A discrete relational model built from local difference, rotation, and closure — k-Flip Theory (A–E)

Abstract

Dear Researcher, I am sharing a working research archive titled k-Flip Theory, now available on Zenodo as a five-part set (A–E). The project began from a deliberately simple question: If two physical contributions cancel to zero, what exactly has disappeared? The working premise is that zero net value need not erase the fact that a difference, interaction, or ordered history occurred. In the language used throughout the project: “What disappeared was only the total. The event in which the two differed has already happened.” From this starting point, the project develops a small executable relational kernel rather than beginning with particles, spacetime coordinates, or a predefined metric. The current CORE uses twelve signed local sockets, which reduce operationally to six independent axes. Each local interaction is implemented through an explicit act/respond contract: an action changes only the acting node’s own state, while opening a legal response for the counterpart. No node directly writes another node’s internal state. The kernel itself contains no primitive position, metric distance, velocity, physical clock, or continuous spacetime. These quantities are deliberately left to downstream physical “readers.” Despite this minimal construction, several nontrivial structures appear in exhaustive tests. In particular, 60° operation pairs are noncommutative while coaxial and 90° supports behave differently; some histories require unavoidable repair work beyond the minimum reciprocal cycle; and certain relations can enter a sealed state in which the relation remains part of the history but future reactivation becomes inaccessible. These structures are treated as computational results of the kernel, not as physical identifications by themselves. The accompanying volumes then ask whether familiar physical phenomena can be read from this same relational grammar. Part A develops the underlying relational and geometric grammar. Part B is an explicitly unfinished quantum investigation centered on interference, measurement, Bell/CHSH structure, and the significance of the sequence \(2 \rightarrow 2\sqrt{2} \rightarrow 4\). Part C explores particle and composite interpretations, including recurrent K2-like structures, hadron-like closure, femtometer-scale effective separation, and twisted-exchange reconfiguration as a possible alternative to a primitive “cut” operation. Part D investigates gravity as a change in the mapping from CORE history to physical metric and clock observables, rather than as literal contraction of a microscopic spatial lattice. Its present candidate uses a local reader-conversion factor \(q(x)\), with gravitational time dilation, path geometry, and frequency shift retained as acceptance tests rather than assumed consequences. A central theme emerging from the work is that vacuum and matter may not require different microscopic rules. The present reader hypothesis treats vacuum as an active balanced state in which relational differences continue to update while macroscopic residue cancels, whereas matter may correspond to bounded relational closures in which difference becomes trapped in a recurrent topology. The project is highly speculative and is not presented as an established physical theory. The distinction between executable CORE results, reader-level hypotheses, unresolved questions, and discarded models is maintained throughout the archive. In fact, failed hypotheses and negative results are intentionally preserved because the project was developed as a forensic record: models may die while the questions that produced them remain useful. I am particularly interested in independent criticism from researchers in discrete physics, foundations of quantum mechanics, lattice/network models, quantum information, and gravitation. The most useful response would not be agreement, but identification of hidden assumptions, mathematical equivalences to known structures, decisive counterexamples, or small computational tests that could falsify the remaining hypotheses.