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arxiv: 2605.06793 · v1 · submitted 2026-05-07 · ✦ hep-th

Recognition: no theorem link

Sharpened Dynamical Cobordism

Andriana Makridou , Alejandro Javier Puga G\'omez
Authors on Pith no claims yet

Pith reviewed 2026-05-11 00:46 UTC · model grok-4.3

classification ✦ hep-th
keywords dynamical cobordismtransition to nothingcritical exponentcobordism conjecturesingularitiesquantum gravitystring theoryGubser criterion
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The pith

A theory's physical structure fixes an allowed range for the critical exponent δ that marks whether a singularity truly ends spacetime or carries a blocking global charge.

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

The paper sharpens the dynamical cobordism idea by letting the theory's physical structure ξ fix a range R^ξ for the critical exponent δ of a singularity. Singularities whose δ falls inside R^ξ count as genuine transitions to nothing that terminate spacetime, while those outside the range signal a non-trivial cobordism global charge that cannot exist in quantum gravity. The authors give a concrete way to compute R^ξ, drawing on the Gubser criterion for good singularities, and show that adding a higher-form gauge field widens or shifts the allowed interval relative to a scalar-only effective theory. They then check the sharpened rule on massive IIA with O8-planes, the Janis-Newman-Winicour and Garfinkle-Horowitz-Strominger black holes, and certain D-brane distributions, finding consistency with known physics. If the sharpening holds, any apparent inconsistency can be removed by enlarging the structure with new fields and defects.

Core claim

We propose a sharpened version of Dynamical Cobordism, where the physical structure ξ of the theory in question determines an allowed range R^ξ for the critical exponent δ. We interpret a singularity with δ ∈ R^ξ as a true transition-to-nothing, i.e., a configuration ending spacetime, while a singularity with δ ∉ R^ξ indicates some obstruction to such a transition, i.e., the presence of a non-trivial cobordism global charge, which is incompatible with a theory of quantum gravity. In the spirit of the original Cobordism Conjecture, this apparent inconsistency of the theory can be alleviated via the modification of the structure, for instance by introducing new degrees of freedom and of the G

What carries the argument

The structure-dependent allowed range R^ξ for the critical exponent δ, which separates true transitions-to-nothing from singularities blocked by cobordism global charges.

If this is right

  • Singularities with δ inside R^ξ are genuine transitions-to-nothing that end spacetime.
  • Singularities with δ outside R^ξ carry non-trivial cobordism global charges and are forbidden unless the theory is enlarged with new fields and defects.
  • Introducing a higher-form gauge field changes the allowed interval for δ relative to a scalar-only effective theory.
  • In massive IIA string theory the sharpened rule is compatible with the presence of O8-planes.
  • The Janis-Newman-Winicour, Garfinkle-Horowitz-Strominger black holes and certain D-brane distributions satisfy the sharpened conjecture.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same range-construction method could be applied to other classes of singularities, such as those in cosmological or higher-dimensional solutions, to test whether they terminate spacetime.
  • This criterion may help decide which effective field theories can be consistently embedded in quantum gravity by ruling out those whose singularities fall outside the allowed range.
  • If the Gubser-inspired prescription for R^ξ generalizes, it could provide a practical test for consistency when new matter fields or fluxes are added to a theory.
  • The approach might link to broader questions about which global charges can be screened or cancelled in string theory compactifications.

Load-bearing premise

The physical structure ξ of a theory can be used to fix a definite range R^ξ for δ that reliably distinguishes genuine spacetime-ending singularities from those obstructed by global charges.

What would settle it

A calculation or observation in a known consistent theory, such as a specific black-hole or string-theory singularity, where the measured δ lies outside the predicted R^ξ yet no global charge or obstruction appears, or lies inside R^ξ yet spacetime does not end.

Figures

Figures reproduced from arXiv: 2605.06793 by Alejandro Javier Puga G\'omez, Andriana Makridou.

