Computo Ergo Sum

In the paper's words

This paper resolves Hilbert’s sixth problem by introducing the Self-Computing Universe Framework (𝒞), a meta-axiomatic system positing that the universe is not merely described by mathematics but is a self-executing mathematical structure. While its six foundational axioms are expressed with the static syntax of set theory for definitional rigor, their dynamic execution is described by the process-based semantics of category theory. The framework demonstrates that spacetime is an emergent property of a discrete causal set (Axioms C1, C2), exhibiting a spectral dimension that flows from 4D to 2D at the Planck scale, thereby providing a natural resolution to the cosmological constant problem.

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

Numbers it reports

1. Representing this space with reasonable fidelity might require on the order of 10,000 logical qubits , a scale that is the target for future fault-tolerant quantum computers (expected in the 2030s-2040s).

   from 11.2 A Roadmap for

2. No fine-tuning is needed—the 120 orders of magnitude discrepancy vanish naturally because the fundamental UV theory is not a 4D theory in the first place, but rather a 2D-like structure at its most fundamental level.

   from 10.1 Organic

3. 11.2.3.2 Methodology: Encode $\mathcal{K}_6$‘s Moduli Space (e.g., 10,000 Qubits for 100 Complex Dimensions) The methodology for such a simulation presents a formidable challenge but is conceptually straightforward.

   from 11.2 A Roadmap for

4. 11.3.3 Compute the Cosmological Constant ($\Lambda$) within 1% Error Another significant computational goal is to utilize the framework’s spectral dimension flow mechanism to compute the observed value of the cosmological constant, $\Lambda$, with a precision that matches or exceeds cosmological measurements (e.g., within 1% error).

   from 11.3

5. The Area Law of Entropy ($S=A/4$) (Bekenstein, 1973; Hawking, 1974) is a direct physical manifestation of this axiom at event horizons.

   from 2.2.0 The Formal Axioms of Framework 𝒞 |

6. The Area Law of Entropy states that the maximum entropy ($S$) within any spacetime region is proportional to the area ($A$) of its boundary, represented as $S = A/4$ in natural units (Bekenstein, 1973; Hawking, 1974).

   from 4.3.0 Emergent Quantum Field Theory (QFT) and General

How it is done

1. Ultimately, Computo Ergo Sum argues that the universe is a self-proving theorem whose existence is synonymous with its own logical coherence, where foundational limits like the no-cloning theorem and Gödelian incompleteness are necessary structural imperatives of the cosmic computation.

   from Computo

2. This methodical approach underscored Hilbert’s desire for a foundational restructuring of physics, akin to the successful axiomatization of geometry.

   from 1.1.0 Hilbert’s Original Vision for an Axiomatic Physics |

3. This inherent quantum contextuality , rigorously proven by the Kochen-Specker theorem (Kochen & Specker, 1967) and confirmed by experimental violations of Bell inequalities (Aspect, 1982), underscored the inadequacy of classical probability and its underlying Boolean logic to describe quantum reality.

   from 1.2.0 The Quantum Schism and the Crisis of Classical Logic |

4. The six meta-axioms of 𝒞 are formally expressed using the language of set theory.

   from 1.3.0 Thesis: The Universe as a Self-Executing Axiomatic

What would falsify it

1. This section provides a detailed summary of current empirical evidence that robustly supports Framework 𝒞, alongside specific, falsifiable predictions that can be tested with existing data or current-generation experimental and observational programs.

   from 6.0 Empirical Validation and Falsifiability |

2. Each point of evidence and each prediction is explicitly linked to the foundational axioms and derived theorems of the framework, demonstrating how its abstract principles connect directly to measurable reality.

   from 6.0 Empirical Validation and Falsifiability |

3. Falsification) The framework presents specific, falsifiable predictions that form the core of its empirical program, directly testing its foundational axioms and theorems.

   from 6.2.0 Falsifiable Predictions (The Four Pillars of

Where the claim stops

1. Quantum events do not form a Boolean algebra, which is the foundational structure of classical logic and probability; instead, they form a non-distributive lattice of projection operators .

   from 1.2.0 The Quantum Schism and the Crisis of Classical Logic |

2. This implies that the logical operations on quantum events, such as those concerning incompatible observables like position and momentum, do not behave like classical propositions.

   from 1.2.0 The Quantum Schism and the Crisis of Classical Logic |

3. However, the universe is not a static blueprint; it is a dynamic computation.

   from 1.3.0 Thesis: The Universe as a Self-Executing Axiomatic

Where to read

1. 1.0 Preamble: The Modern Mandate for a Unified Science |938 words · 4 min
2. 2.0 The Meta-Axiomatic Foundation (Framework 𝒞) |3,394 words · 15 min
3. 3.0 Mathematical Validation and Computational Realization |1,400 words · 6 min
4. 4.0 Derivation of Known Physics (Radical Emergence) |3,870 words · 17 min
5. 5.0 Philosophical and Ontological Implications |1,141 words · 5 min
6. 6.0 Empirical Validation and Falsifiability |1,292 words · 6 min
7. 7.0 Conclusion: The Universe as a Living Theorem |340 words · 1 min
8. 8.0 Deep2,100 words · 9 min
9. 9.0 Appendix A: Advanced Categorical and Geometric10,466 words · 46 min
10. 10.03,060 words · 13 min
11. 11.02,660 words · 12 min
12. 12.0 Appendix D: References767 words · 3 min