Topological void nucleation in stochastic Regge calculus on a pentachoral 3+1 complex: oblate geometry produces χ = 0 void boundaries via discrete bead-merger geometry

Stochastic Regge calculus on a 4D pentachoral (3+1 staircase) complex spontaneouslyproduces persistent χ = 0-bounded voids from oblate baryonic potential wells, with nodark-sector fields, no modified gravity, and no imposed dynamics. The cosmologically loadbearingobservable is the integer-arithmetic filter χ (∂V) = V − E + F = 0 together withnon-trivial interior chain-complex homology bint1 ≥1 (consumed by Paper 2 2). Curvature-coupling specificity (lead result). Under pre-registered |T|-bins committedbefore re-binning to track the lattice edge length ¯ℓ0 (N) (|T|∗ (N) = 60, 120· (20k/N) 1/3, anchored at A5/N=20k), the within-bin Regge / matched-cluster-size correlated-fracturenull χ = 0 ratio across A5/N=20k and R5/N∈40, 80, 120k pools to ORCMH = 5. 41 (95%CI 3. 54, 8. 25; BreslowDay OR-homogeneity χ2=5. 04, p = 0. 17, not rejected) ; all fourper-cell Wilson 95% lower bounds exceed 1, and the matched null produces zero χ = 0events at the pre-registered R5/N=40k bin |T|∈47. 6, 95. 3 against Regge's 28/184 = 15. 2% (Tab. 32). A complementary matched-fdead=0. 15 random-damage null at N=20k (20 seeds) gives a 36× per-seed mean-peak Regge/random ratio at 4× lower dead fraction (Fisher exactone-sided p = 1. 28×10−8 on the 20 × 20 contingency). Topological prediction. The protocol-invariant cosmological prediction is the b int1 -confirmed fraction of χ = 0 clusters: 0. 88 ± 0. 04 across τsever ∈ 50, 100, 200, 400, 600 (12-fold span; CV 4%; Tab. 39). Boundary 2-complex topology by gold-standard integerSmith Normal Form (full census on 209 A5/N=20k and 671 R5/N=120k clusters): truetorus T 2 in 75. 6% (A5) and 79. 4% (R5) ; Klein bottle 0% at both resolutions; an earlierBFS-orientability census is retracted via a synthetic-T 2 count-4 injection test (App. G). Operating point and scaling. At N=20, 000, 18. 3 ± 3. 8 (10 seeds) bint1 -verified χ = 0voids form per seed at the canonical τsever=100 working point (≥ 10× above directlymeasuredτrelax ≲ 10 Sorkin steps at N∈5, 10k; ¯ℓ 20 -extrapolated to ≲ 4 at N=20k) ;cooldown-reconnect peak counts scale faster-than-linearly on average to 134 ± 7 at N=120k (local intervals non-monotonic; Sec. 22. 4). The dead-tetrahedron fraction follows a Hill saturationfdead (N) = Nn/ (Nn + N n1/2) with N1/2≈105 and nfit = 1. 815 ± 0. 016 (±5%rebuild systematic; Hill family preferred at ΔAICc≥13 over stretched-exponential and ≥22over exponential-saturation). A geometric persistence parameter ρ (N) = 2πa/ ¯ℓ0 (N) bracketsthe transition at ρc ∈ (10. 7, 12. 6) (10/10 seeds at N=16k). At fixed physical blobradius the void count per blob is resolution-independent (¯ℓ 00) across N ∈20, 120k, yieldingthe void-areal-density σvoid = N (blob) void / (2πaphys ·2cphys) handed to Paper 3 4 for lensingcomparison; the bare per-tetrahedron ¯ℓ−3. 050 scaling is retracted as a finite-resolution latticeartefact. A 4D-Lorentzian Schur consistency check gives |C−/C+| = 0. 85 ± 0. 15 as a diagnostic;the cosmological inference depends only on the integer-arithmetic χ count and is robustagainst any of three identified readings of the 15% residual (Sec. 17. 8).