The Asymmetrically Symmetric Universe: A Low-Cutoff Obstruction Program for Cyclic E10 Cosmology

This record contains the full manuscript and companion computational pipeline for "The Asymmetrically Symmetric Universe: A Low-Cutoff Obstruction Program for Cyclic E10 Cosmology". The paper examines a finite algebraic obstruction in a filtered E10/K(E10) framework. The local eleven-dimensional supergravity description is treated as a directional tensor-shadow quotient of a larger indefinite algebraic structure, rather than the complete state space. The core calculation tests whether the projected local sector can close its first ordinary-local algebraic obstruction (the d=2 derivative rank defect) without ad-hoc repairs. The main result is that the ordinary p8 label at level four has a unique primitive null support root of height 38 and norm zero. Peterson recursion on the finite coefficient box yields multiplicity eight. Under the stated tensor-shadow dictionary (A9-equivariant, quotient-compatible, primitive on ordinary supports), this root forces the required ordinary closure column (up to sign) and closes the rank defect. A self-contained appendix proves the global first-gate support uniqueness using only rational linear algebra over the A9 Cartan matrix, together with the finite Peterson multiplicity computation. The accompanying code bundle (e10_a9_pipeline.py and companions) fully reproduces the low-cutoff root enumeration, dominance equation solutions, Peterson multiplicities, shadow matrices, ranks, left-null vectors, and SHA-256 digests. It is deliberately limited to the first gate and is not a full outer-multiplicity engine. The scope is intentionally narrow. This work clears one concrete low-level algebraic gate. It does not claim a complete cyclic cosmology, derived BFSS coefficients, a full outer atlas, dynamical wall system, or observational transfer functions. Those remain open problems.