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This research investigates the mechanism of colour confinement using a record-grammar approach within a finite quantum error correction (QEC) substrate.

July 2, 2026Open Access

Colour confinement as finite record geometry: Closed-cell triality, Wilson strings, tensor-network entropy, and the baryon Y-junction in a bond-bipyramid QEC substrate

Key Points

This research investigates the mechanism of colour confinement using a record-grammar approach within a finite quantum error correction (QEC) substrate.
Developed a kinematic and dynamical model for colour confinement using exact formulations and leading strong coupling principles.
Analyzed bond-centred bipyramid structures and calculated string tensions using the Creutz ratio and other metrics.
Extended isotropy analysis to include off-axis directions through rigorous mathematical constructs.
Identified that fundamental quarks lack gauge-invariant records while mesons and baryons exhibit unique triality records.
Determined a string tension of sigma=-log(beta/18) indicative of effective confinement properties.
Established reproducible finite values for all outcomes, distinguishing them from continuum Quantum Chromodynamics (QCD).

Abstract

Colour confinement as finite record geometry: Closed-cell triality, Wilson strings, tensor-network entropy, and the baryon Y-junction in a bond-bipyramid QEC substrate. A finite, executable account of colour confinement in the record-grammar formulation of the finite-QEC substrate, separating the kinematic and dynamical halves. Kinematic (exact): on a closed oriented colour cell the F₃ Gauss-law incidence map has image equal to the total-triality-zero subspace, so a lone fundamental quark has no gauge-invariant record while a q-qbar meson and a qqq-epsilon baryon do; the proton colour sector is the unique minimal three-fundamental triality-zero record. Dynamical (leading strong coupling): on the licensed bond-centred bipyramid bulk, edge-loop Wilson records have Aᵣef=4RT and P=4 (R+T) -2, and the Creutz ratio isolates a string tension sigma=-log (beta/18). The exact fixed-strip transfer matrix gives Nₘin=2^ ( (R-1) (T-1) ) and bond dimension DR=2^ (R-1), placing the Wilson ledger in a two-dimensional tensor-network class (tractable at fixed width, not fixed-bond-dimension) and resolving the foundation paper's open tractability question. A finite isotropy gate shows zero cubic-axis spread to numerical precision. The same bulk graph supports a gauge-invariant qqq-epsilon baryon Y-string whose junction is the SU (3) epsilon tensor and lands on the graph Steiner point, sharing the meson string tension; matched lengths give LM=2n, LY=3n. All results are finite and reproducible by short scripts; none is continuum QCD (no continuum string tension, mass gap, or proton mass is claimed). Sequel to the executable record-grammar foundation paper (DOI 10. 5281/zenodo. 21034325). This record is part of the finite-QEC substrate / It-from-Bit publication refresh. 2026-06-30 canon refresh: Version 2 adds the primitive off-axis isotropy gate: rhombi from all three primitive triangular-sheet directions (1, 0), (0, 1), (1, -1) give the same leading-order string tension (Creutz spread ~3e-14), extending the cubic-axis isotropy result to primitive off-axis directions. Scope unchanged: finite leading strong coupling, not continuum SO (3), nonprimitive graph directions, off-axis roughening entropy, weak-coupling scaling, or physical Lorentz-violation bounds.

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