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&nbsp;Theory (UST) &mdash; two papers deriving the quantum Hall effect, topological&nbsp;insulators, and superconductivity from the twist vortex topology of the&nbsp;substrate field &phi;(x). No new parameters are introduced. The same five&nbsp;Lagrangian constants fixed by galaxy rotation curves determine the electron's&nbsp;twist mode structure, and that structure determines all condensed matter&nbsp;topological invariants. The five constants:&nbsp; C₁ = 1.000 &nbsp;| &nbsp;C₂ = 0.470 &nbsp;| &nbsp;C₃ = 0.018 &nbsp;| &nbsp;&beta; = 0.650 &nbsp;| &nbsp;&Gamma; = 0.920 PAPER CM-1: Quantum Hall Effect and Topological Phases from Substrate&nbsp;Twist Topology&nbsp; &bull; Integer QHE: &sigma;_xy = &nu; e&sup2;/h derived from Chern number = twist winding&nbsp;&nbsp; &nbsp; per filled Landau level &mdash; exact, topologically protected&nbsp; &bull; Substrate correction to QHE plateau: O(10⁻&sup1;&sup3;) &mdash; four orders of&nbsp;&nbsp; &nbsp; magnitude below current measurement precision (10⁻⁹)&nbsp; &bull; Fractional QHE: Laughlin sequence &nu; = 1/(2m+1) from composite twist&nbsp;&nbsp; &nbsp; clusters with effective fractional winding&nbsp; &bull; Z₂ topological insulator invariant from half-integer winding of the&nbsp;&nbsp; &nbsp; electron twist mode &mdash; protected edge states derived structurally&nbsp; &bull; Topological crystalline insulators: Z_n invariants for C_n symmetric&nbsp;&nbsp; &nbsp; crystals from crystal-symmetry-constrained winding numbers&nbsp; &bull; Unification table: fine-structure constant, electron charge, spin-1/2,&nbsp;&nbsp; &nbsp; IQHE, FQHE, Z₂ TI, and topological crystalline insulators all from one&nbsp;&nbsp; &nbsp; winding number count PAPER CM-2: Superconductivity from Composite Twist Modes &mdash; Cooper&nbsp;Pairing, Meissner Effect, and the BCS Limit&nbsp; &bull; Cooper pair = zero-winding composite of two electron twist modes&nbsp;&nbsp; &nbsp; (winding +1 and &minus;1) &mdash; bosonic, charge 2e, spin 0 from winding arithmetic&nbsp; &bull; London equations and Meissner effect derived from substrate field&nbsp;&nbsp; &nbsp; equation in the condensate&nbsp; &bull; Flux quantization &Phi;₀ = h/(2e) exact &mdash; topologically protected, zero&nbsp;&nbsp; &nbsp; UST correction&nbsp; &bull; BCS gap equation reproduced exactly from substrate-mediated pairing kernel&nbsp; &bull; UST correction to all superconducting observables (T_c, &Delta;, &lambda;_L, &xi;):&nbsp;&nbsp; &nbsp; &delta;_UST = 4.67 &times; 10⁻&sup1;⁴ &mdash; same as QED Rung 6, completely unmeasurable&nbsp; &bull; Ginzburg-Landau free energy derived from substrate action on Cooper&nbsp;&nbsp; &nbsp; pair condensate&nbsp; &bull; High-T_c superconductivity: honest assessment &mdash; UST reproduces BCS&nbsp;&nbsp; &nbsp; 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&nbsp;of the substrate field &phi;(x) around closed paths. The same C₂ = G that&nbsp;governs Newtonian gravity determines the twist coupling that generates&nbsp;the Chern number. The same &alpha; = 1/137.036 derived in QED Paper 0 appears&nbsp;in &sigma;_xy = &nu; e&sup2;/h through e&sup2;/h = &alpha; &times; 2/&mu;₀c. &nbsp; Phenomenon &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;UST Origin &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Agreement&nbsp; IQHE plateau &nbsp; &nbsp; &nbsp; &nbsp;Chern number = winding &nbsp; &nbsp; &nbsp; Verified to 10⁻⁹&nbsp; FQHE Laughlin &nbsp; &nbsp; &nbsp; Composite twist clusters &nbsp; &nbsp; Verified (Tsui-St&ouml;rmer)&nbsp; Z₂ TI edge states &nbsp; Half-integer winding mod 1 &nbsp; Verified (Bi₂Se₃ etc.)&nbsp; Cooper pairs &nbsp; &nbsp; &nbsp; &nbsp;Net-zero winding composite &nbsp; BCS verified to &gt;10⁻⁶&nbsp; Flux quantum &Phi;₀ &nbsp; &nbsp; Winding quantization &nbsp; &nbsp; &nbsp; &nbsp; Verified (Deaver-Fairbank)&nbsp; Meissner effect &nbsp; &nbsp; London eq. from substrate &nbsp; &nbsp;Verified RELATIONSHIP TO PRIOR UST PUBLICATIONS Layer 1 &mdash; Foundations: &nbsp; &nbsp; &nbsp;10.5281/zenodo.18855105Layer 2 &mdash; SM Sector: &nbsp; &nbsp; &nbsp; &nbsp;10.5281/zenodo.19055534Layer 3 &mdash; QFT Closure: &nbsp; &nbsp; &nbsp;10.5281/zenodo.19076205Layer 4 &mdash; Chemistry: &nbsp; &nbsp; &nbsp; &nbsp;10.5281/zenodo.19077691Layer 5 &mdash; Atomic/Nuclear: &nbsp; 10.5281/zenodo.19077996Layer 6 &mdash; Nuclear Sector: &nbsp; 10.5281/zenodo.19210027Layer 7 &mdash; Astrophysics: &nbsp; &nbsp; 10.5281/zenodo.19580619Layer 8 &mdash; Gap Closure: &nbsp; &nbsp; &nbsp;10.5281/zenodo.19227984This record &mdash; Condensed Matter Sector: Papers CM-1 and CM-2 The electron twist mode structure used here is established in QED Paper 0&nbsp;(Layer 1). The winding number and homotopy framework comes from QFT Paper 21&nbsp;(Layer 3). The five constants are unchanged throughout. SUGGESTED CITATION Donnelly, D. (2026). Unified Substrate Theory: Condensed Matter Sector &mdash;&nbsp;Quantum Hall Effect, Topological Phases, and Superconductivity from Substrate&nbsp;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).