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At least 181 records · Page 10Linked to original sources
arXiv2026

A Human Audit of OpenAIs AI-Generated Mathematical Proofs

We assess 18 chapter-specific reviews of the ten mathematical results announced by OpenAI on 1 August 2026, alongside review standards, Lean formalizations, subsequent research, and mathematical references. The article audits this review record without claiming a complete reconstruction of all ten proofs. No confirmed substantive mathematical error in a principal result remains in the examined assessments, although review depth varies and some dependencies remain partly checked. Chapter 8 presents the strongest reservation: a specialist review requests major revision of compressed analytic arguments. In Chapter 6, an apparent polarity error was withdrawn after an overbar lost during PDF extraction was recovered from the typeset source. Subsequent research independently reuses the Chapter 3 proof mechanism and confirms that Connes's rigidity conjecture is false, without independently reproducing Chapter 4's stronger infinite-family result. Among the cited follow-ups, Chapter 7 receives the strongest direct theorem-level corroboration through a stronger hardness theorem. Related equality results in Chapter 8 do not verify the analytic inequality proof. Some follow-ups disclose material AI assistance. We argue that confidence should combine formal checking, human reconstruction, independent mathematical use, and a public record supporting correction of both proofs and reviews.

cs.AI↗
arXiv2026

The Mathematical Evolution of Addressing: From Yushchenko's Address Programming Language to A Mathematics of Arrays How Addressing Evolved into a Mathematical Theory of Indexing, Array Computation, and Machine Realization

This article argues that a central development in the history of computing is the mathematical evolution of addressing. During the three decades separating Kateryna Yushchenko's Address Programming Language (1958) from Lenore Mullin's A Mathematics of Arrays (1988), addressing evolved from a machine-level mechanism for locating data into a formal theory of indexing, reduction, and machine realization, passing through Kenneth Iverson's algebra of arrays and Philip Abrams' recognition of shape as an architectural resource. Mullin's theory establishes indexing itself, via the function ψ, as the primitive from which array operations compose, reduce to a Denotational Normal Form, transform into an Operational Normal Form, and realize on hardware through dimension lifting. Historical claims are sourced against primary material, with inferences flagged as such; mathematical claims are stated as identities; performance claims are marked validated, theoretically established, or provisional. The result links programming languages, array mathematics, and computer architecture in one account.

cs.GL↗
arXiv2026

OnBodyAI - Why the Next AI Needs a Body

The next AI will not win by knowing more about the world. It will win because it knows you: because it lives on your body, works for you and answers to you. That is what the term OnBodyAI stands for. It describes what happens when large language models are given a body, and what research and industry need to make that happen. This article is based on my talk in the Industrial Panel at UbiComp/ISWC 2026 in Shanghai (October 13, 2026) and follows its ten key statements.

cs.HC↗
arXiv2000

Take-home Complexity

We discuss the use of projects in first-year graduate complexity theory courses.

cs.CY↗
arXiv2000

Questions for a Materialist Philosophy Implying the Equivalence of Computers and Human Cognition

Issues related to a materialist philosophy are explored as concerns the implied equivalence of computers running software and human observers. One issue explored concerns the measurement process in quantum mechanics. Another issue explored concerns the nature of experience as revealed by the existence of dreams. Some difficulties stemming from a materialist philosophy as regards these issues are pointed out. For example, a gedankenexperiment involving what has been called "negative" observation is discussed that illustrates the difficulty with a materialist assumption in quantum mechanics. Based on an exploration of these difficulties, specifications are outlined briefly that would provide a means to demonstrate the equivalence of of computers running software and human experience given a materialist assumption.

cs.GL↗
arXiv2001

Multiple-Size Divide-and-Conquer Recurrences

This short note reports a master theorem on tight asymptotic solutions to divide-and-conquer recurrences with more than one recursive term: for example, T(n) = 1/4 T(n/16) + 1/3 T(3n/5) + 4 T(n/100) + 10 T(n/300) + n^2.

cs.GL↗
arXiv2001

ENUM: The Collision of Telephony and DNS Policy

ENUM marks either the convergence or collision of the public telephone network with the Internet. ENUM is an innovation in the domain name system (DNS). It starts with numerical domain names that are used to query DNS name servers. The servers respond with address information found in DNS records. This can be telephone numbers, email addresses, fax numbers, SIP addresses, or other information. The concept is to use a single number in order to obtain a plethora of contact information. By convention, the Internet Engineering Task Force (IETF) ENUM Working Group determined that an ENUM number would be the same numerical string as a telephone number. In addition, the assignee of an ENUM number would be the assignee of that telephone number. But ENUM could work with any numerical string or, in fact, any domain name. The IETF is already working on using E.212 numbers with ENUM. [Abridged]

cs.GL↗
arXiv2003

Classical and Nonextensive Information Theory

In this work we firstly review some results in Classical Information Theory. Next, we try to generalize these results by using the Tsallis entropy. We present a preliminary result and discuss our aims in this field.

