Anomaly Freedom of BI-6: The Modified Bianchi Identity (BI-6) for the Six-Force, Six-Dimensional Bulk (GG-6)

Abstract

For half a century a quantum anomaly has been described as a flaw that shows up only when a classical symmetry is run through the quantum machine. This paper makes the opposite case: the anomaly is, at bottom, a classical and geometric fact about a higher-dimensional space, and the quantum calculation merely detects it. The lineage is old — Bianchi wrote the geometric ancestor in 1902, and Green and Schwarz, in 1984, modified it for higher dimensions — and it is geometric at every step. We show that the six-dimensional bulk of GG-Theory, built from the four axioms and seven postulates of its constitutional charter, passes the anomaly test completely. The proof has two halves: a local part that closes the usual one-loop consistency in a single line, and a global part that closes it under every large gauge transformation — with no restriction on the topology of the four-dimensional base, because the relevant spin bordism groups of the gauge group's classifying space are shown to vanish. We also show that the five small integers (1,3,5;7,35) that fix every normalization in the theory are locked rather than fitted: the unified block size is forced by single-tensor consistency alone, the color index by the dual-lock closure together with the block embedding, and the remaining two by the same closure identity. No step of the cascade consumes a measured quantity. Read alongside the companion papers, this places BI-6 on the same foundational layer as the 1984 Green–Schwarz mechanism it generalizes — a program, begun with Riemann and Bianchi, of the geometrization of gauge in higher dimensions rather than the quantization of geometry. What makes a theory meaningful is not the cleverness of its calculations but the discipline of its consistency tests, and this is the sharpest one we know how to write down. Part of the GG-Theory program, a series of preprints developing a six-dimensional geometric framework and its consequences for particle physics, cosmology, and open-system dynamics. The complete series is available at https://preprints.arisaka-gg.org/