Patrice Portemann Independent Researcher in Applied Mathematics & Physics

My work focuses on breaking the paradigm of statistical induction in Artificial Intelligence — and deriving physical structure from geometric first principles.

A reproducible computational environment for testing field-theoretic structures. Given a candidate model (ansatz, Lagrangian, symmetry-breaking pattern) and measured anchoring data, it returns a verdict — existence, spectrum, quantisation, regime — with documented invariants, frozen protocols, and SHA-256 hashed artefacts.

Core predictions (P0–P4):

• 🎯 P0: BPS mass calibration — C(ρ=1) = 1.3098 (literature 1.24–1.31)
• 🎯 P1: Bound-state spectrum — Coulomb pure to 10⁻⁴, a₀ = 137 l.u.
• 🎯 P2: Dirac charge quantisation — e·g = 2π exact, n = 1
• 🎯 P3: Nucleus–ring bridge — flux tube confinement emergent
• 🎯 P4: Phase diagram — 2 regimes (gauge-core / Higgs-core), ρ* ≈ 0.75

Applications (P7–P31) — 24 successes, 7 partials, 0 falsifications:

• ✅ P7: Isotope shifts in Cl — non-perturbative exact; perturbation theory fails by 18× (electronic) to 10⁷ (muonic saturation)
• ✅ P8: EMC effect — SRC preferred over mean-field by form of modification; matches DIS correlation, saturation, and isospin dependence
• ⚠️ P9: PREX–CREX neutron-skin puzzle — good magnitude, wrong fine/thick switching; boundary located (discrete shell model fails continuous surface density)
• ✅ P10: ANU bridge / periodic-table identity cards — N/18 points to dominant isotopes; core hierarchy validated (88 elements)
• ⚠️ P11: Valley of stability — form captured (trough, beta-line); absolute scale approximate (RMS 0.25 MeV)
• ✅ P12: Chemistry / Hückel valence — octet, 4n+2 aromaticity, Jahn-Teller from degeneracy
• ✅ P13: Stability as form of potential — Geiger-Nuttall slope 1.60 vs 1.57; Regge slope 0.884 vs 0.9 GeV⁻²
• ✅ P14: Atomic identity cards H→U — electron boundary at Z=12; muon saturated everywhere
• ✅ P15: Hadron spectrum — Regge universal slope + charmonium Cornell spacings within 1%
• ⚠️ P16: Unified decay mode map — 18/24 correct; α and β⁺ perfect; boundary cases escape
• ✅ P17: Aharonov–Bohm — periodicity Φ₀=h/e; gap closure at ½-flux; persistent current
• ✅ P18: Topological states — Chern (1,−2,1); SSH protected zero-modes
• ✅ P19: Diffuse surface bound — failure P9/P11 becomes measured bound: a ≈ 0.28 fm required
• ✅ P20: H₂⁺ molecular frontier — exact LCAO; R_eq=2.353 a₀; frontier located (multi-body beyond)
• ✅ P21: Bond polarity — χ=(IE+EA)/2 lever; 13/14 directions correct; Spearman 0.99; zero parameter
• ⚠️ P22: Double-beta decay — pairing mechanism derived; 5/6 criteria; ²⁷⁶Ge suppression escapes
• ✅ P23: Nuclear magnetic moments — Schmidt lines; signs 12/12; within 10% for single-particle
• ✅ P24: Fractional quantum Hall — Jain sequence ν=n/(2pn±1); 6/6 criteria
• ✅ P25: Topological insulators — 2D/3D Z₂ invariant; 6/6 criteria
• ⚠️ P26: Surface diffusivity — a≈0.28 fm confirmed across 5 nuclei; sharp-core overpredicts radii
• ✅ P27: Two-electron correlation — He energy 2%, ionization 10%; in-out recovery 45%
• ✅ P28: Unification — surface + correlation structural link; κ_opt discriminates
• ✅ P29: Isovector calibration — κ_opt≈0; discriminating success 5/6
• ⚠️ P30: Kato cusp — cusp ratio 1.9 vs 2.0; correlated tail approximate
• ⚠️ P31: r₁₂ frontier — explicit r₁₂ declared constitutive for He beyond 2%

A research programme constructing falsifiable physical predictions from non-commutative spectral triples. Four theorems proved, a new arithmetic law established, and numerical benchmarks validated on the Gross–Pitaevskii solver.

Key results:

• 🧮 Theorem T1: dim H_F ≥ 2R+1 (exact, saturated) — Standard Model emerges at R=3, dim=7
• 🧮 Theorem T2: k ≥ 2 (no field without at least 2 vertices)
• 🧮 Theorem T3: max(m_ij) ≥ 3 for 3 pairs + chiral zero (proved via odd-margin lemma, 622,560 cases, 0 violations)
• 🧮 Theorem T4: Non-uniqueness of the minimal class at dim 7 (33,148 solutions)
• 📐 KO-6 Arithmetic Law: At m ≤ 2, all margins are even or odd perfect squares; ranks 5 and 7 forbidden; 9 = 3² is the largest exact bound

For the past two decades, I have been developing a Topological Fractional AI framework. The core hypothesis is that complex systems (biological signals, fluid dynamics, materials) should not be approximated by massive flat tensors (Deep Learning), but solved by embedding strict geometric priors directly into the state-space equations.

My engine replaces standard gradient descent with:

• Orthogonal Spectral Decomposition: Forcing the system into strict independent subspaces.
• Causal Coupling Matrices (M_ij): Solving transduction rules via algebraic inversion instead of backpropagation.
• Atangana-Baleanu Fractional Calculus: Embedding non-local memory (Mittag-Leffler kernel) to respect the true thermodynamics of the modeled system.

A "Gray-Box" solver capable of mapping complex non-Markovian dynamics with only 28 parameters, achieving comparable AUC to 10,000+ parameter Graph Neural Networks.

For institutional evaluation, technology transfer, or licensing inquiries: [email protected]