cs.GL↗
arXiv2004

The pre-history of quantum computation

The main ideas behind developments in the theory and technology of quantum computation were formulated in the late 1970s and early 1980s by two physicists in the West and a mathematician in the former Soviet Union. It is not generally known in the West that the subject has roots in the Russian technical literature. The author hopes to present as impartial a synthesis as possible of the early history of thought on this subject. The role of reversible and irreversible computational processes is examined briefly as it relates to the origins of quantum computing and the so-called Information Paradox in physics.

cs.GL↗
arXiv2004

Demolishing Searle's Chinese Room

Searle's Chinese Room argument is refuted by showing that he has actually given two different versions of the room, which fail for different reasons. Hence, Searle does not achieve his stated goal of showing ``that a system could have input and output capabilities that duplicated those of a native Chinese speaker and still not understand Chinese''.

cs.AI↗
arXiv2004

DAB Content Annotation and Receiver Hardware Control with XML

The Eureka-147 Digital Audio Broadcasting (DAB) standard defines the 'dynamic labels' data field for holding information about the transmission content. However, this information does not follow a well-defined structure since it is designed to carry text for direct output to displays, for human interpretation. This poses a problem when machine interpretation of DAB content information is desired. Extensible Markup Language (XML) was developed to allow for the well-defined, structured machine-to-machine exchange of data over computer networks. This article proposes a novel technique of machine-interpretable DAB content annotation and receiver hardware control, involving the utilisation of XML as metadata in the transmitted DAB frames.

cs.GL↗
arXiv2004

The Persistent Buffer Tree : An I/O-efficient Index for Temporal Data

In a variety of applications, we need to keep track of the development of a data set over time. For maintaining and querying this multi version data I/O-efficiently, external memory data structures are required. In this paper, we present a probabilistic self-balancing persistent data structure in external memory called the persistent buffer tree, which supports insertions, updates and deletions of data items at the present version and range queries for any version, past or present. The persistent buffer tree is I/O-optimal in the sense that the expected amortized I/O performance bounds are asymptotically the same as the deterministic amortized bounds of the (single version) buffer tree in the worst case.

cs.GL↗
arXiv2004

Uncovering the epistemological and ontological assumptions of software designers

The ontological and epistemological positions adopted by information systems design methods are incommensur-able when pushed to their extremes. Information systems research has therefore tended to focus on the similarities between different positions, usually in search of a single, unifying position. However, by focusing on the similari-ties, the clarity of argument provided by any one philoso-phical position is necessarily diminished. Consequently, researchers often treat the philosophical foundations of design methods as being of only minor importance. In this paper, we have deliberately chosen to focus on the differences between various philosophical positions. From this focus, we believe we can offer a clearer under-standing of the empirical behaviour of software as viewed from particular philosophical positions. Since the em-pirical evidence does not favour any single position, we conclude by arguing for the validity of ad hoc approaches to software design which we believe provides a stronger and more theoretically grounded approach to software design.

cs.SE↗
arXiv2004

Why Two Sexes?

Evolutionary role of the separation into two sexes from a cyberneticist's point of view. [I translated this 1965 article from Russian "Nauka i Zhizn" (Science and Life) in 1988. In a popular form, the article puts forward several useful ideas not all of which even today are necessarily well known or widely accepted. Boris Lubachevsky, bdl@bell-labs.com ]

cs.NE↗
arXiv2004

Some first thoughts on the stability of the asynchronous systems

The (non-initialized, non-deterministic) asynchronous systems (in the input-output sense) are multi-valued functions from m-dimensional signals to sets of n-dimensional signals, the concept being inspired by the modeling of the asynchronous circuits. Our purpose is to state the problem of the their stability.

cs.GL↗
arXiv2004

The equations of the ideal latches

The latches are simple circuits with feedback from the digital electrical engineering. We have included in our work the C element of Muller, the RS latch, the clocked RS latch, the D latch and also circuits containing two interconnected latches: the edge triggered RS flip-flop, the D flip-flop, the JK flip-flop, the T flip-flop. The purpose of this study is to model with equations the previous circuits, considered to be ideal, i.e. non-inertial. The technique of analysis is the pseudoboolean differential calculus.

cs.GL↗