Figure 1
Figure 1. Figure 1: figure 1 [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: Pictorial representation of cobordant configurations with corresponding EFTs. Side a depicts k-dimensional manifolds embedded in a d-dimensional spacetime, the corresponding (d − k)- dimensional EFTs and the interpolating Domain Wall. Side b shows the case of a k-dimensional manifold cobordant to nothing, together with the corresponding codimension-1 end-of-the-world con￾figuration (ETW domain wall) in the… view at source ↗
Figure 2
Figure 2. Figure 2: Representation of the allowed region in the (a, δ) plane, adding a three-form and assuming d = 10. The colors identify the origin of each region. The orange area corresponds to (3.17a); the blue to (3.17b); and the green to (3.22). As we have used the Gubser horizon criterion to motivate R, it becomes interesting to examine the exact differences between our proposed bounds and the good singularities of Gub… view at source ↗
Figure 3
Figure 3. Figure 3: Representation of the region compatible with CV < 0 in the (a, δ) plane adding a top form and assuming d = 10. The blue line marks R10,1 , the orange line R10,2 , and the green region R10,3 . C Finite action and R In this appendix we want to discuss an alternative way of establishing the allowed region, which pertains to demanding that the solution corresponds to a finite action. This is not an unreasonabl… view at source ↗
Figure 4
Figure 4. Figure 4: Allowed values of δ in the (a, δ) plane for 4a requiring finiteness of the action, and 4b CV ≤ 0 for d = 10, q = 3. The colors blue, orange and green are the same as in figure 2, while the black line marks a new constraint given by δ = −a √ 2/(q − 1). 40 [PITH_FULL_IMAGE:figures/full_fig_p040_4.png] view at source ↗
read the original abstract

We propose a sharpened version of Dynamical Cobordism, where the physical structure $\xi$ of the theory in question determines an allowed range $R^\xi$ for the critical exponent $\delta$. We interpret a singularity with $\delta \in R^\xi$ as a true transition-to-nothing, i.e., a configuration ending spacetime, while a singularity with $\delta \notin R^\xi$ indicates some obstruction to such a transition, i.e., the presence of a non-trivial cobordism global charge, which is incompatible with a theory of quantum gravity. In the spirit of the original Cobordism Conjecture, this apparent inconsistency of the theory can be alleviated via the modification of the structure, for instance by introducing new degrees of freedom and associated defects. Inspired by the Gubser criterion for good singularities, we propose a way to determine $R^\xi$. As a proof-of-concept we show explicitly how the introduction of a higher-form gauge field changes the allowed range of $\delta$ compared to an EFT with only scalars. We test this sharpened version of Dynamical Cobordism against several examples, such as massive IIA string theory, where it is notably compatible with the presence of O8-planes; the Janis-Newman-Winicour and Garfinkle-Horowitz-Strominger black hole solutions; and certain singular distributions of D-branes. In all these cases, the Sharpened Dynamical Cobordism Conjecture leads to results consistent with our expectations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a sharpened version of the Dynamical Cobordism conjecture. The physical structure ξ of the theory determines an allowed range R^ξ for the critical exponent δ. A singularity with δ in R^ξ is a true transition-to-nothing ending spacetime, while δ not in R^ξ indicates an obstruction from a non-trivial cobordism global charge. The range R^ξ is proposed using a method inspired by the Gubser criterion. As proof-of-concept, introducing a higher-form gauge field changes the allowed δ range compared to scalar-only EFT. Tests on massive IIA string theory (O8-planes), Janis-Newman-Winicour and Garfinkle-Horowitz-Strominger black holes, and singular D-brane distributions show consistency with expectations.

Significance. If the result holds, the sharpened conjecture would provide a criterion to classify singularities in quantum gravity as either genuine spacetime terminations or those obstructed by global charges, consistent with the Cobordism Conjecture. The explicit proof-of-concept demonstrating the effect of higher-form fields on R^ξ and the consistency with known string theory objects like O8-planes represent strengths. These tests offer concrete illustrations in physically relevant settings, enhancing the proposal's utility if the general method can be formalized.

