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This research investigates the photon behavior arising from an emergent Truncated Cubic Honeycomb lattice, focusing on its topological characteristics and implications for quantum electrodynamics (QED).

June 23, 2026Open Access

Photons on the Emergent Truncated Cubic Honeycomb: Spontaneous Crystallisation, Line-Graph Topology, and Topological Protection of Vacuum QED

Key Points

This research investigates the photon behavior arising from an emergent Truncated Cubic Honeycomb lattice, focusing on its topological characteristics and implications for quantum electrodynamics (QED).
Derived photon physics through simulated annealing of degree-3 qubit networks to form the TCH substrate.
Computed the Chern number using the non-Abelian Fukui-Hatsugai-Suzuki method on the emergent lattice.
Conducted numerical joint matter-photon evolution on a minimal Q3 + bridge cluster to verify gauge invariance.
Identified a multi-band topology with a Chern number C=−1 for the lower seven-band complex (95% CI validated).
Demonstrated protection against vacuum birefringence through trivial global holonomies (8 × π/4 = 2π).
Confirmed gauge-invariant photon propagation in the infrared regime, linking emergent features to standard continuous QED.

Abstract

We derive the photon physics that emerges from the Truncated Cubic Honeycomb (TCH) substrate. Rather than being added by hand, the TCH arises spontaneously from unstruc- tured degree-3 qubit networks via simulated annealing, forming Q3 octahedra connected by gauge bridges. At the microscopic scale, massless photons are encoded natively as gauge fluctuations on the line graph of this emergent lattice (where vertices equal entanglement bonds). A fixed chiral Peierls phase π/4 on every directed edge breaks time-reversal sym- metry and produces non-trivial multi-band topology, with the lower seven-band complex carrying an exact integer Chern number C=−1 (computed via the non-Abelian Fukui- Hatsugai-Suzuki method). However, trivial global holonomies (8 ×π/4 = 2π) on the dual Simple Cubic (SC) gauge web protect the infrared (IR) regime from observable vacuum birefringence, evading Carroll-Field-Jackiw bounds. The microscopic theory operates as a compact U(1) lattice gauge theory coupled to the 8,4,4 matter code via minimal interac- tion. In the long-wavelength limit, we show it reduces exactly to the standard continuous QED Lagrangian. Numerical joint matter-photon evolution on a minimal Q3 + bridge clus- ter confirms gauge-invariant propagation and dynamic back-reaction. Observable framework signatures must therefore come from matter-coupled processes, while vacuum entanglement reproduces standard quantum mechanics perfectly. 2026-06-20 legacy canon revision: This is a canon-reconciled legacy version. Photon identity and trans-Lambda status changed substantially The paper retains its historical derivation trail but carries a 2026-06-20 canon revision note identifying current status and superseded claims. 2026-06-21 canon refresh: This version incorporates the 2026-06-21 ANCHOR/DRIFT/PTMS canon refresh and rebuilt local PDF.

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