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A New Way to Build Physics from Pure Logic

A plain-language version of “Computational Syntax of Reality”

2 min readNo jargon, no mathematicsPhysics

The short version

This paper proposes that reality is made of logical distinctions, not continuous space or matter. It uses two basic building blocks—"Mark" and "Void"—to derive particles, forces, and mass without starting from space or numbers.

Why Old Physics Hits a Wall

Current physics treats space and matter as smooth and continuous. This leads to infinite values that cannot be removed. The paper argues that smoothness is an illusion created by limited observers. A finite observer compresses infinite detail into what looks like continuous space. The paper proposes replacing continuous stuff with discrete logical relationships.

Two Building Blocks for Everything

The system uses only "Mark" and "Void." Mark means drawing a boundary. Void means no boundary. These are like the difference between "yes" and "no." All structures are built by putting Marks next to each other or inside each other. This replaces the idea of points in space with nested boundaries. The paper says this is enough to build all of physics without assuming space or numbers first.

Three Rules That Run the Universe

Three fixed rules govern how Marks change: Calling, Crossing, and Void elimination. Calling says two identical side-by-side Marks become one. Crossing says a boundary inside its own boundary cancels out. Void elimination says Void does nothing when combined with anything. These rules always lead to a single stable result, never loops or contradictions. This stability matches how physical particles stay the same over time.

How Particles Appear from Logic

Stable patterns of Marks act like particles. The simplest stable pattern acts like a photon. A deeper nested pattern acts like an electron. Patterns that survive the three rules match known particle types. Bosons and fermions differ by how their patterns swap places. The paper claims the graviton pattern cancels itself out entirely. This means gravity cannot be a particle in this system.

What This Says About Mass

Mass comes from how deeply nested a pattern is, measured by comparing four related boundaries. This measure stays the same no matter how you look at it. The paper says this generates mass values without putting numbers in by hand. It predicts small differences in how the Higgs particle interacts with other particles. It also predicts wiggles in the oldest light in the universe, with peaks at specific intervals.

What This Paper Does Not Show

The paper admits several limits. Current computers cannot simulate enough nesting depth for large-scale predictions. The mass measure uses an approximation, not pure geometry. Three-generation neutrino behavior remains unsolved. The paper does not fully connect its system to a complete theory using advanced number theory. These gaps require future work with better algorithms and more computing power.

Words used here

Cross-ratio
a way to compare four related boundaries that gives the same answer no matter how you view them, like finding which of four people is tallest relative to the others
Normal form
the simplest stable pattern that rules reduce to, like a final answer that cannot be simplified further
Renormalizable infinities
unwanted infinite values that appear when smooth physics breaks down at small scales
Ultrametric
a way to measure distance where going through a third point never makes the total path shorter, like a tree with no shortcuts between branches

Learn more in plain language

This plain-language version was written by an AI model from the text of the paper and checked against plain-language rules: everyday words, no mathematics, no unexplained names. It leaves details out and can still be wrong; the paper is the source of record. To report a problem, open the paper, select the passage and choose Report.

For specialists: the technical digest, quoted from the paper

In the paper's words

The persistent reliance on continuous, substance-based ontologies in theoretical physics has precipitated a crisis of non-renormalizable infinities, demanding a radical shift toward discrete relational foundations. By shifting to an epistemic foundation built entirely on a finite substrate of relational boundaries, the Syntactic Token Calculus (STC) organically replaces these problematic geometries. This manuscript formally establishes that physical reality is derived not from pre-existing scalar fields, but from the binary syntax of the ‘Mark’ and the ‘Void’, aligning seamlessly with multiway hypergraph models.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

  1. Lexicographical depth reduction guarantees that no recursive loops can infinitely cycle without resolution (Gorard & Arsiwalla, 2025).

    from 2.4 Confluence and Normal

  2. The standard four-token cross-ratio formulation perfectly captures projective equivalence classes within the discrete web (Anderson, 2018).

    from 2.5 Syntactic

  3. The up quark aligns with the depth-3 configuration ((M)M), generating a +2/3 relative invariant mark ratio (Gorard & Arsiwalla, 2025).

    from 3.4 The Quark Matrix

  4. Calculating a particle’s mass requires anchoring its topological depth against the asymptotic boundary scaling via the cross-ratio metric (Ostoma & Trushyk, 1998).

    from 4.1 The Relational Definition

  5. This vacuum condensate structure mathematically manifests as an infinite string of Void-canceling tokens that locally distorts interaction reduction paths (Minic, 2024).

    from 4.2 The Vacuum Condensate

  6. Enclosing a particle token with a juxtaposed vacuum mark mathematically increases its topological depth and shifts its cross-ratio logarithmically (‘t Hooft, 2015).

    from 4.3 The Mass Operator M(P)

How it is done

  1. This manuscript formally establishes that physical reality is derived not from pre-existing scalar fields, but from the binary syntax of the ‘Mark’ and the ‘Void’, aligning seamlessly with multiway hypergraph models.

    from Addressing

  2. This pure semiotic approach successfully eliminates all requirements for pre-existing vector spaces and scalar fields.

    from 2.1 The Act of Distinction:

  3. Verifying the causal integrity of these rules requires mathematical proof of confluence.

    from 2.3 The Universal Reduction

  4. This explicit proof ensures that the syntactic universe is free from causal paradoxes and temporal paradoxes.

    from 2.4 Confluence and Normal

What would falsify it

  1. Generating the exact generation filigree of the Standard Model requires linking discrete topological depth directly to observable mass scale metrics (Marchesano et al., 2024).

    from 1.5 Limitations in

  2. Particle-vacuum interaction is formalized via the Mass Operator, which physically translates topological depth into observable mass.

    from 4.3 The Mass Operator M(P)

  3. Deviations in Colliders The composite nature of the topological Higgs token guarantees fractional cross-ratio deviations observable in high-energy interactions.

    from 6.3 Higgs Coupling

Where the claim stops

  1. The algorithmic generation of the mass proxy metric successfully utilizes a continuous polynomial projection to approximate the pure geometric cross-ratio, representing an empirical interpolation bridging discrete networks to numerical geometry.

    from 7.4 Limitations of the

  2. While purists may highlight these approximation limitations, the structural soundness of the underlying deterministic logic remains computationally flawless.

    from 7.4 Limitations of the

  3. Standard paradigms assume infinite continuous background manifolds, struggling deeply with absolute background dependence and non-renormalizable infinities (Whitworth, 2018).

    from 1.1 Context and Motivation

Where to read

  1. Addressing230 words · 1 min
  2. 1.0 Introduction &846 words · 4 min
  3. 2.0 Foundational Syntax &786 words · 3 min
  4. 3.0 Emergence of the833 words · 4 min
  5. 4.0 Mass Invariants &886 words · 4 min
  6. 5.0 Cosmology and867 words · 4 min
  7. 6.0 Discussion and Empirical867 words · 4 min
  8. 7.0 Conclusion & Systemic864 words · 4 min
  9. Appendices663 words · 3 min

Read from the paper itself: 68 sections, 7,127 words. Nothing in this digest is written by a model; a line that is not a sentence of the paper is not shown. Have a specific question? Ask this paper.

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