major comments (2)
  1. The central claim requires that ξ determines a definite range R^ξ such that δ membership distinguishes true transitions-to-nothing from obstructed ones. However, the Gubser-inspired criterion is translated from holographic AdS setups to the dynamical cobordism context without a first-principles derivation or general algorithm. The manuscript illustrates the range change for higher-form fields versus scalars but does not state a universal procedure for arbitrary ξ. This is load-bearing for applying the conjecture beyond the tested cases. (Proposal of the sharpened conjecture)
  2. While the results are stated to be consistent with expectations for O8-planes, JNW/GHS black holes, and D-brane distributions, the description provides no explicit computations of R^ξ or verification that the method avoids post-hoc adjustments. Without these derivations, it is unclear if the classifications follow uniquely from ξ. (Tests and examples section)
minor comments (2)
  1. The notation for the physical structure ξ and the range R^ξ would benefit from a clear introductory definition or table summarizing the ranges for different ξ.
  2. Consider adding a dedicated subsection outlining the general steps of the Gubser-inspired method before the proof-of-concept example.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which help clarify the scope and presentation of the sharpened Dynamical Cobordism conjecture. We respond point by point to the major comments below.

read point-by-point responses

  1. Referee: The central claim requires that ξ determines a definite range R^ξ such that δ membership distinguishes true transitions-to-nothing from obstructed ones. However, the Gubser-inspired criterion is translated from holographic AdS setups to the dynamical cobordism context without a first-principles derivation or general algorithm. The manuscript illustrates the range change for higher-form fields versus scalars but does not state a universal procedure for arbitrary ξ. This is load-bearing for applying the conjecture beyond the tested cases. (Proposal of the sharpened conjecture)

    Authors: We agree that the method for determining R^ξ is inspired by the Gubser criterion rather than derived from first principles in the dynamical cobordism setting, and that no universal algorithm for arbitrary ξ is provided. The manuscript presents the sharpened conjecture as a proposal, using the higher-form gauge field example as a proof-of-concept to illustrate how ξ modifies the allowed range. In the revised version we will add explicit language stating that the criterion is conjectural and inspired by holography, that a general procedure remains an open question, and that the claim is therefore positioned as applying reliably to the tested classes of theories while inviting further development for broader use. revision: partial

  2. Referee: While the results are stated to be consistent with expectations for O8-planes, JNW/GHS black holes, and D-brane distributions, the description provides no explicit computations of R^ξ or verification that the method avoids post-hoc adjustments. Without these derivations, it is unclear if the classifications follow uniquely from ξ. (Tests and examples section)

    Authors: We acknowledge that the main text does not display the explicit intermediate steps used to compute R^ξ for each example. In the revised manuscript we will add a dedicated appendix containing the detailed calculations for the massive IIA O8-plane case, the Janis-Newman-Winicour and Garfinkle-Horowitz-Strominger solutions, and the singular D-brane distributions. These will show how R^ξ is obtained directly from the structure ξ in each instance, confirming that the resulting classifications follow from the proposed method without post-hoc tuning. revision: yes

Circularity Check

0 steps flagged

Proposal of sharpened dynamical cobordism remains self-contained without circular reduction to inputs

full rationale

The paper explicitly frames its core contribution as a proposal: the physical structure ξ determines an allowed range R^ξ for δ, with the mapping inspired by (but not derived from) the Gubser criterion and illustrated via explicit examples such as the effect of higher-form fields versus scalars. No equation or step in the provided abstract or description reduces the classification of singularities (true transition-to-nothing vs. obstructed by cobordism charge) to a fitted parameter or self-citation by construction; the tests on massive IIA, O8-planes, JNW/GHS solutions, and D-brane distributions are presented as consistency checks rather than predictions forced by the inputs. The derivation chain is therefore independent of the target result and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only; limited visibility into full assumptions. Core idea rests on interpreting δ via structure ξ and Gubser criterion without independent derivation shown.

axioms (2)
  • domain assumption Physical structure ξ determines an allowed range R^ξ for critical exponent δ
    Central to the sharpened conjecture as stated in the abstract.
  • domain assumption δ ∈ R^ξ corresponds to true transition-to-nothing while δ ∉ R^ξ signals non-trivial cobordism charge
    Key interpretive rule proposed without further justification in abstract.

pith-pipeline@v0.9.0 · 5570 in / 1422 out tokens · 70403 ms · 2026-05-11T00:46:20.307808+00:00 · methodology

discussion (0)

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