Fractional Canonical Distribution: A Formal Mathematical Framework for Copyright Violation Suppression, Instance-Bound Completion Architecture, and Secure Physical Media Deployment

Synopsis of the Paper This dissertation proposes a new cryptographic systems architecture called Fractional Canonical Distribution (FCD). The central objective of the work is to redesign the mechanics of software distribution so that industrial-scale copyright violation becomes structurally impossible rather than merely discouraged. Traditional software distribution typically involves shipping a complete executable artifact, which can then be copied and redistributed once a single working copy exists. The model developed in this paper rejects that paradigm and instead proposes that software distribution should occur as incomplete canonical artifacts that require individualized cryptographic completion before execution is possible. The thesis constructs this architecture from established primitives in cryptography, information theory, and secure hardware. These primitives include hash commitments, HMAC authentication, Merkle structures, encryption standards, and device-binding protocols. Through a sequence of formal derivations and theorems, the author argues that these components can be arranged into a coherent system in which each distributed instance of software is uniquely completed and governed by authorization predicates rather than by the artifact alone. The work is organized into several structural layers. The early chapters define the canonical software object and introduce a partition model that separates software into a prefix and remainder component. This partition algebra ensures that the distributed artifact is structurally incomplete and cannot function independently. Subsequent chapters introduce instance-binding mechanisms, cryptographic commitment chains, nonce-based authorization controls, and entropy-based defenses designed to prevent large-scale cracking attempts. A runtime governance layer is then developed through a formal state machine architecture that controls execution conditions, authorization status, and lifecycle transitions of software instances. The system also integrates forensic attribution mechanisms, including watermark embedding and propagation analysis, enabling identification of the origin of leaked copies. The dissertation continues by formalizing a security model and adversarial framework, in which the architecture is evaluated against probabilistic polynomial-time attackers under standard cryptographic assumptions. From these foundations the author derives a central suppression theorem asserting that the economic and technical conditions required for mass piracy are removed when the architecture is implemented. QUALIFIED RESEARCH COLLABORATION NOTICE Work TitleFractional Canonical Distribution: A Formal Mathematical Framework for Copyright Violation Suppression, Instance-Bound Completion Architecture, and Secure Physical Media Deployment AuthorLance Thomas DavidsonORCID: 0009-0006-1245-1644 Purpose of This Notice Researchers, engineers, and technical specialists who are interested in examining, evaluating, or extending the framework described in this publication are invited to make contact with the author. This work represents one component of a broader research portfolio currently under development. At this stage, the primary objective is engagement with qualified individuals who wish to interact with the model as a technical architecture, research artifact, or potential implementation framework. Fields of Interest Individuals with expertise in the following areas may find the model particularly relevant: • Cryptography• Cybersecurity• Distributed systems architecture• Secure hardware design• Information security engineering• Systems engineering• Computational mathematics• Software distribution infrastructure Nature of Engagement Interested parties may wish to participate in one or more of the following capacities: • Technical evaluation of the architecture• Stress-testing of the theoretical model• Identification of practical implementation pathways• Optimization of cryptographic or systems components• Cross-domain application of the framework• Formal academic critique or validation Collaboration and Authorship Individuals who provide meaningful contributions through analytical development, structural improvements, optimization of the internal logical architecture, or domain-specific extensions of the framework may be considered for formal acknowledgment or co-authorship, depending on the scope and significance of the contribution. Communication Requirement Prospective collaborators should contact the author prior to publishing derivative analyses, reinterpretations, or extensions of the model. This ensures that any collaborative engagement remains consistent with the licensing terms and preserves the structural integrity of the framework. Licensing Context This publication is distributed under a Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International License. The work may be shared in its original form with proper attribution but may not be modified or used for commercial purposes without the author’s explicit permission. Invitation Qualified researchers and technical practitioners who are interested in engaging with the model, exploring implementation strategies, or conducting rigorous technical review are encouraged to initiate direct communication with the author to discuss potential collaboration.