Enter, 06-I-D-v5, 2026, pp. 1-71
I-D-v5 Dynamical Spacetime Enter over Two Prescribed Hosts
Ngo Cheung
21 October 2026
Abstract
New in v5. (i) Census, computer-assisted (U8). The v3/v4 resonance census of settled Host B in the box Re ω ∈ [0. 05, 2. 5], Im ω ∈ [−0. 75, −0. 005] is now enclosed in Arb ball arithmetic (computer-assisted). For each m ∈ {0, 1, 2} and parity, a validated Taylor-model integration of the interior equation (Cauchy–Gronwall tails, flat-zone perturbation bounds, log-norm propagation), Taylor series in ω with Cauchy remainders, and Gronwall-bounded Hankel data give a rigorous winding number of the matching Wronskian on the box boundary. The counts are (0, e) 7, (0, o) 6, (1, e) 8, (1, o) 7, (2, e) 8, (2, o) 8 (44 in total), equal to the v3 counts. Each zero is simple and lies in a Rouché disk of radius 10^{−14} around a refined v3 root, and every resonance in the box has |Im ω| ≥ 0. 12816. Outside the box nothing is claimed. (ii) Host-A pulse (U9 extended). In the settled pulse exterior, the full Einstein tensor, including G_{0̂r̂}, has the form Bη_{(tr)} + (A − B) l ⊗ l + 2B e_{ẑ} ⊗ e_{ẑ}, where l is the outgoing null covector, A = βQs^{′′}/c^2 and B = βs^{′}/c > 0 (with a positive prefactor 1/(a_{∞}^2F_A)). Consequences: its trace is 4B ≠ 0, so no Maxwell field reproduces it. Where A ≠ B it is of Hawking–Ellis (Segre) type II, so no anisotropic fluid with any p_r, p_{φ}, p_z and no Letelier string cloud, axial or azimuthal, reproduces it, not even algebraically. It violates the null energy condition everywhere in the pulse shell (T_kk ≈ −Bθ^2 for null k near the outgoing direction). Axial Maxwell fields have the wrong anisotropy sign even with v4's scalar/fluid/Λ fillers. Single-component azimuthal fields are excluded by the Bianchi identity even with free currents. For ξRφ^2 we derive the exact anisotropy transport law (1 − ξφ^2)Δ = ξ⟨mathop dF, mathop dφ^2⟩/(a^2F) and exclude the critical branch ξφ^2 ≡ 1, but the general case is not decided and is typed open. Nothing closes, so no scoped subgate and no Host-A source is recorded. (iii) Interface moments (U6 follow-up). No natural, selected Host-B source among those tested gives Γ_1 = Γ_2 = 0. These are the constant reference, Λ, and the conserved power family σ_x = kF^{−n} (Casimir-type n = 4 included). The family n = 2 has Γ_2 = 0 but Γ_1 = −k ≠ 0. Vanishing of both needs at least two tuned constants. The free data are the source modulo two linear conditions, χ on the flat stretches, and one constant per mantle. This is typed as an open item. We also record a correction: Hawk07-G-v3's variance constant 2^10ζ(3) tightens to ζ(3), with proof. (iv) Housekeeping. The two 3.3pt overfull verdict rows are fixed. Retained. Host A and Host B remain separate prescribed backgrounds. There is no third geometry, Host C stays rejected, and there is no semiclassical formation, phantom quantization, or global nonlinear solution. All seven programme entries remain open, with O. 1 = texttt NOT_CLOSED. XVI-N is not discharged, XV-B is not opened, and no inherited coefficient is admitted.
Bibliographic record
- Title
- I-D-v5 Dynamical Spacetime Enter over Two Prescribed Hosts
- Author
- Cheung, Ngo
- Publication date
- 2026/10/21
- Institution
- Enter
- Report number
- 06-I-D-v5
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 71
- Language
- en