# References

This example pack supports the “RU-centered universality bridge” narrative with primary anchors and a small set of widely used reviews.

Conventions

- arXiv identifiers are included where available.
- When a journal version is standard, a DOI is included.
- Items are grouped by application thread so readers can follow a single theme end-to-end.

## Core string foundations and consistency

- Green, M. B. and Schwarz, J. H., “Anomaly Cancellation in Supersymmetric D=10 Gauge Theory and Superstring Theory,” *Physics Letters B* 149 (1984) 117–122. DOI: 10.1016/0370-2693(84)91565-X.
- Polchinski, J., “Dirichlet-Branes and Ramond-Ramond Charges,” *Physical Review Letters* 75 (1995) 4724–4727. arXiv:hep-th/9510017. DOI: 10.1103/PhysRevLett.75.4724.


## Compactification, vacuum structure, and the constraint viewpoint

- Candelas, P., Horowitz, G. T., Strominger, A., and Witten, E., “Vacuum Configurations for Superstrings,” *Nuclear Physics B* 258 (1985) 46–74. DOI: 10.1016/0550-3213(85)90602-9.
- Palti, E., “The Swampland: Introduction and Review,” *Fortschritte der Physik* 67 (2019) 1900037. arXiv:1903.06239. DOI: 10.1002/prop.201900037.
- van Beest, M., Calderón-Infante, J., Mirfendereski, S., Valenzuela, I., and others, “Lectures on the Swampland Program in String Compactifications,” *Physics Reports* 927 (2021) 1–125. arXiv:2102.01111.

## Protected quantities, indices, and localization

- Witten, E., “Constraints on Supersymmetry Breaking,” *Nuclear Physics B* 202 (1982) 253–316. DOI: 10.1016/0550-3213(82)90071-2.
- Witten, E., “Elliptic Genera and Quantum Field Theory,” *Communications in Mathematical Physics* 109 (1987) 525–536. DOI: 10.1007/BF01208956.
- Dijkgraaf, R., Verlinde, E., and Verlinde, H., “Counting Dyons in N=4 String Theory,” arXiv:hep-th/9607026.

## Black holes, microstates, and entropy

- Strominger, A. and Vafa, C., “Microscopic Origin of the Bekenstein–Hawking Entropy,” *Physics Letters B* 379 (1996) 99–104. arXiv:hep-th/9601029. DOI: 10.1016/0370-2693(96)00345-0.
- Skenderis, K., “Black holes and branes in string theory,” *Lecture Notes in Physics* 541 (2000) 325–364. arXiv:hep-th/9901050.

## Holography and AdS/CFT (core papers and dictionary)

- Maldacena, J. M., “The Large N Limit of Superconformal Field Theories and Supergravity,” arXiv:hep-th/9711200; *Advances in Theoretical and Mathematical Physics* 2 (1998) 231–252.
- Gubser, S. S., Klebanov, I. R., Polyakov, A. M., “Gauge Theory Correlators from Non-Critical String Theory,” *Physics Letters B* 428 (1998) 105–114. arXiv:hep-th/9802109. DOI: 10.1016/S0370-2693(98)00377-3.
- Witten, E., “Anti de Sitter Space and Holography,” arXiv:hep-th/9802150; *Advances in Theoretical and Mathematical Physics* 2 (1998) 253–290. DOI: 10.4310/ATMP.1998.v2.n2.a2.

## Finite-temperature holography, real-time response, and transport

- Son, D. T. and Starinets, A. O., “Minkowski-space correlators in AdS/CFT correspondence: recipe and applications,” arXiv:hep-th/0205051.
- Policastro, G., Son, D. T., Starinets, A. O., “From AdS/CFT correspondence to hydrodynamics,” arXiv:hep-th/0205052.
- Kovtun, P., Son, D. T., Starinets, A. O., “Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics,” arXiv:hep-th/0405231; *Physical Review Letters* 94 (2005) 111601. DOI: 10.1103/PhysRevLett.94.111601.

## Holographic condensed matter and quantum matter without quasiparticles

- Hartnoll, S. A., Herzog, C. P., Horowitz, G. T., “Holographic Superconductors,” arXiv:0810.1563; *JHEP* 0812 (2008) 015.
- Herzog, C. P., “Lectures on Holographic Superfluidity and Superconductivity,” arXiv:0904.1975.
- Horowitz, G. T., “Introduction to Holographic Superconductors,” arXiv:1002.1722.
- Hartnoll, S. A., Lucas, A., Sachdev, S., “Holographic quantum matter,” arXiv:1612.07324.

