Doctoral Dissertation — Interactive Guide
A Formal Theory of Phonological Equivalence
Alexandre Menezes Barroso
Institute of Language Studies — UNICAMP, 2027
Advisor: Prof. Dr. Maria Filomena Spatti Sandalo
What is this guide?
This is an interactive walkthrough of the entire dissertation, explaining every equation, theorem, and proof in an accessible way for linguists and phonologists who are not specialized in mathematics. Every mathematical concept is introduced with analogies, concrete examples, and step-by-step explanations. You can click on equation symbols to see what each one means.
Lean 4
Computer-verified formal proofs
Python 3
Runnable exact calculations
Wolfram
Symbolic algebra
Dissertation Structure
The Problem of Phonological Equivalence
Why "the same analysis" is incomplete without a declared scope
Analysis Contracts and the Qualified Finite Calculus
Formation, admission, and the exact decision theorem
Finite Representation, Recovery, and Information
Carriers, orbits, lattices, and irreversible loss
Exact Equivalence in Finite Maximum Entropy Grammar
Probability laws, normalization, and algebraic carriers
Inheritance, Prior Art, and the Contribution
What is inherited, specialized, or new
Exact Finite Persistence in Continuous Harmonic Grammar
Unique optimizer, finite support, and scaling limits
Consequences for Published Analyses
McCollum, Goldrick-Daland, Basic Syllable, and more
Finite Empirical Demonstrations
Portuguese, English, and Mandarin decision ledgers
Consequences, Limits, and the Research Program
Nine consequences and what remains open
References
Complete dissertation bibliography