The Field-Stack Unification: A Capstone Thesis for Governing Hard Problems as Executable Subfields

Hard problems resist closure not only because they are technically deep, but because validity fails to travel across regimes: assumptions, representations, toolchains, institutions, and time. Building on prior instantiations — (i) executable subfield programs for complexity-class progress and (ii) landmark portfolio languages for deep problem sets — our work presents a capstone unification that turns the transport bottleneck into a computable governance program. We define the field-stack (subfield, field, metafield, overfield, metaoverfield) as an executable semantics for admissibility, promotion, and publication under explicit budgets and drift-bounded re-description. The core contribution is a runtime discipline for governing the governors: MetaField declarations (MF₀), MetaOverfield arbitration receipts (MOF₀), cycle-safe dual-route maps, and universal stop rules that make negative results and budget walls first-class outputs. We introduce a Minimum Publishable Evidence Surface (MPES) that makes “executable” and “publishable under restriction” operational rather than rhetorical. MPES defines a minimal, testable surface for any fragment: explicit scope and admissible movement, declared verification and drift budgets, fatal invariants expressed as checks, at least one falsifier with a minimization rule that produces a concrete obstruction, and a compact receipt spine that supports replay under substitution. Publication is then treated as ACCEPT_RESTRICTED by default: the restriction stamp is part of the claim, not a disclaimer, and redistribution that drops restrictions, regressions, or receipts invalidates the artifact rather than merely “weakening” it. In parallel, we specify a class-generic orchestrator for hard problems that treats subfields as the unit of long-horizon work across problem classes (complexity, PDE/continuum, geometry/topology, algebra/number theory, physics, software, structural governance, and open landmark portfolios). The orchestrator is not a solver; it is a governance loop that seeds minimal subfields, executes admissible transforms and MF₀-defined cross-route checks, mines failures into minimal obstructions, converts those obstructions into regression assets, and promotes fragments only when portability improves within the stamped corridor. When closure cannot be achieved under budget, the orchestrator does not inflate claims; it publishes barrier receipts and stop rules as first-class outcomes, ensuring that progress remains contestable, replayable, and cumulative without implying solutions to open problems.