Transport Receipts for AI-Discovered Singularities: Making Numerical Discovery Admissible Under the Transportable Proof Conjecture

Recent AI-assisted advances in nonlinear PDE research — most visibly DeepMind’s systematic discovery of unstable self-similar singularities — suggest that “finding the address” of a potential blow-up event is becoming easier than proving what that address implies. However, the limiting factor for high-stakes mathematical claims is not discovery throughput but admissibility throughput: whether a claim can be independently verified cheaply, repeatedly, and across contexts (different teams, toolchains, discretizations, or proof venues). Building on the Transportable Proof Conjecture (TPC), this paper proposes Transport Receipts for Singularities (TRS): a portable certificate bundle that separates (i) heuristic discovery from (ii) rigorous certification and (iii) optional formal proof spines. TRS is designed to let an independent verifier confirm a singularity claim (or reject it) without replaying the original ML pipeline. We define the receipt layers, map them to established “proof-carrying” traditions from SAT/NP verification, proof assistants, and rigorous numerics, and illustrate how TRS would reframe the verification pathway for AI-discovered singularity candidates. The result is a governance-first standard for moving PDE evidence across contexts with bounded drift, bounded verification time, and explicit falsifiers.