Add comprehensive academic proofs and formal verification

[hyperpolymath]

Add complete formal academic documentation covering:

Proofs and Metatheory:

• Type system soundness (progress/preservation theorems)
• Quantitative type theory (linearity proofs, semiring laws)
• Algebraic effects formal semantics (handlers, row polymorphism)
• Ownership/borrowing verification (memory safety proofs)
• Row polymorphism (unification, coherence)
• Dependent types and refinement types (normalization, SMT)
• Coherence and parametricity (free theorems)
• Type inference algorithm specification

Formal Verification:

• Operational semantics (small-step, evaluation contexts)
• Denotational semantics (domain theory, logical relations)
• Axiomatic semantics (Hoare logic, separation logic)

Mathematical Foundations:

• Categorical semantics (LCCCs, graded comonads, Freyd categories)
• Logic foundations (Curry-Howard, linear logic correspondence)
• Complexity and decidability analysis

White Papers:

• Language design rationale and related work comparison

Mechanized Proofs (stubs):

• Coq formalization structure
• Lean 4 formalization structure
• Agda formalization structure

All documents include:

• Complete formal definitions and inference rules
• Detailed proof sketches and theorem statements
• Implementation dependencies marked with [IMPL-DEP] tags
• References to academic literature
• Connections to the existing codebase (lib/ast.ml, etc.)