Content-Independent Growth in E8 Self-Binding and the TMF Classification of the Void: Vesica Walk Proves Lattice Determines Structure, Not Content

We present two independent results from the Omuo Genesis Engine v3.2.0 that together establish the geometric nature of the engine's 168/72 invariant and identify the mathematical framework governing the 72 void axes. Result 1 (Vesica Walk): A new geometric expansion mode grows a manifold from a single concept by binding with E8 root axes generation by generation, with no language model involvement. Three semantically unrelated seeds — "eta-invariant" (spectral geometry), "photosynthesis" (biology), and "the 72 unreachable directions" (meta-description) — all produced identical growth patterns: 1,555 nodes, ~215/240 axes used, 93% axis overlap. The growth pattern is determined by the E8 lattice, not the semantic content. Result 2 (Run 7): A 2,563-node synthesis run targeting the question "what mathematical structure constitutes the external completion?" converged on Topological Modular Forms (TMF) as the framework classifying the 72 void axes — not E9 (affine Kac-Moody) or E10 (hyperbolic). The vesica walk is the first LLM-free, reproducible-in-seconds experiment showing that E8 imposes a content-independent geometric skeleton. Combined with Run 7's identification of TMF, these results establish that the 168/72 invariant encodes genuine mathematical structure at the intersection of algebraic topology, number theory, and string theory.