## Gauge/string duality for hot QCD and heavy-ion phenomenology

- Casalderrey-Solana, J., Liu, H., Mateos, D., Rajagopal, K., Wiedemann, U. A., “Gauge/String Duality, Hot QCD and Heavy Ion Collisions,” arXiv:1101.0618.

## Scattering amplitudes, gauge–gravity relations, and double copy

- Kawai, H., Lewellen, D. C., Tye, S.-H. H., “A Relation Between Tree Amplitudes of Closed and Open Strings,” *Nuclear Physics B* 269 (1986) 1–23. DOI: 10.1016/0550-3213(86)90362-7.
- Bern, Z., Carrasco, J. J. M., Johansson, H., “New Relations for Gauge-Theory Amplitudes,” arXiv:0805.3993; *Physical Review D* 78 (2008) 085011. DOI: 10.1103/PhysRevD.78.085011.
- Bern, Z., “The Duality Between Color and Kinematics and its Applications,” arXiv:1909.01358.

## Compactification and string phenomenology (historical anchors)

- Candelas, P., Horowitz, G. T., Strominger, A., Witten, E., “Vacuum configurations for superstrings,” *Nuclear Physics B* 258 (1985) 46–74. DOI: 10.1016/0550-3213(85)90602-9.

## Mathematics exports (topology and invariants)

- Witten, E., “Quantum Field Theory and the Jones Polynomial,” *Communications in Mathematical Physics* 121 (1989) 351–399. DOI: 10.1007/BF01217730.

## Black hole information and the Page curve (selected pillars)

These references support the “information-loss and unitarity” discussion at a level suitable for readers who want primary sources.

- Hawking, S. W., “Breakdown of Predictability in Gravitational Collapse,” *Physical Review D* 14 (1976) 2460–2473. DOI: 10.1103/PhysRevD.14.2460.
- Page, D. N., “Average Entropy of a Subsystem,” *Physical Review Letters* 71 (1993) 1291–1294. arXiv:gr-qc/9305007. DOI: 10.1103/PhysRevLett.71.1291.
- Almheiri, A., Marolf, D., Polchinski, J., Sully, J., “Black Holes: Complementarity or Firewalls?,” arXiv:1207.3123; *JHEP* 02 (2013) 062.
- Penington, G., “Entanglement Wedge Reconstruction and the Information Paradox,” arXiv:1905.08255; *JHEP* 09 (2020) 002.
- Almheiri, A., Engelhardt, N., Marolf, D., Maxfield, H., “The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole,” arXiv:1905.08762.
- Almheiri, A., Hartman, T., Maldacena, J., Shaghoulian, E., Tajdini, A., “Replica Wormholes and the Entropy of Hawking Radiation,” arXiv:1911.12333; *JHEP* 05 (2020) 013.
- Almheiri, A., Mahajan, R., Maldacena, J., Zhao, Y., “The Page curve of Hawking radiation from semiclassical geometry,” arXiv:1908.10996; *JHEP* 03 (2020) 149.
- Almheiri, A., Engelhardt, N., Marolf, D., Maxfield, H., Penington, G., Shaghoulian, E., “The entropy of Hawking radiation,” *Reviews of Modern Physics* 93 (2021) 035002. DOI: 10.1103/RevModPhys.93.035002.

## Bridge-to-RU primary sources included in this engine

- RU v19 submission PDF (local copy): `sources/ru/rigidity_gapfree_global_universality_v19.pdf`
- Robust certificate schema: `sources/ru/robust_certificate_schema.json`
- Robust certificate example: `sources/ru/examples/robust_certificate_example.json`
- Global universality report schema: `sources/ru/global_universality_report_schema.json`
- Global universality report example: `sources/ru/global_universality_report_example.json`

## Suggested standard references for the string-theory side of the bridge

These are canonical background sources for the specific bridge examples used in the new documents.

- P. Di Francesco, P. Mathieu, D. Sénéchal, *Conformal Field Theory*, Springer.
- A. Kirillov Jr., V. Ostrik, writings on fusion categories and modular tensor categories.
- B. Bakalov, A. Kirillov Jr., *Lectures on Tensor Categories and Modular Functors*, AMS.
- E. Verlinde, “Fusion rules and modular transformations in 2D conformal field theory,” *Nuclear Physics B* 300 (1988) 360–376.

