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

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
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Pre-Polar Signed Ownership, Affine Obstructions, and Terminal-Source Tangent Transport in a Five-Wall Quadratic Moving-Incidence Model

Tao Lin
Zenodo (CERN European Organization for Nuclear Research)
Topological Materials and Phenomena
preprint

Pre-Polar Signed Ownership, Affine Obstructions, and Terminal-Source Tangent Transport in a Five-Wall Quadratic Moving-Incidence Model

Tao Lin
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Topological Materials and Phenomena
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.