Identity-Preserving Local Holonomy Dynamics on Cochains: A unified, reproducible realization of gauge, causality, and topology at finite resolution

Background : Core identities across lattice gauge theory, quantum many‑body locality, and quantum information are typically realized in separate formalisms. Methods : We implement a cochain‑first, local‑holonomy dynamics on oriented cell complexes with a functorial blocking map R that commutes with the coboundary d (R∘d=d∘R). Degrees of freedom live on cells; edge holonomies encode gauge structure; time updates are finite‑depth local circuits. Results : In a single NumPy‑only suite, we verify at finite resolution and machine precision: Wilson‑loop gauge invariance and discrete Bianchi closure; Lieb–Robinson‑consistent light‑cone speeds matched between a split‑step QCA and tight‑binding (1.96945 sites/step); Aharonov–Bohm 2π spectral periodicity (max spectral diff at 2π = 2.44249e-15); Ward transversality with link‑centred Fourier phases (residuals 2.34e-19→5.68e-19 under local spin‑frame similarities); persistent‑current thermo–micro equality; spectral‑dimension flow (UV≈0.24, mid≈1.07, IR≈1.01); and stabilizer graph‑state entropy equaling the GF(2) cut rank on trees. Conclusions : We do not claim new theorems; rather, a unified, identity‑preserving cochain‑holonomy framework that realizes and verifies standard identities concurrently at finite resolution, with identities preserved by coarse‑graining.