Destructuring Physics: A functional derivation of spacetime

Ettore Minguzzi

REVIEW 4 major objections 3 minor 44 references

Destructuring Physics: A functional derivation of spacetime

T0 review · 4 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Spacetime may be nothing more than functions on a set

desk verdict The abstract is readable and intriguing; the full text in our copy is corrupted, and the real test is whether the initial topology recovers the manifold topology and upper semi-continuity. read the letter →

arxiv 2508.11949 v1 pith:53AWYWQO submitted 2025-08-16 gr-qc

Ettore Minguzzi This is my paper · ORCID

classification gr-qc MSC 53C5083C7554E15 PACS 04.20.-q

keywords minimalspacetimestructurestableLorentziandistancesteeptimefunctionsfunctionalderivationcausalarbitrarysetformulaquasi-uniformities

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that physics can be formulated with minimal mathematical structure, and proposes that spacetime itself is one such minimal object: an arbitrary set equipped with a family of real-valued functions. Using the stable Lorentzian distance framework as a reference, the author shows how the properties of stable distances and steep time functions can be abstracted into conditions on a family of functions. The central claim is that this functional representation preserves the most fundamental physical properties of spacetime: causal order, topology, and metric information. If correct, this would mean that the full apparatus of Lorentzian geometry can be derived from a strikingly lean primitive.

What carries the argument

The central mechanism is the functional representation of a stable spacetime by a family of upper semi-continuous Lorentzian distances and steep time functions, followed by the abstraction of that representation to an arbitrary set. The family of functions carries the causal, topological, and metric content: causality can be read off from which functions remain ordered along timelike curves, and the Lorentzian distance can be reconstructed from a sup formula over target functions (the Lorentzian distance formula).

What would settle it

Exhibit an arbitrary set with a family of functions meeting the proposed axioms whose induced causal order and topology cannot be reproduced by any stable Lorentzian distance on any manifold. If such an example exists, the claim that the function family faithfully preserves spacetime structure would be disproved.

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Extended reading notes

Core claim

The paper's central claim is that spacetime can be introduced in a general and minimalistic way as nothing more than a family of functions defined over an arbitrary set. The author takes the stable Lorentzian distance framework as the reference: stable spacetimes admit an upper semi-continuous Lorentzian distance and steep time functions. Abstracting from these, the paper defines spacetime as a set $X$ together with a family of real-valued functions that reproduce the essential causal, topological, and metric features. The discovery is that this family-of-functions structure is not a weakened toy model but is claimed to preserve the fundamental physical properties of spacetime.

Load-bearing premise

The stable Lorentzian distance framework, including upper semi-continuous distances and steep time functions, is assumed to capture all physically essential spacetime structure, so that the family-of-functions abstraction is faithful.

Editorial extensions

If this is right

If the claim is correct, foundational physics need not presuppose a manifold; the metric and causal structure become derived properties of a function family.
The minimal description may help quantum-gravity approaches that discretize spacetime, since arbitrary sets with function families are natural for combinatorial or causal-set models.
The representation could unify causality and topology under a single functional language, making it possible to define continuity and causal order from the same data.
Existing results on stable Lorentzian distances, such as the existence of steep time functions, would carry over to the abstraction and provide a ready-made toolkit.
The Lorentzian distance formula itself emerges as a primary object, potentially more fundamental than the metric tensor.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the functional representation is truly equivalent to stable Lorentzian geometry, the continuum manifold structure of general relativity may be an emergent effective description rather than a primitive input; this could be tested by formulating Einstein dynamics directly in the function-family language.
The abstraction might provide a bridge to causal set theory: a family of functions on a locally finite set could encode order information and serve as a dictionary between causal sets and Lorentzian manifolds.
A potential extension is to relax the 'stable' assumption and ask whether every globally hyperbolic spacetime, not just stable ones, admits a faithful functional representation; the answer likely requires additional axioms on the function family.
A concrete next step would be to state the Einstein field equations purely as conditions on the family of functions (e.g., as equations for the distance poles), which would test whether the minimal arena is computationally viable.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The abstract is the only readable part of the file I have; the body is mojibake and the file ends with a header from a different arXiv paper. So any judgment is provisional. But the abstract alone is enough to see what is being claimed and where the soft spot will be.

Minguzzi proposes that a stable Lorentzian spacetime can be reduced to an arbitrary set X plus a family of real-valued functions F. This is genuinely minimal: no manifold, no metric tensor, no assumed topology. The abstract situates the proposal within his prior program (stable distances, steep time functions, the product trick) and says the new notion is built "as a reference" to that framework. If the derivation works, this is a useful conceptual step for quantum gravity and singularity theory. Credit where due: the author knows the literature, the line of attack is coherent, and the goal—find the least structure that preserves causal and metric information—is well motivated.

