MathRosetta: Universal Translation with Zero Sorry

We introduce \emph{MathRosetta}, a formally verified mathematical translation framework designed to provide syntax-independent reasoning across heterogeneous mathematical languages and computational systems. The central objective of MathRosetta is to separate mathematical meaning from syntactic representation by translating diverse input languages—including \LaTeX{}, SymPy, Lean~4, symbolic algebra systems, and controlled natural language—into a canonical intermediate representation, \emph{MathIR}. Once expressed in this semantic form, mathematical objects become independent of their original notation, allowing automated reasoning, formal verification, symbolic manipulation, numerical computation, and theorem proving to operate over a unified representation. The architecture consists of four principal stages. First, language-specific parsers transform source syntax into abstract semantic trees while preserving mathematical intent. Second, these semantic structures are normalized into MathIR, an intermediate language designed to represent algebraic expressions, logical propositions, geometric constructions, differential systems, optimization problems, categorical morphisms, and formal proofs within a common typed framework. Third, a Prolog-based orchestration engine performs semantic classification and dispatches each mathematical object to the solver best suited for its computational domain. Finally, all solver outputs are independently verified before being accompanied by cryptographically authenticated WORM receipts, producing deterministic computational provenance for every mathematical result. The primary theoretical contribution of this work is the \emph{Sovereign Stack Correctness Theorem}. We prove that, given a pure fact specification, a well-formed circuit netlist, and corresponding Verilog-A semantic annotations, the complete verification pipeline simultaneously satisfies five fundamental correctness properties: The verification pipeline simultaneously satisfies five correctness properties: Collectively, these invariants establish that semantic meaning is preserved throughout parsing, normalization, solver execution, and verification, ensuring that equivalent mathematical structures remain equivalent across every supported representation. The resulting system provides deterministic mathematical execution together with reproducible verification artifacts suitable for long-term audit and independent validation. All formal correctness results are mechanized in Lean~4. The current development consists of eighteen formally verified theorems, each completed without placeholder axioms, admitted lemmas, or \texttt{sorry} declarations, yielding a fully machine-checkable proof corpus within the declared trusted computing base. MathRosetta integrates a heterogeneous collection of symbolic, numeric, geometric, logical, and formal reasoning engines through a common semantic interface. Current supported backends include: \[\text{Z3},\quad\text{SymPy},\quad\text{CVODE},\quad\text{Singular},\quad\text{Lean~4},\quad\text{CGAL},\quad\text{Julia},\quad\text{DeepONet}.\] Rather than selecting computational engines statically, MathRosetta employs semantic dispatch rules implemented in Prolog to determine the optimal solver for each problem class. This architecture allows symbolic algebra, numerical integration, geometric computation, optimization, partial differential equations, and formal theorem proving to coexist within a unified reasoning environment while maintaining a common verification protocol. A distinguishing feature of the framework is its trust-aware execution model. Mathematical computations are assigned verification policies according to application domain. General symbolic computations may terminate upon successful solver completion, whereas applications involving finance, medicine, infrastructure, aerospace, or other safety-critical systems require complete Lean~4 proof certificates together with Ed25519 cryptographic signatures and immutable WORM provenance records before results are considered authenticated. This layered trust architecture permits computational efficiency for routine problems while preserving maximal assurance where correctness carries legal, scientific, or engineering significance. More broadly, MathRosetta advances the principle that mathematical reasoning should be fundamentally semantic rather than syntactic. Mathematical truth is invariant under notation, and the diversity of existing mathematical languages should be viewed as multiple interfaces to a common underlying semantic structure rather than independent computational ecosystems. By introducing MathIR as a canonical intermediate representation, the framework demonstrates that theorem proving, symbolic computation, numerical analysis, and automated reasoning can interoperate without sacrificing formal correctness, reproducibility, or expressive power. The central philosophy of the project is summarized by the guiding principle: \[\boxed{\textit{Syntax is liability. Semantics are truth.}}\] MathRosetta therefore proposes a universal semantic substrate for mathematical computation, combining formal verification, heterogeneous solver orchestration, authenticated provenance, and syntax-independent reasoning within a single mathematically verified framework. \end{abstract}