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

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 F_3 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 A_ref=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 N_min=2^((R-1)(T-1)) and bond dimension D_R=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 L_M=2n, L_Y=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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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-30
DOI
https://doi.org/10.5281/zenodo.21085532
Primary Topic
Black Holes and Theoretical Physics
Type
preprint
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preprint

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

David Elliman
Zenodo (CERN European Organization for Nuclear Research)
Black Holes and Theoretical Physics
preprint

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

David Elliman
preprint en

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 F_3 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 A_ref=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 N_min=2^((R-1)(T-1)) and bond dimension D_R=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 L_M=2n, L_Y=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.

Zenodo (CERN European Organization for Nuclear Research)
Catholic University of Mozambique (MZ)
Black Holes and Theoretical Physics
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