The Omnisyndetic Framework is an open access research programme and alternative formalism.
The fundamental move of the framework, and its motive, is an exploration of an inversion of the formal logic predicate assumption that identity is fundamental.
Here we explore the idea that it is not, and what structures may be mathematically and logically reasoned by treating identity not as the first, but its resolve through the negotiation of equality into inequality, while identity can be classified and catalogued into non-self-asserting modes of distinction.
This website serves as a central interactive hub where the published works, tools, archives, registers and pre-papers are available completely for free in transparent access, such that anyone can dive in, audit, reproduce, and pick up the work for themselves.
Across the website are a number of calculators, interactive demonstrations, and tools that show where this ongoing program is going.
Thus far, in exploring this question, we have reasoned a first-order logic system that is able to be used as a diagnostic tool to preemptively identify and filter paradoxes from resolvable statements, showing examples of simple Curry and Gödel-like incompleteness forms and statements that are separated into three distinct categories:
From there, the work has moved into a formal geometric register, diagnosing and filtering structures that are able to individuate into resolved identity from those that fundamentally can't.
Interestingly, in exploring this question, the geometry set discovered a forced geometric derivation that, when read directly, can recount the symmetry group bookkeeping unit state space, flavor hypercharge, and isospin, combined with an energy ledger derived from the same commitments in exploring this very simple question and inversion.
The geometry has been shown to be able to classify and structure baryons into predetermined margins, recovering and accurately classifying the spin one half ground states of base flavor combinations and their immediate spin three half lowest lying resonances into their quantified predicted bounds as a pure geometry-based derivation readout.
Giving us what effectively appears to be a functioning, pre-dynamical catalog system, but the most important and interesting result is that as shown, this work was the product of a linear derivation of entirely forced, rigid geometric constructions.
The covenant commitment with the question means that the use of tensors, coefficients, or non-geometrically derived constants and limits are strictly forbidden, as these would violate the base commitment by depending on essentialism.
This means that the mathematics and geometry shown here, though elementary and primarily using only simple forms of algebra and trigonometry, are incredibly overdetermined and forced by the constructional nature of the question itself, Meaning that the classification system discovered is an overdetermined system that began not by trying to fit to PDG masses, but by applying a formal logic set for identifying paradoxes, and instead returns that these base constructions are the only admissible forms of structure.
The work is metaphysically motivated, yes, but the approach to the work is non-speculative. It is, a genuine exploration, used to discover the structural consequences of this simple inversion.
For anyone interested in pre-dynamical or geometric explanations, alternative formalism within logical foundations, or more generally in relational ontology, then this website is aimed and designed for you.
Accessibility is incredibly important to us and to the integrity of the Project. To aid and help with this, the website has been designed to be visually colourful and interactive.
Though highly technical, this has been done with neurodiversity and reading styles in mind. As such, the website contains a searchable glossary, but there are also colour coded printout versions of the glossary uploaded to the archives that can be directly referenced through their DOI on the Open Science Framework.
The work is public with a share-alike licence, meaning anyone who enters it, if this forms a part of your work or your later reasoning, please stay committed to the open access transparency commitment that this paper moves and establishes with.
All of this is opened and offered entirely for free, completely transparently, and the work is conducted without funding.
Anyone is welcome to join, question, and think along with it. For anyone entering the work and wanting to know where to begin, the best place to start is with the interactive calculators and geometric derivations themselves.
They're completely navigable from within the website, but they are mainly hosted on the archives for formal citation and reference on the Open Science Framework.
You can also find interactive downloadable calculators in the archives as well as the project GitHub of the exploration.
The lineage of this question can be found primarily in a coherence theory of truth, structuralism, process philosophers such as Alfred Whitehead, George Spencer Brown, Gilbert Simondon and finally Gödel, whose work on self-settlement and assertion in formal systems have heavily influenced the language and terminology used throughout the framework.
To anyone who has found the website and has taken the time to explore and look, thank you. A great deal of time has been put into presenting all of this work, designing, building the calculators, diagrams, interactive tools, as well as the formal register work and volumes.