryTechnicalArchiveFullTreatise" (714 pp) DOI 10. 5281/zenodo. 19708570. Expanded proof architecture and technical background. Available on request. We prove a positive mass gap for pure Yang–Mills on R⁴ for everycompact simple gauge group G, via the chain Wilson lattice → Osterwalder–Schrader reconstruction → Tomita–Takesaki modular theory → void circuit closure (0 ≡ ∞). No assumption enters beyond the Wilson action and compact simple G. Bakry–Émery curvature κBE = h∨/ (4g²), Holley–Stroock perturbation, Mosco convergence, and OS reconstruction yield a Wightman QFT withmYM ≥ 4 aOS λ* > 0. Void-boundary ergodic invariance (VEI) forcesλᵥoid = π and mYM = π·aOS; Petz saturation (free-fermion sharpMLSI at k = h∨) locks g² = h∨/π, aOS = 1/ (2π), mYM = 1/2. The same VEI yields a tilt-invariant emergent Newton constantGₑff = π²/16 (pure number, independent of the tilt B, of the collar, and of the gauge group G) ; the product law k (R) k (1/R) = (h∨) ² closescalibration, yielding g² (R) → 0. Einstein's equations emerge fromthe entanglement-package identity. The 0 ≡ ∞ closure yields twelveblack-hole information theorems (Page curve, information loss, AMPS/monogamy, firewalls, cloning, complementarity, censorship/no-mining, trans-Planckian, stable remnant exclusion, Bekensteinbound, no-hiding, third law/unattainability of extremality) ;gravitationally induced entanglement (GIE) follows from Gₑff > 0and the entanglement-package identity.

Yang–Mills Mass Gap, Emergent Newton Constant, and Black-Hole Information from Void Circuit Closure (0≡∞) Main manuscript PRE PRINT

Key Points

Abstract

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