References

Junction-condition and matching-surface literature, named here for readers approaching Open Problem B-JP. References are sparse by design: the structural content comes from the axiom and from AP04, not from the literature framework; the literature provides the formal vocabulary in which the structural fact is most naturally stated.

Israel, W. (1966). Singular hypersurfaces and thin shells in general relativity. Il Nuovo Cimento B 44, 1–14 (errata 48, 463). The original Israel junction conditions: induced-metric continuity and extrinsic-curvature jump on a matching hypersurface. The formal vocabulary in which J1 and J2 are stated.

Arkuszewski, W., Kopczyński, W., and Ponomariev, V. N. (1975). Matching conditions in the Einstein-Cartan theory of gravitation. Communications in Mathematical Physics 45, 183–190. The ECSK extension of Israel’s conditions — matching across a hypersurface in the Einstein-Cartan-Sciama-Kibble framework with torsion. The framework in which B-JP is posed.

Popławski, N. J. (2010). Cosmology with torsion: An alternative to cosmic inflation. Physics Letters B 694, 181–185. (2016). Universe in a black hole in Einstein-Cartan gravity. The Astrophysical Journal 832, 96. The torsion-driven bounce cosmologies AP05 distinguishes itself from in section 3.1. The dynamical-bounce alternative against which the junction formulation is empirically tested by KS-B.1.

Lucat, S., and Prokopec, T. (2017). Cosmological singularities and bounce in Cartan-Einstein theory. Journal of Cosmology and Astroparticle Physics 1710, 047. Further work in the torsion-driven bounce lineage; named alongside Popławski as the relevant comparison class for KS-B.1.

Planck Collaboration. (2020). Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6. The CMB measurements that anchor n_s ≈ 0.965 (the scalar spectral index referenced in KS-B.2’s staged operational test once B-JP and the spectrum mapping are in hand).

Kantowski, R., and Sachs, R. K. (1966). Some spatially homogeneous anisotropic relativistic cosmological models. Journal of Mathematical Physics 7, 443. The anisotropic cosmological geometry on whose interior B-JP is posed.

Internal references to The 420 Code (AP01, AP03, AP04, AP06, AP08, AP10, AP20, AP24, Resolutions Ø, Predictions Ø) are catalogued in the Conditionality Footer above. The 420 Code is published copyleft and free at the420code.org; the 420 Code links to all referenced internal papers.

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the420code.org

Series The 420 Code

Catalogue Ø Artist’s Proofs

Proof Number AP05

Title The Break

Subtitle Symmetry Breaking

Medium Physics

Artist G

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