Quantifier-Scoped Neural Agents for P versus NP

Research toward P versus NP requires control over quantifier dependencies, computational models, and asymptotic guarantees. This paper proposes a joint neural and multi-agent architecture in which one compiled mathematical contract controls witness generation, inter-agent proof transport, and verification. An obligation fork shares context across separate source and target streams and generates proofs of the implications needed to reuse an intermediate result. A quantifier-scoped witness decoder constructs typed terms in binder-specific environments: a candidate polynomial-time SAT machine and its bound are fixed before the universally quantified input, whereas a separation witness may depend on the candidate machine and bound. A certificate-directed repair loop turns unresolved bridges into versioned proof tasks while preserving the scope of accepted source theorems. Dependency-indexed memory connects these mechanisms to context reuse. Elementary propositions specify valid transfers and failure modes. A Lean-checked, scripted execution trace follows one source theorem through an unresolved obligation, repair, and target acceptance. A controlled scheduling simulation evaluates four allocation policies on 600 generated workloads. At the primary setting, transport-frontier allocation exceeds target-first allocation by 1.21 percentage points in completed targets, but falls below it in 89 of 135 sensitivity cells. Higher coordination costs reverse its advantage over uniform allocation. These results concern scheduling under the stated synthetic model; the neural mechanisms remain to be evaluated. Companion research artifacts (v1.0.0): https://github.com/Ox24/quantifier-scoped-agents. The versioned release includes the scripted Lean conformance trace, scheduling simulations, raw outcomes, and reproduction tools.