This deposit provides the formal mathematical manuscript and the associated numerical evaluation engines for the Geometric-Orchestration Obstructions program. The Theoretical Framework The included manuscript introduces a supergeometric framework for representing 3-SAT instances as clause-coupled energy landscapes over a bosonic-fermionic supermanifold. Key theoretical contributions include: Kamboj Orchestration Action: A path functional measuring the energetic, geometric, and fermionic cost of navigating a SAT landscape. Geometric Obstruction Width (WOmega): A continuous geometric analogue to Resolution Width, measured via the rank of the clause-curvature interaction matrix. Sheaf of Satisfying Deformations: A formal sheaf-theoretic treatment of local satisfying flows and their failure to glue into global computational sections. Numerical Validation (The Engines) To establish Level (ii) Non-Vacuous Strength, this deposit includes Python-based numerical engines used to validate the core algebraic claims of the framework. Asymmetric XOR Gadget: Demonstrates the "Symmetry Breaking" required to prevent catastrophic curvature cancellation. Tensorization Proof: Validates that the geometric obstruction rank compounds and scales linearly as parity gadgets are connected across an expander graph. Rank-Saturation Analysis: Confirms that the curvature matrix for the asymmetric gadget strictly achieves full rank, shattering the "Symmetry Trap" of naive SAT encodings. Scope and Limitations This work is a programmatic mathematical framework and a restricted lower-bound theory. It proves rigorous lower bounds for a specific class of continuous, local, and sheaf-compatible orchestration flows. The framework does not claim a full proof of P != NP. Instead, it isolates the Orchestration Completeness Conjecture as the central simulation-level gap required to transfer these geometric lower bounds to arbitrary deterministic polynomial-time computation.
Prithvidev Kamboj (Thu,) studied this question.