Flux-System: A Deterministic Symbolic Rewrite Algebra (Version 1.2)

Flux-System: A Deterministic Symbolic Rewrite Algebra (Version 1.2) Flux-System is a formal symbolic rewrite algebra built from four primitive symbols: ▮ Hold, ◈ Spark, ⨀ Pulse, and · Gap. The system is governed by two rewrite rules: Fusion: ◈◈ → ▮Fission: ⨀▮ → ◈◈ Using deterministic leftmost-first reduction, finite symbolic configurations reduce to stable normal forms. The resulting stable language consists of words that avoid the substrings ◈◈ and ⨀▮. This archive contains the main research paper, theorem and proof notes, validation reports, machine-readable verification results, reproducible source code, metadata files, citation files, and supporting documentation. Validated properties documented in this package include deterministic reduction, stable normal forms, spark parity invariance, non-associativity, gap factorization, connected normal-form enumeration, recurrence verification, and bounded cycle searches. The Flux-System is presented as a formal symbolic and combinatorial structure. No physical, engineering, experimental, or scientific claims are made beyond the mathematical rewrite system itself. This record represents the first public archival release of the Flux-System and includes the organized Version 1.2 evidence package. Author: Abraham Joseph HealdAffiliation: Independent Researcher, Sterling, Illinois, USA Copyright © 2026 Abraham Joseph Heald. All Rights Reserved.