11 papers
A Non-Formulable Theorem: A Fundamental Limit of Finite Syntactic Systems and Its Consequences for Security and AI
Fabio F. G. Buono
For every coherent and sufficiently expressive finite syntactic system S, we prove the existence of at least one theorem that S cannot produce autonomously. The result is a metathe…
What Syntax Cannot See: The Dynamic Syntactic Invariance Principle and Several Instances of the Same Hidden Assumption, and a Contradiction
Fabio F. G. Buono
This paper develops a single method, find what an accepted result silently assumed, make it a variable, and prove what follows once it is dropped, and shows it keeps working across…
Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods
Fabio F. G. Buono
This work introduces a general obstructional framework, the "Double Bind," exposing intrinsic structural limitations of formal verification across computational complexity, mathema…
Witness Complexity of Short Descriptions: A Cryptographic Perspective
Fabio F. G. Buono
In cryptographic practice, where protocols impose strict time bounds, implementations demand predictable resource usage, and real-world systems require immediate verification for s…
Syntactic Separation Implies Computational Indistinguishability: An Abstract Obstruction Theorem
Fabio F. G. Buono
We prove that syntactic separation implies computational indistinguishability. A local syntactic system R acts on terms within radius r0 without consulting any model; when two Skol…
Observers, Symmetries, and the Hierarchy of Language Classes: A Theory of Computation Parameterized by the Observer
Fabio F. G. Buono
We introduce the \emph{observational hierarchy}, a new axis of classification for formal languages, orthogonal to the Chomsky hierarchy. An observer is a function t…
The Observer World: A Cryptographic Extension of Impagliazzo's Five Worlds
Fabio F. G. Buono
Impagliazzo's five worlds classify computational assumptions along a single axis, the existence of cryptographic primitives. All five worlds implicitly assume that every party, inc…
From Bits to Mixed-Radix Keys: Horner Decomposition, Uniform Sampling, and the Information-Theoretic QKD Interface of the MR-OTP
Fabio F. G. Buono
The Mixed-Radix One-Time Pad (MR-OTP) extends the classical OTP to heterogeneous alphabets while preserving perfect secrecy. We provide a practical, bias-free method to convert raw…
Syntactic Systems Cannot See Semantic Invariants
Fabio F. G. Buono
We start from a small open question, where Hetzl and Vierling asked whether two theories of induction, open induction and clause set cycles, are incomparable. They proved one direc…
New Ideas on a New Old Type of Cipher:The Mixed-Radix One-Time Pad
Fabio F. G. Buono
In a short 2012 preprint, an unconventional cipher was introduced, now in this note we take that representational core, formalize it, and use it as the basis for a clean generaliza…
A New Type of Cipher
Fabio F. G. Buono
We will define a new type of cipher that doesn't use neither an easy to calcualate and hard to invert matematical function like RSA nor a classical mono or polyalphabetic cipher.