Pre-Polar Signed Ownership, Affine Obstructions, and Terminal-Source Tangent Transport in a Five-Wall Quadratic Moving-Incidence Model
We isolate a terminal structural mechanism in a prime-power, five-wall quadratic moving-incidence model. The starting point is a signed one-shell representation with terminal suppression $\vert{}E_{\mathrm{term}}\vert{} \ge c_0 \delta^5$ and total signed pair-sector variation $O(\delta T^2)$. Retaining the sign before polarisation gives quantitative pre-polar sector coherence. Pair Parseval then yields $m_\gamma \le \varpi_\gamma T^4$, converting coherent sector total variation into physical outer mass. At the critical amplitude $T \sim \delta^{3/2}$, a constant-mass set of outer states has normalized common-parent signed coefficient $\vert{}\Lambda_\gamma\vert{} / T^4 \ge c \delta$ and physical $L^2$ phase ownership of order $\delta^2$. For the explicit five-role quadratic wall, no nonzero additive physical source line makes four active undifferenced offsets simultaneously affine, whereas one physical difference affineizes every role exactly. At fixed outer witness the owned common-parent coefficient is independent of the terminal curvature source; the genuine source autocorrelation is exactly a Fresnel–Dirichlet multiplier. The quadratic midpoint identity identifies this residual source transport with the tangent-transport object selected by Hilbert–polar descent. The resulting critical survivor has a selected tangent tube with tube-restricted pair-sector TV mass at least $c \delta^9 / T^2$ and, separately, at least one pair factor has parent Fourier energy at the same lower scale. The intrinsic residual length is $L_{\mathrm{tan}} \sim N / Q_*$, with $Q_* \sim T^4 / \delta^8$; only under the inherited wall regime does this become $D^{1/2 - o(1)}$. If neither a shell-compatible tangent density increment nor the certified source-return mechanism occurs, the survivor belongs to a frozen residual tangent-transport obstruction class. This final statement is conditional and does not assert nonemptiness of the no-return class, construct a minimax counterexample, prove a minimax lower bound, or establish universal impossibility.
Authors
- Tao Lin (ORCID: https://orcid.org/0009-0004-1291-515X)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-09-09
- DOI
- https://doi.org/10.5281/zenodo.22670264
- Primary Topic
- Topological Materials and Phenomena
- Type
- preprint