Unified Substrate Theory: Condensed Matter Sector — Quantum Hall Effect,  Topological Phases, and Superconductivity from Substrate Twist Topology

OVERVIEW  This record contains the condensed matter sector of the Unified Substrate Theory (UST) — two papers deriving the quantum Hall effect, topological insulators, and superconductivity from the twist vortex topology of the substrate field φ(x). No new parameters are introduced. The same five Lagrangian constants fixed by galaxy rotation curves determine the electron's twist mode structure, and that structure determines all condensed matter topological invariants.  The five constants:  C₁ = 1.000  |  C₂ = 0.470  |  C₃ = 0.018  |  β = 0.650  |  Γ = 0.920  PAPER CM-1: Quantum Hall Effect and Topological Phases from Substrate Twist Topology  • Integer QHE: σ_xy = ν e²/h derived from Chern number = twist winding     per filled Landau level — exact, topologically protected  • Substrate correction to QHE plateau: O(10⁻¹³) — four orders of     magnitude below current measurement precision (10⁻⁹)  • Fractional QHE: Laughlin sequence ν = 1/(2m+1) from composite twist     clusters with effective fractional winding  • Z₂ topological insulator invariant from half-integer winding of the     electron twist mode — protected edge states derived structurally  • Topological crystalline insulators: Z_n invariants for C_n symmetric     crystals from crystal-symmetry-constrained winding numbers  • Unification table: fine-structure constant, electron charge, spin-1/2,     IQHE, FQHE, Z₂ TI, and topological crystalline insulators all from one     winding number count  PAPER CM-2: Superconductivity from Composite Twist Modes — Cooper Pairing, Meissner Effect, and the BCS Limit  • Cooper pair = zero-winding composite of two electron twist modes     (winding +1 and −1) — bosonic, charge 2e, spin 0 from winding arithmetic  • London equations and Meissner effect derived from substrate field     equation in the condensate  • Flux quantization Φ₀ = h/(2e) exact — topologically protected, zero     UST correction  • BCS gap equation reproduced exactly from substrate-mediated pairing kernel  • UST correction to all superconducting observables (T_c, Δ, λ_L, ξ):     δ_UST = 4.67 × 10⁻¹⁴ — same as QED Rung 6, completely unmeasurable  • Ginzburg-Landau free energy derived from substrate action on Cooper     pair condensate  • High-T_c superconductivity: honest assessment — UST reproduces BCS     exactly, high-T_c is materials-specific, no new UST pairing mechanism  THE UNIFYING STRUCTURE  Both papers derive from a single topological principle: the winding number of the substrate field φ(x) around closed paths. The same C₂ = G that governs Newtonian gravity determines the twist coupling that generates the Chern number. The same α = 1/137.036 derived in QED Paper 0 appears in σ_xy = ν e²/h through e²/h = α × 2/μ₀c.    Phenomenon          UST Origin                  Agreement  IQHE plateau        Chern number = winding       Verified to 10⁻⁹  FQHE Laughlin       Composite twist clusters     Verified (Tsui-Störmer)  Z₂ TI edge states   Half-integer winding mod 1   Verified (Bi₂Se₃ etc.)  Cooper pairs        Net-zero winding composite   BCS verified to >10⁻⁶  Flux quantum Φ₀     Winding quantization         Verified (Deaver-Fairbank)  Meissner effect     London eq. from substrate    Verified  RELATIONSHIP TO PRIOR UST PUBLICATIONS  Layer 1 — Foundations:      10.5281/zenodo.18855105Layer 2 — SM Sector:        10.5281/zenodo.19055534Layer 3 — QFT Closure:      10.5281/zenodo.19076205Layer 4 — Chemistry:        10.5281/zenodo.19077691Layer 5 — Atomic/Nuclear:   10.5281/zenodo.19077996Layer 6 — Nuclear Sector:   10.5281/zenodo.19210027Layer 7 — Astrophysics:     10.5281/zenodo.19580619Layer 8 — Gap Closure:      10.5281/zenodo.19227984This record — Condensed Matter Sector: Papers CM-1 and CM-2  The electron twist mode structure used here is established in QED Paper 0 (Layer 1). The winding number and homotopy framework comes from QFT Paper 21 (Layer 3). The five constants are unchanged throughout.  SUGGESTED CITATION  Donnelly, D. (2026). Unified Substrate Theory: Condensed Matter Sector — Quantum Hall Effect, Topological Phases, and Superconductivity from Substrate Twist Topology [Preprint]. Zenodo. https://doi.org/10.5281/zenodo.19616692  Keywords  Unified Substrate Theoryquantum Hall effectinteger quantum Hall effectfractional quantum Hall effecttopological insulatorChern numberLaughlin fractionsZ2 invariantKane-Melecomposite fermionsuperconductivityCooper pairsBCS theoryMeissner effectflux quantizationGinzburg-Landauwinding numbertwist vortex topologysubstrate fieldfive constants  Correspondence: unifiedsubstrate@gmail.com   For inquiries, collaboration, or technical questions related to the Unified Substrate Theory (UST).