The soft spot is exactly the one the stress-test note identifies. Upper semi-continuity is defined relative to a topology. On an arbitrary set, the only canonical topology is the initial topology generated by F. The abstract claims topological and metric information is preserved but never states that this initial topology equals the manifold topology, or that the reconstructed distance is upper semi-continuous in it. That is not a technicality: if the initial topology is coarser than the manifold topology, steep functions need not be continuous; if finer, you get spurious discontinuities. Stability lives in that topological property. So the "arbitrary set" framing can silently drop physical content unless the paper proves both statements. The reader's circularity score of 5 is also fair in a milder form: if F is chosen to encode the stable distance's properties, preservation holds by construction rather than as a new result. The paper needs to show the functions are not just a recoding.

A second issue is that the abstract gives no conditions on F. Can any family of functions represent a spacetime, or must they satisfy a stability axiom? Without that, the claim "nothing more than a family of functions" is too broad.

The idea is plausible, the framing is honest, but the full text is unreadable in my copy and the topology-recovery problem is load-bearing. I would send it to peer review—a referee with the actual PDF can check whether the initial topology and upper semi-continuity are handled. I would not cite it until I can read the proof. It is a "maybe" for the reading group.

Recommendation: accept for peer review; the paper deserves referee time, but the referee should focus tightly on the topology gap and on whether the minimal structure is genuinely minimal or a repackaging of stable distances.

Referee Report

4 major / 3 minor

Summary. The paper proposes a minimal notion of spacetime as an arbitrary set X together with a family F of real-valued functions. It motivates this by reviewing previous work on measure closed ordered spaces, quasi-uniformities, the product trick, upper semi-continuous (stable) Lorentzian distances, steep time functions, and a Lorentzian distance formula. Using the properties of the stable distance over stable spacetimes as a reference, the author argues that spacetime can be introduced as (X,F) while preserving its most fundamental physical properties, including causal, topological, and metric information. The abstract states this conclusion but gives no equations, definitions, proof outline, or explicit conditions on F. The supplied full text is corrupted and unreadable, so the derivation cannot be checked.

Significance. If the result holds, it would provide a striking conceptual simplification: spacetime as a mere function family over an arbitrary set, unifying causality, topology, and metricity. The paper connects to concrete prior constructions (stable Lorentzian distances, steep time functions) rather than pure speculation, which is a strength. However, the significance is conditional and currently unverified: the abstract alone does not establish the preservation claim, and no machine-checked proofs or reproducible derivations are visible in the available material. The paper's value cannot be assessed without a readable, rigorous technical development.

major comments (4)

[Abstract] The central claim is asserted without formal statement. The abstract says spacetime can be introduced as 'a family of functions defined over an arbitrary set' and that this 'preserves its most fundamental physical properties,' but it does not define those properties, the allowed function families, or the sense of preservation. No theorem or proof outline is given. This is load-bearing because the entire paper is the derivation of this claim.
[Abstract / Topology-stability gap] The reference framework includes upper semi-continuous (stable) Lorentzian distances, a property defined relative to a topology. In the proposed (X,F) arena, the only canonical topology is the initial topology τ_F generated by F. The abstract does not state or prove that τ_F reproduces the manifold topology when (X,F) is derived from a stable spacetime, nor that the reconstructed distance is upper semi-continuous with respect to τ_F. If τ_F is coarser, steep time functions need not be continuous and stability may be lost; if finer, non-physical discontinuities can be introduced. Without addressing this, the preservation claim is unsupported.
[Abstract / Potential circularity] The new notion is introduced 'using the properties of the stable distance over stable spacetimes as a reference.' If the function family F is chosen to encode exactly the causal, topological, and metric properties one later claims are preserved, then the preservation statement may be true by construction rather than as a substantive result. The manuscript needs to rule out this circular reading: for example, by specifying independent axioms on F that do not presuppose a target spacetime, or by showing that the construction is not selective.
[Full text] The body of the manuscript as provided is corrupted (mojibake) and unreadable. I cannot verify any specific definition, equation, theorem, or proof. This is not a routine typo but a complete barrier to technical assessment. I flag it explicitly per the reviewing instructions. A clean, readable version is necessary before the derivation can be evaluated.

minor comments (3)

[Abstract] Terms such as 'upper semi-continuous (stable) Lorentzian distances' and 'steep time functions' are used without definition or reference. A brief gloss or citations to the author's prior work would help readers outside this specific line of research.
[Abstract] The phrase 'several research directions explored in previous work' is vague. A numbered list of the relevant papers would improve traceability and allow the reader to locate the referenced constructions.
[Title] The title 'Destructuring Physics' is evocative but not informative about the content. A more descriptive subtitle, such as 'A functional derivation of spacetime via stable distances,' would better signal the topic.

Circularity Check

1 steps flagged · score 6.0 of 10

The new notion is defined by reference to the stable-distance framework, so its preservation claim is inherited from the design input.

self definitional [Abstract, second paragraph]
"Subsequently, the properties of the stable distance over stable spacetimes are used as a reference to propose a simplified, abstract notion of spacetime. The discussion shows that spacetime can be introduced in a general and minimalistic way as nothing more than a family of functions defined over an arbitrary set. This abstraction removes unnecessary mathematical complexity, reducing spacetime to its essential elements while preserving its most fundamental physical properties."

