nwt-substrate: a substrate-algebraic computation library for Null Worldtube Theory

⛔ DEPRECATED / RETIRED — July 2026. The Null Worldtube Theory program is retired; this library's physical claims did not survive precision audit (31 of 36 registered dimensionless claims excluded at their own 1σ; the integer-menu constant-fitting matches ~83% of random targets inside Newton's-G's ±22 ppm error bar). The software remains installable and its tests pass, but no claim it computes should be cited as a confirmed prediction. Full accounting: Retirement Retrospective (DOI 10.5281/zenodo.21339662). nwt-substrate v0.5.0 — the field-theoretic construct/measure layer Version DOI: backfilled after the GitHub release (Zenodo mints it on publish); concept DOI 10.5281/zenodo.20012027 (resolves to latest). Install / upgrade pip install --upgrade git+https://github.com/JimGalasyn/nwt-substrate.git@v0.5.0 python -c "from nwt_substrate.solitons import BoxGrid; from nwt_substrate.solitons.faddeev import rational_hopfion, n_from_Z, whitehead_hopf_charge; g=BoxGrid(N=64,L=16.0); Z1,Z2=rational_hopfion(g,R=3.5); print(whitehead_hopf_charge(*n_from_Z(Z1,Z2),g))" The story Through v0.4.x the library was overwhelmingly algebraic: substrate constants, the K₇/Spin(7) structure, mass and coupling formulae, and the benchmark/closure tooling that audits them. The carriers — the knotted field configurations those numbers are supposed to describe — were drawn (diagrams) but not computed. v0.5.0 closes that gap. It ships the construct/measure layer of NWT's field content: the code that builds a carrier field configuration and reads physical quantities off it — Hopf charge, energy, form factor, linking number — without yet minimising anything. The energy-minimising relaxers (the expensive, GPU-shaped half) live in the separate jax-solitons engine; the relationship is one-way, and deliberately so: these pure-numpy primitives are that engine's reference oracle, and as of this release a live cross-engine test pins this package and checks the two independent implementations agree to ~1e-16 (so neither can silently drift). Nothing here changes a published number; it adds the machinery the next round of papers measures with. 1. Faddeev-Skyrme (Hopf) solitons — solitons.faddeev The forward, diagnostic half of NWT's L₃ Skyrme-Faddeev sector (Paper 16), pure-numpy and rendering-free: n_from_Z — the CP¹ → S² map nᵃ = Z†σᵃZ / Z†Z. solid_angle_triangle / plaquette_area_form — the faithful Berg-Lüscher area form: the signed spherical area an S² field sweeps per lattice plaquette (two Van Oosterom-Strackee triangles). Summed over a closed surface it is exactly 2π·(integer), which is what supplies the lattice unwinding barrier the naive same-index ∂ᵢn×∂ⱼn density lacks — that one is only O(dx)-accurate and lets a discrete hopfion unwind to vacuum at every resolution. whitehead_hopf_charge — the field-theoretic Whitehead Hopf charge Q_H = (1/16π²)∫A·B (B from the area form; curl A = B solved spectrally in Coulomb gauge). Distinct from the algebraic carrier-knot topology.hopf_charge(p, m) = p·m; they coincide in value for the field that realises a given knot but are computed from entirely different data. rational_hopfion — a smooth, compact, in-basin hopfion seed (Battye-Sutcliffe / Hietarinta-Salo rational map): no 0/0 spinor singularity on the core ring, and it reaches the south-pole vacuum exactly beyond a finite tube radius (periodic-safe), with charge Q_H = n·m. faddeev_energy / energy_density (forward-difference E₂ — no Nyquist null space — plus the area-form E₄) and soliton_size (energy-weighted RMS radius + the E₂/E₄ virial split). Together these stabilised the first lattice hopfion in the project: Q_H holds at +0.998 where every prior seed unwound to Q→0, energy converges as O(dx²), and the Derrick E ∝ √c₄ scaling holds to 0.02%. 15 tests. 2. Classical EM + form factors — em, amplitudes The bridge from a carrier's charge/supercurrent density to its observable electromagnetic signature: em — FFT-Poisson solvers for the fields a carrier radiates: electric_field (∇²φ = −ρ), magnetic_field (∇²A = −μ₀j, Biot-Savart), divergence/curl, source deposition, field-line tracing, and multipole_moments. Both bc="periodic" (neutralizing background, Gauss-law-clean near the source) and bc="open" (zero-padded free-space Green's function — no image charges). maxwell_eh adds the optional Euler-Heisenberg nonlinear-vacuum correction (L_EH = ξ[(E²−B²)² + 7(E·B)²]), with a convergence guard that stops early on tol and warns if pushed into the non-convergent strong-field regime. amplitudes + em form factors — form_factor (spherically-averaged elastic |F(q)|, F(0)=1; open-BC option for clean low-q), mean_square_radius (signed ⟨r²⟩ — negative allowed for a net-neutral neutron-like distribution), mott_cross_section, and elastic_form_factor_cross_section (dσ/dΩ = (dσ/dΩ)_Mott·|F(q²)|²). The full charge-density → form-factor → scattering chain, for testing NWT carrier form factors against the proton dipole / neutron Galster shapes. 3. Gauged Ginzburg-Landau vortices at any κ — condensate.solve_gl_vortex Generalises the self-dual solve_bps_vortex (κ=1, first-order shooting) to the full second-order GL / de Vega-Schaposnik system by boundary-value collocation: scalar f(ρ) + gauge a(ρ) for any κ = λ/ξ and any winding n. κ=1 reproduces the BPS point to