The Boson/Fermion Distinction: Spin-Statistics as Structural Invariant

In the paper's words

The textbook dichotomy between bosons and fermions is commonly presented as a primitive classification of nature. This paper argues that the dichotomy is a derived, dimension-dependent shadow of a single structural relation: the exchange phase of identical particles equals their topological spin, R = e^{2pi is}. The relation holds across relativistic quantum field theory, topological field theory, and condensed-matter anyon systems; dimension enters only by quantizing the allowed values of the spin parameter.

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

Numbers it reports

No sentence of this paper reports a figure with a unit or a quantity word, so none is shown.

How it is done

1. The textbook dichotomy between bosons and fermions is commonly presented as a primitive classification of nature, with the spin-statistics theorem as its iron law.

   from Abstract

2. The spin-statistics theorem states which sign is realized: $\eta = (-1)^{2s}$, where $s$ is the spin (Pauli, 1940; Duck and Sudarshan, 1998). [ESTABLISHED] This paper makes two claims.

   from 1. Introduction

3. The pre-registered derivation program (T1–T3) carries falsifiability conditions (F1, F2′), and — unusually — the decisive test has already been run , honestly, with a mechanism: the abelian-pair postulate is ASSUMED (definitive — scalar exchange follows from abelianity; the calculus does not deliver it), and involutivity ($\sigma^2 = 1$) is a condition on the target category (symmetric, or Temperley–Lieb at $A^4 = 1$), not a theorem of the calculus (verified by executed code in the rigor-pass cycle).

   from 2. So What? Why Should a Reader Care About This Research?

4. The spin-statistics theorem is about the symmetry of the joint state of two identical marks under exchange; the calculus provides a phase for a single mark under rotation, but never constructs the exchange of two marks.

   from 5. The calculus of distinctions and its silent assumption

What would falsify it

1. If a stable, local, relativistic excitation in $3{+}1$ dimensions is observed with exchange phase $\eta \neq e^{2\pi i s}$ — for example, a spin-$\tfrac{1}{2}$ particle obeying Bose-Einstein statistics, or a spin-$0$ particle obeying Fermi-Dirac statistics — the claim that $R = e^{2\pi i s}$ is the universal invariant is disconfirmed.

   from 7. Falsifiability conditions

2. If the mark calculus cannot reproduce the two one-dimensional representations of $S_n$ (trivial and sign) from the primitive distinction, compact closure, an involutive braiding, and the abelian-pair postulate alone — without importing microcausality, Lorentz structure, or any other physical postulate — the derivation program is disconfirmed, and the monograph's spin-statistics claim stands as an asserted correspondence.

   from 7. Falsifiability conditions

3. F2 as written above is disconfirmed in its strong form and is restated as follows.

   from 7. Falsifiability conditions

Where the claim stops

1. The paper formalizes the required construction — two modal exponentials (symmetric and exterior), the braiding of two marks in a compact closed category (with the abelian-pair postulate made explicit), and the ribbon condition linking twist to exchange — and states the falsifiability conditions under which the derivation program succeeds or fails. [NOT YET EVIDENCE] The derivation is pre-registered here; it is not yet executed.

   from Abstract

2. Second, a distinction-based foundation of physics — a calculus whose only primitive is the act of drawing a boundary — must, to claim the spin-statistics connection, derive exchange statistics from the primitive; the current state of that program contains a silent assumption that this paper identifies and replaces with a concrete derivation target.

   from 1. Introduction

3. The boson/fermion dichotomy is an input to every quantum theory: chemistry, the standard model, and condensed matter all assume it.

   from 2. So What? Why Should a Reader Care About This Research?

Where to read

1. Abstract242 words · 1 min
2. 1. Introduction175 words · 1 min
3. 2. So What? Why Should a Reader Care About This Research?675 words · 3 min
4. 3. The invariant: exchange phase equals topological spin159 words · 1 min
5. 3.1 The 3+1D shadow55 words · 1 min
6. 3.2 The 2+1D generalization52 words · 1 min
7. 3.3 What is invariant50 words · 1 min
8. 4. Dimension quantization: bosons and fermions as a 3+1D shadow126 words · 1 min
9. 5. The calculus of distinctions and its silent assumption237 words · 1 min
10. 6. A derivation program580 words · 3 min
11. 7. Falsifiability conditions520 words · 2 min
12. 8. Relation to existing programs176 words · 1 min