NEW LANGUAGE FOR MATH

In the paper's words

This report presents a fundamental reframing of Causal Set Theory (CST) within the language of category theory, establishing a relational process ontology (RPO) for fundamental physics. By recasting causal sets as small, thin categories, this framework achieves a categorical reification of causality, where causal relations (morphisms) become ontologically primary to events (objects). The dynamics of spacetime growth are modeled as a quantum sequential growth functor, leading to a functorial path integral whose measure is canonically defined by a Kan extension, resolving a key ambiguity in quantum gravity.

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

Numbers it reports

1. This aligns with Axiom IV (Skeletality) from Part II (Section 2.1.3.4), where causally indistinguishable events are identical. $\quad$ Built-in Occam’s Razor: The weighting factor $1/|\text{Aut}(\mathcal{C})|$ means that highly symmetric, simple histories (those with a large automorphism group, $|\text{Aut}(\mathcal{C})|$) are weighted less heavily in the sum, while complex, asymmetric histories (with a small automorphism group) are weighted more.

   from 4.3.

2. It ensures that the path integral correctly accounts for the indistinguishability of fundamental spacetime atoms (as per Axiom IV in Part II, Section 2.1.3.4), providing a deep physical rationale for this otherwise arbitrary-looking factor.

   from 4.3.

3. This is often referred to as the “entropy problem” (Section 1.1.3.3).

   from 5.1. The

4. For example, numerical analysis suggests that in four dimensions, if the discreteness scale $\ell$ is greater than approximately $1.136$ times the Planck length ($\ell_p$), the suppression factor for these pathological histories can be astronomically large, on the order of $\exp(-10^{260})$ for a cosmologically-sized universe.

   from 5.1. The

5. In the continuum limit (as $N \to \infty$), by the Law of Large Numbers , this combinatorial ratio is conjectured to converge to the squared amplitude: $$ P(A) = \frac{\text{Total \# paths to } A}{\text{Total \# paths}} \to |\langle A \mid \psi \rangle|^2 \quad (8.2.2.3.1) $$ This is a statistical derivation: it is the frequency of actualized paths in the ensemble of all possibilities that gives rise to the quantum probability.

   from 8.2.

How it is done

1. Yet even standard Causal Set Theory remains grounded in set-theoretic foundations, formally defining a causet as a pair comprising a set and a binary relation.

   from Part

2. Its critical role in determining spacetime conformal geometry is rigorously established by Malament’s Theorem, which demonstrates that the causal structure of a spacetime manifold uniquely determines its conformal metric.

   from 1.1.

3. As demonstrated in “Computo Ergo Sum” (Quni-Gudzinas, 2025a), this aligns with the view of physical laws as immanent theorems, where processes are the fundamental “proof steps” of reality.

   from 1.2.

4. II: The Causal Category: Reifying Causality as the Fundamental Relational Substrate This part formally introduces the core mathematical object of the reframed theory: the Causal Category ($\mathcal{C}$) .

   from Part

What would falsify it

1. This categorical RPO thus offers a unified, falsifiable, and conceptually coherent foundation for a background-independent theory of quantum gravity.

   from A

2. The Distinction Between Methodological and Ontological Relationalism Standard Causal Set Theory successfully achieves methodological relationalism , where observable quantities are defined purely by relations between events.

   from 1.1.

3. In CST, the lack of a canonical quantum measure for the path integral over causal histories leads to arbitrary weighting choices, which can yield unphysical results or prevent robust calculation and prediction, hindering the theory’s predictive power.

   from 1.1.

Where the claim stops

1. The Legacy and Limitations of Standard Causal Set Theory The established framework of Causal Set Theory, despite its successes, carries inherent limitations stemming from its foundational assumptions.

   from 1.1.

2. This principle posits that the number of causal set elements within a region is approximately proportional to the continuous volume of that region, expressed as $N \approx \rho V$.

   from 1.1.

3. It also sidesteps issues such as Weyl’s tile argument , which highlights inconsistencies when attempting to approximate continuous geometry with discrete, rigid units.

   from 1.1.

Where to read

1. Part3,556 words · 15 min
2. Part2,659 words · 12 min
3. Part3,289 words · 14 min
4. Part2,813 words · 12 min
5. Part3,586 words · 16 min
6. Part3,023 words · 13 min
7. Part2,848 words · 12 min
8. Part3,123 words · 14 min
9. Part2,891 words · 13 min
10. Part3,277 words · 14 min
11. 11.0 References739 words · 3 min
12. 12.0 Appendices2,263 words · 10 min