Third-Generation Branch

The Third-Generation Branch is the position the book assigns to our universe in the recursive cosmological tree: recursion level n ≈ 202 from the prime domain, the merger-compressed branch of a lineage with one merger, at our origin, which compressed the Pulse Diameter. The book reaches it from our universe's compression factor at the Kerr floor, C(⇌) ≈ 0.932, the book's working hypothesis, the signature of an Extreme-Compression Null Well Origin. Every level after a merger inherits its compression constant, so a merger compresses the whole lineage below it. Starting from a prime domain whose Pulse Diameter equals the Zinf Diameter, PD₀ = ☫⊕, every level carries the baseline heritage f₀ of an uncompressed (Schwarzschild) lineage and each merger applies a compression constant on top, so PD(n) = ☫⊕ × 2ⁿ × f₀ⁿ × ∏ᵢ₌₁ᵍ Cᵢ = ☫⊕ × 2ⁿ × fⁿ, where g is the number of merger events in the lineage and Cᵢ the compression factor of each. The merger compressions are part of the heritage f of Chapter 2: fⁿ = f₀ⁿ × ∏Cᵢ. The book reads its consequences: our branch is the one opened by the high-compression Kerr–Kerr merger at our own origin, our Pulse Diameter is about 7% shorter than an equivalent Schwarzschild lineage's, and compressed Planck time sped early structure formation. For our universe the book takes g = 1 and C₁ ≈ 0.93, the Kerr floor 1 − κ·0.998² ≈ 0.93227, so ∏Cᵢ = C₁ ≈ 0.93 and PD ≈ ☫⊕ × 2²⁰² × f₀²⁰² × 0.93 = ☫⊕ × 2²⁰² × f²⁰², where ☫⊕ is the Zinf Diameter, 𝒞→·ℨ/2 ≈ 3.423 × 10⁻⁹⁸ m [𝕃], PD our Pulse Diameter [𝕃], f²⁰² ≈ 36.7 the net heritage of our lineage (f ≈ 1.018) and f₀²⁰² = 36.7 / 0.93 ≈ 39.5 the baseline heritage the lineage would have carried without the merger (f₀ ≈ 1.0184), all heritage terms [∅]: a net compression of about 7% from baseline. The Third-Generation Branch connects to Extreme-Compression Null Well Origin, Recursive Cosmological Tree, Pulse Diameter Variability, Our Universes Net Compression Heritage and Compression Factor.