Is there a physical basis in relativistic Dirac-Fock models for a reversed capacity symmetry bounding the periodic table at $Z=172$?

In the relativistic quantum mechanics of superheavy elements (e.g., Greiner, Müller, Rafelski; and multi-configuration Dirac–Fock calculations by Pyykkö and Fricke), the extended periodic table is predicted to terminate around $Z \approx 172$ . At this critical charge, the $1s_{1/2}$ state dives into the negative-energy Dirac sea ( $E_{1s} \le -m_e c^2$ ), triggering spontaneous positron emission in a supercritical Coulomb field. In the non-relativistic regime, the Madelung ( $n+\ell$ ) rule generates period capacities according to the well-known sequence: $C(k) = 2 \left\lfloor \frac{k + 3}{2} \right\rfloor^2$ yielding the standard progression: 2, 8, 8, 18, 18, 32... The cumulative sum through the 6th period (terminating at Radon, $Z = 86$ ) is exactly: $\sum_{k=0}^{5} C(k) = 2 + 8 + 8 + 18 + 18 + 32 = 86$ Intriguingly, in Pyykkö’s extended Dirac–Fock calculations (2011), the total number of predicted elements between Francium ( $Z = 87$ ) and the terminal noble-gas-like closure at $Z = 172$ ( $8p_{3/2}^4$ ) is also exactly: $172 - 86 = 86 \text{ elements}$ While some extended models predict an expansion into a massive 50-element 8th period (introducing an uncontracted 18-element $g$ -block), relativistic calculations show severe spin-orbit splitting: $8p_{1/2}$ and $9s_{1/2}$ states undergo drastic contraction, fundamentally shifting the Aufbau sequence and leading to predictions like a solid-state noble gas at $Z=118$ (Oganesson). If one maps the remaining 86 elements under a strictly reversed capacity constraint mirroring the Madelung sequence—defined as $C_{\text{rel}}(k) = C(11 - k)$ —it forms the symmetric 12-tier scheme illustrated below. The 86 non-relativistic elements ( $Z = 1 \dots 86$ ) perfectly mirror the 86 relativistic elements ( $Z = 87 \dots 172$ ). What makes this grouping particularly perplexing from a theoretical standpoint is the convergence of two completely decoupled physical mechanisms at the exact same integer $Z = 172$ : The Core / QED Scale: The breakdown of neutral atomic existence is dictated by the innermost $1s_{1/2}$ state diving into the negative continuum ( $Z_{\text{cr}} \approx 172$ ). This threshold is strictly governed by nuclear volume effects ( $R \sim A^{1/3}$ ) and short-range QED vacuum polarization (Uehling potential). The Valence / Chemical Scale: Simultaneously, $Z = 172$ is identified by Pyykkö as a formal closed-shell "noble" configuration ( $8p_{3/2}^4$ ). Here, the closing subshell is separated from its spin-orbit partner $8p_{1/2}^2$ (which fills $\sim 50$ elements earlier at $Z = 121\text{--}122$ ) by an unprecedented spin-orbit splitting that spans the entire 8th period. In non-relativistic physics, the period-doubling of the Madelung rule (2, 8, 8, 18, 18, 32, 32) is deeply tied to the dynamical $SO(4)$ Fock symmetry of the Coulomb problem (as analyzed in the Demkov–Ostrovsky model). When relativistic Dirac kinematics explicitly break this $SO(4)$ symmetry down to central-field $j$ - $j$ coupling, one would expect the arithmetic symmetry of the shell capacities to shatter entirely. My questions are: From the perspective of relativistic Dirac–Fock / QED calculations, is there any dynamical mechanism (such as extreme spin-orbit splitting, Darwin terms, or vacuum polarization) that justifies grouping superheavy subshell capacities into a contracting sequence $C(11 - k)$ as $Z \to 172$ ? Is this exact $86 \leftrightarrow 86$ partition strictly a coincidental arithmetic artifact arising from the fact that Pyykkö’s $8p_{3/2}^4$ shell closure happens to occur near the QED critical charge $Z_{\text{cr}} \approx 172$ ? Is there any hidden group-theoretic constraint (perhaps an embedding of the broken $SO(4)$ symmetry into a relativistic dynamical group) that forces the total number of bound relativistic states up to the nuclear QED diving limit ( $Z_{\text{cr}}$ ) to preserve the exact integer dimension of the first six non-relativistic periods ( $\sum_{k=0}^{5} C(k) = 86$ )? References: P. Pyykkö, A suggested periodic table up to $Z \le 172$ , based on Dirac–Fock calculations on atoms and ions , Phys. Chem. Chem. Phys. 13, 161–168 (2011). B. Fricke, W. Greiner, J. T. Waber, The continuation of the periodic table up to Z = 172 , Theor. Chim. Acta 21, 235–260 (1971). Yu. N. Demkov, V. N. Ostrovsky, $n+\ell$ filling rule in the periodic system and focusing of electrons in a modified Coulomb field , Zh. Eksp. Teor. Fiz. 62, 125–132 (1972).