Advanced Manifold Topology Planning Framework
Budget: $30 – $250 USD
I’m building a rigorous mathematical framework that brings manifold theory into AI-assisted planning, with a very specific goal: I want to verify, from first principles, that any plan generated by an algorithm is both adequate and sufficient for its stated objectives.
Your task is to help me formalise this idea end-to-end. We will treat the space of possible plans as a manifold, define the relevant charts and transition maps, and then construct operators that capture feasibility, optimality and robustness. The heart of the job is to supply rock-solid analytical proofs that these operators behave exactly as intended—no simulations or empirical testing, strictly formal mathematics.
Key deliverables
• A clear statement of assumptions and definitions underpinning the manifold model of the planning space
• Formal theorems expressing adequacy and sufficiency conditions, followed by complete, meticulously written proofs
• A concise explanatory document showing how the framework can be embedded in an AI planning pipeline (e.g., as a validation layer after plan generation)
• Microsoft word Equation Editor source for all mathematics so the work can be compiled directly into my existing documentation set
I’m comfortable with advanced topology, category theory and logic, so feel free to write at graduate-research level. If you enjoy pushing the boundaries of pure mathematics applied to AI, we should be an excellent fit.
Your task is to help me formalise this idea end-to-end. We will treat the space of possible plans as a manifold, define the relevant charts and transition maps, and then construct operators that capture feasibility, optimality and robustness. The heart of the job is to supply rock-solid analytical proofs that these operators behave exactly as intended—no simulations or empirical testing, strictly formal mathematics.
Key deliverables
• A clear statement of assumptions and definitions underpinning the manifold model of the planning space
• Formal theorems expressing adequacy and sufficiency conditions, followed by complete, meticulously written proofs
• A concise explanatory document showing how the framework can be embedded in an AI planning pipeline (e.g., as a validation layer after plan generation)
• Microsoft word Equation Editor source for all mathematics so the work can be compiled directly into my existing documentation set
I’m comfortable with advanced topology, category theory and logic, so feel free to write at graduate-research level. If you enjoy pushing the boundaries of pure mathematics applied to AI, we should be an excellent fit.