The minimal notion (X,F) is explicitly proposed by taking the stable Lorentzian distance properties as the reference. If 'most fundamental physical properties' are identified with the properties of the stable-distance framework, then the claim that (X,F) preserves them is built into the construction: the family of functions is chosen to encode exactly those reference properties. The abstract provides no independent derivation that would establish preservation without assuming the reference framework, so the central preservation claim reduces by construction to the input used to design the abstraction.

full rationale

The readable portion of the paper is the abstract. It states that the new spacetime notion is proposed 'using the properties of the stable distance over stable spacetimes as a reference.' The concluding claim that this abstraction 'preserves its most fundamental physical properties' therefore appears to be a restatement of the design constraint rather than an independent result, unless a separate representation theorem is supplied elsewhere. No such theorem or independent axiom set for (X,F) is visible in the quoted material. The topology/stability gap raised in the reader's note is a correctness concern, not a circularity concern, and cannot be evaluated without the full definitions. Because the preservation claim is asserted to follow from the reference framework by construction, the circularity score is 6; if the full paper proves an independent equivalence between arbitrary (X,F) and stable spacetimes, the score would need to be lowered.

Assumptions & free parameters 0 free parameters · 3 assumptions · 1 invented entities

The paper introduces no fitted numerical parameters. Its claims rest on the adequacy of the stable-distance framework as a source model, on prior encoding constructions (quasi-uniformities, product trick), and on standard causality theory. The one new structural entity is the abstract family-of-functions spacetime, which has no independent empirical evidence attached.

assumptions (3)

domain assumption The stable Lorentzian distance framework (upper semi-continuous distances, steep time functions) captures the physically essential structure of spacetime.
The abstract states the new abstraction is proposed by using 'the properties of the stable distance over stable spacetimes as a reference'; if this source model omits physical content, the minimal arena inherits the omission.
domain assumption A family of real functions over an arbitrary set, under suitable conditions, can encode topology and causality through quasi-uniformities and the product trick.
These encoding results come from the author's prior work and are invoked as background; the abstract does not re-derive them.
standard math Standard background in Lorentzian causality theory, including the causal ladder and the role of time functions, is valid.
The discussion presupposes the standard machinery of causality theory in general relativity.

invented entities (1)

Minimal spacetime as a set of points plus a family of real-valued functions
purpose: Proposed foundational arena meant to replace the smooth manifold while preserving causal, topological, and metric content.
No empirical prediction or external falsifiable handle is offered; its justification, per the abstract, is internal consistency and equivalence to the prior stable-distance framework.

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Cite this review

Pith. "Pith review of Destructuring Physics: A functional derivation of spacetime." pith.science (2026). https://pith.science/paper/53AWYWQO

@misc{pith2026250811949,
  author       = {Pith},
  title        = {Pith review of: Destructuring Physics: A functional derivation of spacetime},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/53AWYWQO}},
  note         = {Machine review of arXiv:2508.11949}
}

read the original abstract

I propose that Physics should be formulated using minimal mathematical structure, beginning with its foundational arena: spacetime. This paper opens with a concise overview of several research directions explored in previous work. Among these are the proposal to represent spacetime at the quantum scale using (measure) closed ordered spaces; the unification of causality and topology through quasi-uniformities; the concept of the product trick to unify causality and metricity; the introduction of upper semi-continuous (stable) Lorentzian distances; the representation of spacetime via steep time functions; and the formulation of the Lorentzian distance formula. Subsequently, the properties of the stable distance over stable spacetimes are used as a reference to propose a simplified, abstract notion of spacetime. The discussion shows that spacetime can be introduced in a general and minimalistic way as nothing more than a family of functions defined over an arbitrary set. This abstraction removes unnecessary mathematical complexity, reducing spacetime to its essential elements while preserving its most fundamental physical properties.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

44 extracted references · 31 canonical work pages

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

of Phys.: Conf

Minguzzi E 2013 J. of Phys.: Conf. Ser.\/ 442 012034 C ontribution to the proceedings of the conference 'DICE12, Space-Time-Matter-Quantum Mechanics, from the Planck scale to emergent phenomena', C astello P asquini, C astiglioncello (Italy) September 17 - 21, 2012

work page 2013

[2] [2]

Dowker F, Henson J and Sorkin R D 2003 Mod. Phys. Lett.\/ A19 1829--1840

work page 2003

[3] [3]

Surya S 2019 Living Reviews in Relativity\/ 22 5

work page 2019

[4] [4]

Wald R M 1984 General Relativity\/ (Chicago: The U niversity of C hicago P ress)

work page 1984

[5] [5]

Nachbin L 1965 Topology and order\/ (Princeton: D.\ V an N ostrand C ompany, I nc.)

work page 1965

[6] [6]

Hawking S W and Ellis G F R 1973 The Large Scale Structure of Space-Time\/ (Cambridge: Cambridge U niversity P ress)

work page 1973

[7] [7]

Beem J K, Ehrlich P E and Easley K L 1996 Global Lorentzian Geometry\/ (New York: Marcel D ekker I nc.)

work page 1996

[8] [8]

O'N eill B 1983 Semi- R iemannian Geometry\/ (San Diego: Academic P ress)

work page 1983