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PROMOTED UNDER CITY PHYSICAL-CLAIM PROTOCOL. Within the explicitly declared Skyrme field models, the winding-number quantization $B\in\mathbb Z$ for $U:\mathbb R^3\to SU(2)$, the magnetic winding $Q\in\mathbb Z$ for $\mathbf n:\mathbb R^2\to S^2$, the Derrick scaling identity, and the unit-winding hedgehog result under the stated boundary conditions are [T] physical-model theorems. For a declared E47 orbit with the stated stabilizer assumptions, $\pi_3(\mathcal O_{v_0})\cong\mathbb Z$ is likewise a theorem of that continuum model. Not promoted: the claim that nature realizes the E47 orbit, a unique physical coupling/size/mass, RI-Skyrmion identity, propulsion performance, or hardware realization.
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Green Line district · Topological and field realization
Green marks spatial, topological, material, and field-carrier constructions. Exact topological identities remain distinct from numerical solvers and from physical realization claims. Transfer through the Subway Python Transit Map.
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Status: ✅ established topology and canonical $E_{47}$ algebra · ◇ conditional $E_{47}$-orbit Skyrme construction · △ RI identity and dimensional interpretations · ○ propulsion, zero-inertia, metric-lensing, and hardware programs
Skyrmions are topologically nontrivial field configurations classified by integer-valued winding invariants. The Drive corpus proposes that the canonical $E_{47}$ sector supports a Skyrme-type target orbit and that recursive informational persistence may be represented through the same mathematical language. The finite algebra is exact. The continuum construction is conditional on an orbit choice, embedding, coupling normalization, and PDE existence analysis. Physical, cognitive, and propulsion identifications remain open.
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Survey date: July 16, 2026
Scope: Skyrme fields, magnetic Skyrmions, $E_{47}$ orbit geometry, Derrick scaling, hedgehog sectors, RI correspondence, numerical obligations, condensed-matter interpretation, propulsion, metamaterials, and duplicate-export control across Google Drive.
The Drive corpus repeatedly uses the word Skyrmion for two mathematically related but physically different objects. They share integer-valued topology, but they must not be collapsed into a single physical system without an explicit map.
Let
$U:\mathbb R^3\to SU(2)\cong S^3,\qquad L_i=U^{-1}\partial_iU.$
Under finite-energy boundary conditions, spatial infinity compactifies $\mathbb R^3$ to $S^3$, and the topological charge is
$B=\frac{1}{24\pi^2}\int_{\mathbb R^3}\epsilon^{ijk}\operatorname{Tr}(L_iL_jL_k)\,d^3x\in\mathbb Z.$
The sectors are classified by
$\pi_3(S^3)\cong\mathbb Z.$
Let
$\mathbf n:\mathbb R^2\to S^2,\qquad \|\mathbf n\|=1.$
With constant boundary behavior at infinity, the winding number is
$Q=\frac{1}{4\pi}\int_{\mathbb R^2}\mathbf n\cdot(\partial_x\mathbf n\times\partial_y\mathbf n)\,dx\,dy\in\mathbb Z.$