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Showing posts from August, 2026

From Bits to Shards: Relational Reconstruction as the Next Computational Primitive — A Secretary Suite Project

From Bits to Shards Relational Reconstruction as the Next Computational Primitive — A Secretary Suite Project John Swygert August 28, 2026 DOI: To be assigned Abstract Modern computing is built as a hierarchy of abstractions. Physical states support bits; bits are grouped into words and bytes; encoded values become characters, instructions, files, objects, databases, protocols, and increasingly semantic representations. Each layer succeeds by hiding lower-level detail while preserving relationships required by the layer above it. This paper positions Shards within that historical progression. A Shard is defined here not merely as a fragment of data, but as a compact, provenance-aware relational unit designed to support reconstruction of a larger informational object or state. The proposed shift is from asking how many bits must be transmitted to asking which relationships must be transmitted so that the receiver can reconstruct what is needed. This is not a replacement for bits, bytes,...

Relational Compression Mathematics: How Factors, Bases, Symbols, and Representations Reduce Complexity Through Reconstructable Structure

Relational Compression Mathematics How Factors, Bases, Symbols, and Representations Reduce Complexity Through Reconstructable Structure John Swygert August 28, 2026 DOI: To be assigned Abstract Mathematics is commonly described as a system for quantity, structure, space, and change. This paper develops a complementary view: much of mathematical usefulness can be understood as relational compression. A representation becomes powerful when it preserves consequential relationships while reducing the amount of explicit information required to reason, communicate, calculate, or reconstruct. Factors expose reusable multiplicative structure; positional bases reuse place relations; ratios collapse paired quantities into portable relations; geometric constructions encode spatial invariants; algebraic symbols compress families of operations; and digital computation demonstrates how extraordinarily rich representations can be built from minimal primitives. The familiar progression 2, 4, 8, 16, 32...

A Relational Analysis of Galilean Variance and the Verbelli-Searl Energy Framework: Using TSTOEAO as a Lens and Testing System for Unconventional Physical Claims

A Relational Analysis of Galilean Variance and the Verbelli-Searl Energy Framework Using TSTOEAO as a Lens and Testing System for Unconventional Physical Claims John Swygert August 28, 2026 DOI: [to be assigned] Abstract Jason Verbelli presents an unconventional physical program involving source-dependent light velocity, local absorption and re-emission, electron pairing as a possible origin of gravitation, patterned or coded magnetization, coherence, and the Searl Effect Generator (SEG) as an open-system converter of ambient environmental energy. These claims vary dramatically in evidentiary status. Patterned magnetization and spatially engineered magnetic force profiles are established engineering possibilities; the claimed SEG energy surplus, electron-pair gravity mechanism, and Galilean-variance alternative to relativity remain unestablished and require stringent experimental discrimination. This paper uses The Swygert Theory of Everything and All Other Things (TSTOEAO) not as an e...

The TSTOEAO Counterexample Challenge: A Formal Invitation to Identify a System That Violates the Proposed Relational Architecture of Natural Law

The TSTOEAO Counterexample Challenge A Formal Invitation to Identify a System That Violates the Proposed Relational Architecture of Natural Law John Swygert August 28, 2026 DOI: [to be assigned] Abstract The Swygert Theory of Everything and All Other Things (TSTOEAO) proposes that apparently disparate physical, biological, informational, computational, linguistic, planetary, ecological, and engineered systems can be described through a common relational architecture. Across the developing research program, this architecture has repeatedly been expressed through differences or gradients, relational boundaries, interaction, correction, cost, transformation, and movement toward or among equilibrium states. The framework does not claim that every system reaches an ideal equilibrium, nor that every particular hypothesis derived during an application of TSTOEAO must be correct. Rather, it proposes that observable states arise through constrained relationships and that the governing relationa...