Finite Specification, Ontological Indeterminism: The Gisin–Del Santo Program Converges with Autaxys Ontological Closure

In the paper's words

We examine the Gisin--Del Santo program on finite-precision physics and its convergence with the Autaxys Ontological Closure (OC) framework. The Gisin--Del Santo program argues that (1) physical quantities contain only finite information, (2) real numbers are physically unreal --- they are de facto hidden variables of classical mechanics, (3) consequently, classical mechanics is ontologically indeterministic, and (4) this classical indeterminism explains many features traditionally attributed to quantum mechanics. We show that the OC framework, independently derived from D/R procedure operationalism, converges on identical structural conclusions: finite specification implies ontological openness, and real numbers beyond a computable modulus of convergence are not physically real.

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. We show that the OC framework, independently derived from D/R procedure operationalism, converges on identical structural conclusions: finite specification implies ontological openness, and real numbers beyond a computable modulus of convergence are not physically real.

   from Abstract

2. OC holds that a quantity is physically real only if there exists a finite Turing-machine protocol that approximates it with a computable modulus of convergence, yielding measurement-distinguishable predictions [10].

   from 1. Introduction

3. Van der Lugt's Chapter 5 proposes an alternative: a classical-mathematics formalism using "domains of indeterminacy" --- open covers that represent the precision bound at each moment, with indeterminism arising from the choice of which open set a trajectory falls into when it crosses a domain boundary.

   from 2.3 Intuitionistic Mathematics and Physics

4. The OC framework [10] provides an operational criterion for physical reality: A quantity is physically real only if there exists a finite Turing-machine protocol --- a Determination/Resolution (D/R) procedure --- that approximates it with a computable modulus of convergence, yielding measurement-distinguishable predictions.

   from 3.1 Core Principle

What would falsify it

1. Neither the Gisin--Del Santo program nor the OC framework has produced a differential empirical prediction --- something that would be observed if the framework is correct but not if standard physics is correct.

   from R5: No Experimental Predictions [5/5] [HIGH]

2. Chaotic system predictability: The link between chaos and finite precision formalizes in-principle limits on long-range prediction.

   from 7.2 Practical Applications

Where the claim stops

1. Generalizing to Hamiltonian mechanics on symplectic manifolds, relativistic field theory, or quantum field theory is an open problem.

   from R4: Scaling Limitations [3/5] [MEDIUM]

2. The toy-model nature of the van der Lugt formalism is a limitation, not a failure.

   from R4: Scaling Limitations [3/5] [MEDIUM]

3. But this relationship carries an implicit risk: mathematical structures developed independently of physics may, when applied to physical theories, introduce ontological commitments that nature does not honor.

   from 1. Introduction

Where to read

1. 1. Introduction411 words · 2 min
2. 2. The Gisin--Del Santo Program504 words · 2 min
3. 3. Autaxys Ontological Closure (OC)251 words · 1 min
4. 4. Seven Convergent Theses739 words · 3 min
5. 5. Cross-Domain Consilience177 words · 1 min
6. 6. Critical Caveats and Red-Team Findings403 words · 2 min
7. 7. Conclusion and Open Questions256 words · 1 min
8. Declarations152 words · 1 min