Volume IV.2, bench D1: data, code and preregistration for "Finite transport defects in the square lattice: Hall deficiency, non-lazy Ollivier curvature, and nonlocal metric response"

Supplementary material for the preprint "Finite transport defects in the square lattice: Hall deficiency, non-lazy Ollivier curvature, and nonlocal metric response" (I. A. Guerrero Díaz, 2026), included in this record as a PDF. We study finite surgeries of the square lattice that keep the graph simple, connected, 4-regular and triangle-free, and compare three kinds of response: the non-lazy Ollivier curvature κ₀, graph distances (including far-source approximations of Busemann functions), and the continuous-time heat kernel. Proved results (in the preprint and in reports/analytic_notes.md): (i) Hall–Wasserstein bounds η/k ≤ ε ≤ 2η/k for every edge in no triangle of a k-regular graph; (ii) saturation ε = 2η/k on every edge in no 5-cycle, in particular on bipartite graphs; (iii) locality of κ₀: for every finite surgery of Z², κ₀ vanishes on every edge at ℓ¹-distance ≥ 4 from the surgery; (iv) existence and pointwise stabilisation of diagonal Busemann functions for connected finite surgeries, and a parity criterion (bipartite ⇒ the coordinate map Φ is a graph homomorphism to Z², not necessarily injective); (v) an exact Duhamel formula for the two-defect heat-kernel cross term, with a fixed-time Poisson bound. Computational results (preregistered bench D1, tori of side 150 and 300, 23 accepted surgeries): in every instance the curvature is supported on edges at distance ≤ 1 from the surgery, while distances, far-source coordinates and the heat kernel change between points far from it. The bipartite/non-bipartite split of the surgeries coincides exactly with the homomorphism/non-homomorphism split of the far-source coordinate map. Computational statements refer only to the finite toroidal instances and defect families specified in the preregistration. No physical interpretation is claimed. Contents: preprint PDF; repository archive (code, frozen configurations, preregistration PREREG_D1.md with dated amendments, 15 automated tests, reports and figures, LaTeX source, git history tagged d1-v1.0, minimal reproduction script); accepted graphs in sparse6 and edge-list format for L = 150 and L = 300; per-instance outputs for L = 150 and L = 300; SHA256SUMS.txt. Unzip all archives into one folder to rebuild volume_iv_2/. Reproducing: pip install -r requirements.txt; python3 -m pytest -q tests; python3 scripts/minimal_repro.py (≈ 3 min, recomputes the controls, the twisted plaquette, two 2-swaps and one two-defect configuration from scratch and compares them with frozen values); python3 scripts/verify.py for the full chain. Integrity: sha256sum -c MANIFEST.sha256 inside volume_iv_2/. This record continues "Data and code for 'The square lattice admits no finite flat defect'" (doi:10.5281/zenodo.23270728). Code: MIT License. Data, documentation and preprint: CC BY 4.0.