Quantum-Gravity Consistency Claims and Comparison Contract

Quantum-gravity consistency statements range from conditional AdS/CFT deductions to conjectural patterns inferred from controlled compactifications. A useful comparison states the theory class and quantifiers before weighing evidence. Examples can support a conjecture; absence from a searched class cannot prove a universal prohibition.

Required background. Evidence Programs for Holographic Duality supplies evidence classes; Validity, Unitarity, and Breakdown fixes the EFT domain.

Helpful background. Correlated Evidence, Independence, and Triangulation separates dependent examples; Falsifiers, Negative Results, and Counterexamples supplies negative tests; Low-Energy Constraints on UV Completion supplies infrared implications; Energy–Information Bounds: Assumptions and Status supplies bound logic.

Evidence cutoff: 25 July 2026.

Anatomy of a consistency statement

Write a claim as

$$\forall T\in\mathfrak T(\mathcal A): \quad H(T;\mathcal A)\Longrightarrow C(T;\mathcal A),$$

where $\mathfrak T$ is the theory class and $\mathcal A$ records dimension, supersymmetry, asymptotics, gauge global form, spectrum, EFT cutoff, and UV assumptions. The logical status must be one of:

• theorem under stated axioms;
• conditional derivation, such as an AdS/CFT argument;
• semiclassical black-hole or EFT inference;
• conjecture supported by examples;
• empirical bound on a low-energy parameter.

The negation of a universal claim is one controlled $T$ satisfying $H$ but not $C$. A failed construction is not that counterexample unless its failure is proved within the same hypotheses.

First application: compare four claims

Statement	Essential hypothesis	Conclusion	Direct logical implication
no exact global symmetry	exact AdS/CFT plus boundary locality and completeness	corresponding bulk symmetry is gauged	may motivate completeness, does not prove WGC
electric WGC	specified gauge kinetic metric and extremality convention	a superextremal state or variant-specific set exists	supports black-hole discharge
distance conjecture	infinite geodesic distance in moduli space	an exponentially light tower appears	lowers the species cutoff
cobordism conjecture	specified tangential and background structures	relevant quantum-gravity bordism charge is trivialized	predicts defects or topology change

The table prevents a chain of motivations from becoming a chain of theorems. Harlow and Ooguri provide a conditional AdS/CFT result for global symmetries Harlow and Ooguri 2019; the WGC and distance statements were proposed as conjectures from different arguments Arkani-Hamed et al. 2007, Ooguri and Vafa 2007.

Evidence and uncertainty

Record each construction once even if dual descriptions expose several manifestations of the same fact. Separate algebraic consequences, black-hole reasoning, string spectra, and independent numerical tests. Quantitative claims need normalizations, correction scales, and a falsifier; qualitative words such as “order one” require a declared limit.

Adversarial control: leave the domain

Apply an AdS/CFT argument without exact duality, a large-distance law at a finite-distance singularity, or a supersymmetric spectrum claim after supersymmetry breaking. The relevant premise fails, so neither agreement nor disagreement updates the original universal statement. Likewise, counting one compactification as derivation, example, and independent confirmation artificially inflates confidence.

The resulting comparison is deliberately conservative: it preserves strong conditional results while keeping conjectures revisable. No status on this page is evidence that a mutable debate has been settled after the cutoff.

The chapter overview contains the structure diagram and validity and failure diagram. They are embedded there once so that their shared chapter-level context is not repeated on every article.

For the chapter-wide comparison of assumptions, counterevidence, falsifiers, and claim ceilings, see the claim-domain table.

References

• Arkani-Hamed, Nima, Luboš Motl, Alberto Nicolis, and Cumrun Vafa. “The String Landscape, Black Holes and Gravity as the Weakest Force.” Journal of High Energy Physics 2007, 6 (2007): 060. DOI. Open PDF.
• Harlow, Daniel, and Hirosi Ooguri. “Constraints on Symmetries from Holography.” Physical Review Letters 122, 191601 (2019). DOI. Open PDF.
• Ooguri, Hirosi, and Cumrun Vafa. “On the Geometry of the String Landscape and the Swampland.” Nuclear Physics B 766, 21–33 (2007). DOI. Open PDF.