Algorithmic Apotropaics and Bio-Geometric Shielding: A Comparative Study of Tibetan Srung 'khor and Renaissance Sigilla Planetarum

Across pre-modern Eurasian medical traditions, precision-drafted geometric diagrams were deployed not as passive decorative emblems, but as functional material instruments engineered to stabilize subtle physiological currents against macrocosmic perturbation. This study presents a comparative historiographical, mathematical, metallurgical, and neuroaesthetic investigation of two major iatromathematical traditions: the Tibetan tantric protection wheel (srung 'khor) codified within Sowa Rigpa (Rgyud bzhi and Desi Sangye Gyatso's 1688 Vaiḍūrya sngon po), and the European Renaissance planetary talisman (sigillum planetarum) synthesized across Marsilio Ficino's Neoplatonic spiritus therapy (De vita libri tres, 1489), Heinrich Cornelius Agrippa's cryptographic magic squares (De occulta philosophia, 1531/1533), and Paracelsian clinical metallurgy (Archidoxis Magica, 1572). Epistemological Contextualization: We evaluate contemporary bio-electromagnetic translations of these devices—such as characterizing the srung 'khor as a "fractal Faraday cage" or the sigillum as a "sympathetic capacitor" (e.g., Ibrahim Karim's BioGeometry)—within the historiography of esoteric scientism (Olav Hammer), participatory signature ontologies (Brian Copenhaver, Wouter Hanegraaff), and indexical ritual performativity (Stanley Tambiah). Trans-Eurasian Lo Shu Philology: We trace both traditions to a shared mathematical ancestor: the second-century BCE Chinese 3×3 Lo Shu magic square (jiugong), which bifurcated along a Sino-Tibetan Silk Road vector via Dunhuang (becoming the sme ba dgu nested inside polar Buddhist mandalas and srid pa ho charts) and an Indo-Islamic-European vector via Sanskrit perfumery matrices (Varāhamihira, Nārāyaṇa Paṇḍita) and Abbasid/Sufi awfāq treatises (Ikhwān al-Ṣafā', Picatrix, al-Būnī) to form the Cartesian 3×3 through 9×9 planetary kameas. Agrippan Cryptography & Elliptic Curve Torsion: We demonstrate that Agrippa's Hebrew planetary Intelligence and Spirit names function as built-in arithmetic checksums encoding the invariant magic constants M(n) = n(n² + 1)/2 and total grid sums Σ(n) = n²(n² + 1)/2, while decimal digit-truncation operates as an asymmetric one-way hash function. Furthermore, the restriction of planetary kameas to orders n = 3 through 9 sits squarely within the permissible rational N-torsion window E(ℚ)tors of elliptic curves established by Mazur's Torsion Theorem. Paracelsian Metallurgy & Electrum Magicum: We examine the clinical indications and thermodynamic hazards of the seven-metal harmonic alloy Electrum Magicum (35 parts by weight: 10 Au, 10 Ag, 5 Cu, 5 Hg, 2 Sn, 2 Pb, 1 Fe), demonstrating why the 357°C boiling threshold of mercury relative to refractory fusion points necessitated staged low-temperature lead–tin amalgamation. Neuroaesthetics & Autonomic Entrainment: Finally, we evaluate both artifacts through contemporary cognitive neuroscience, demonstrating how view-invariant visual symmetry recruits extrastriate visual networks (V3A, V4, V7, LOC) to generate the cortical Sustained Posterior Negativity (SPN) and right-posterior alpha (8–13 Hz) modulation, coupling with cutaneous vagal mechanoreception and aromatic limbic projection to operate as an exosomatic Phase-Locked Loop (PLL) that entrains a dysregulated autonomic nervous system toward homeostatic equilibrium.