Note on citations

This engine prioritizes auditable reduction and certification. Once web lookup is available, each bridge claim can be augmented with pinpoint citations to sections and theorem statements in the above references.

## Additional bridge anchors (positivity, PF fusion, bootstrap, non-rational extensions)

- J. Preskill (KITP lecture notes), “Topological quantum computing” — includes the statement that the vector of quantum dimensions is the Perron–Frobenius eigenvector of fusion rule matrices.
- L. Lanosa, M. Leston, M. Passaglia, “Interplay between reflection positivity and crossing symmetry in the bootstrap approach to CFT,” JHEP 02 (2022) 171. DOI: 10.1007/JHEP02(2022)171.
- Z. Li, “Symmetries of conformal correlation functions,” Phys. Rev. D 105, 085018 (2022). DOI: 10.1103/PhysRevD.105.085018.
- B. Post, I. Tsiares, “A non-rational Verlinde formula from Virasoro TQFT,” JHEP 04 (2025) 015. DOI: 10.1007/JHEP04(2025)015.
- C. V. Johnson, “Random matrix model of the Virasoro minimal string,” Phys. Rev. D 110, 066015 (2024). DOI: 10.1103/PhysRevD.110.066015.
- M. Mariño, “String theory,” in The Oxford Handbook of Random Matrix Theory (2018). DOI: 10.1093/oxfordhb/9780198744191.013.31.
- nLab, “Frobenius–Perron dimension” (concept background and relation to fusion matrices).


## Real host data anchors (Fibonacci, Ising)

- G. Zhu et al., “Non-Abelian braiding of Fibonacci anyons with a superconducting processor,” Nature Physics (2024). (States τ×τ = 1 + τ.)
- S. Bonesteel (KITP lecture notes), “Braid Topologies for Quantum Computation,” includes Fibonacci fusion rule 1×1 = 0 + 1. 
- Nature Communications (2025) “Universal quantum computation using Ising anyons ” states σ×σ = 1 + ψ and discusses σ, ψ labels.
- J. Preskill, Physics 219 lecture notes “Topological quantum computation,” for standard fusion-space formalism and fusion coefficients.

- Xu, Sun, Wang et al., Non-Abelian braiding of Fibonacci anyons with a superconducting processor, Nature Physics 20, 1469–1475 (2024). DOI: 10.1038/s41567-024-02529-6.

- Burdick et al., Universal quantum computation using Ising anyons from a non-semisimple topological quantum field theory, Nature Communications (2025). DOI: 10.1038/s41467-025-61342-8.


## Anyon condensation and gapped boundaries (for projection/boundary constraints)
- arXiv:2504.19512, “Gapped Boundaries of Kitaev's Quantum Double Models: A Lattice Realization of Anyon Condensation from Lagrangian Algebras” (2025).
- National Science Review 10(3):nwac264, “Uniquely identifying topological order based on boundary-bulk duality and anyon condensation” (2023).


## Mathematical anchors for the RU engine

- G. Birkhoff, Extensions of Jentzsch’s theorem, Transactions of the American Mathematical Society 85 (1957), 219–227.
- P. J. Bushell, Hilbert’s metric and positive contraction mappings in a Banach space, Archive for Rational Mechanics and Analysis 52 (1973), 330–338.
- A. Lemmens and R. Nussbaum, Nonlinear Perron–Frobenius Theory, Cambridge Tracts in Mathematics 189, Cambridge University Press (2012).
- E. Seneta, Non-negative Matrices and Markov Chains, Springer Series in Statistics, Springer (revised editions).
- H. Furstenberg and H. Kesten, Products of random matrices, Annals of Mathematical Statistics 31 (1960), 457–469.
- P. Bougerol and J. Lacroix, Products of Random Matrices with Applications to Schrödinger Operators, Progress in Probability and Statistics 8, Birkhäuser (1985).
- J. F. C. Kingman, The ergodic theory of subadditive stochastic processes, Journal of the Royal Statistical Society, Series B 30 (1968), 499–510.
- A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press (1995). (For cocycles and symbolic dynamics background.)
- D. Ruelle, Thermodynamic Formalism, Addison–Wesley (1978). (For transfer operators and symbolic dynamics perspective.)
