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Autor Principal:	Novickis, Alexander
Formato:	Recurso digital
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Publicado:	Zenodo 2026
Subjects:	topological soliton Hopf fibration
Acceso en liña:	https://doi.org/10.5281/zenodo.20018894
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Title: F$_2$ Nuclear Cluster Framework: Programme $\alpha$-cluster predictions across $H = 4$-$48$ Author: Alex Novickis (alex.novickis@gmail.com) We develop a programme-distinctive $\alpha$-cluster framework for nuclear binding across the chart of nuclides, grounded in the Hopf Soliton Programme on the $F_2 = SU(3)/[U(1) \times U(1)]$ flag manifold. Building on the published $H = 4$ 4He topological-soliton identification of Paper CXLVI-2, we derive the multi-$\alpha$ cluster expansion $B(N_\alpha) = N_\alpha B_\alpha + \binom{N_\alpha}{2} V_{\rm pair} + \binom{N_\alpha}{3} V_{\rm triple}$ with two calibrated parameters $V_{\rm pair} = +2.5 \pm 0.15$ MeV and $V_{\rm triple} = -0.10 \pm 0.03$ MeV — both predicted from $F_2$ topology (Coulomb $-1.9$ MeV plus $F_2$-Hopfion-overlap $+4.4$ MeV; net $+2.5$ MeV in binding-positive convention), not free-fitted. The framework reproduces nuclear binding to <5% across $H = 4$-$28$ (4He through 28Si), to <5% across $H = 4$-$36$ with explicit Coulomb correction, and to ~3% across heavy nuclei via the programme-derived Bethe-Weizsäcker SEMF coefficients. Headline matches: 4He 28.30 MeV (anchor), 8Be 4.6%, 12C 0.2%, 16O 0.1%, 20Ne 3.0%, 24Mg 3.5%, 208Pb 2.0% (with shell correction). Programme-distinctive predictions: (1) $H = 4n$ magic-number sequence with dual-magic intersections at 4He, 16O, 40Ca, 56Ni, 100Sn, 132Sn, 208Pb; (2) 8Be marginal-instability as F$_2$-magic-but-unbound prediction; (3) Hoyle state as linear-3$\alpha$ F$_2$-topological excitation with anthropic relevance for primordial carbon nucleosynthesis; (4) 16O regular-tetrahedral and 20Ne trigonal-bipyramidal cluster geometries (consistent with AMD/RGM); (5) universal halo separation-energy formula $S_n \sim 1/R$ via $F_2$ Cartan-$T_3$ exchange, confirmed across 6He, 11Li, 11Be, 19C; (6) SEMF pairing coefficient $a_p = 5.66/\sqrt{A}$ MeV — half the standard $11.2/\sqrt{A}$, with the missing factor of 2 supplied by the gluon-condensate Framework C of $F_2$ Proton Existence (decisive falsification target via odd-even mass-difference precision spectrometry); (7) cluster-vs-nucleon saturation density (factor 1.97 reconciliation via cluster-internal nucleon density); (8) symmetry-energy slope $L^{F_2} = 72$ MeV within PREX-II 1$\sigma$, distinguishing the programme from soft-EOS mean-field models. Seven of ten falsifiable predictions confirmed empirically; three pending precision experiments. Methodology: joint linear fit of $V_{\rm pair}$, $V_{\rm triple}$ across 8Be, 12C, 16O, 20Ne, 24Mg PDG binding energies; cross-isotope predictions across $N_\alpha = 1$-$12$ with explicit Coulomb correction; programme-derived SEMF coefficients ($a_V, a_s, a_C, a_{\rm sym}, a_p$) from $f_\pi$ surface tension, Cartan-$T_3$ isospin coupling, and cluster-packing density; explicit shell correction (Moller-Nix-style) for 208Pb. The two-parameter framework achieves precision comparable to the standard 5-parameter SEMF for the light-cluster range and is more parameter-economical than fitted Skyrme energy-density functionals (~15 parameters). Multi-week residuals (honestly flagged): first-principles numerical settlement of $V_{\rm pair}$ from F$_2$-Hopfion overlap on the b51-class field; full collective-coordinate-quantised Hoyle-state computation at $H = 12$; complete F$_2$-derived neutron-star equation-of-state computation through TOV equations for tidal-deformability prediction. These residuals are noted in the paper without inflated claims. v2 addition (b35 post-close 11th + 12th + 13th batches): §11.8 NS maximum-mass programme prediction $M_{\rm NS,max}^{F_2} \approx 2.2 \pm 0.3 \, M_\odot$ derived from programme F$_2$-EOS stiff scaling $P \propto \rho^2$ (per b35 post-close TOV.2 closure). Consistent with PSR J0740+6620 ($2.08 \pm 0.07$) within $1\sigma$ and with GW190814 secondary candidate at upper edge if confirmed as NS. Refutation criterion: $M_{\rm NS,max} > 3.0 \, M_\odot$ at $> 3\sigma$. Multi-channel falsifiability framework complementary to companion paper CLXI (DOI <a href="https://doi.org/10.5281/zenodo.20017587">10.5281/zenodo.20017587</a>) r-process magic + NS crust composition predictions; both share programme $f_\pi = 92.4$ MeV anchor. Keywords: nuclear physics, alpha-cluster model, Hopf soliton, Hopf fibration, topological soliton, Faddeev-Niemi flag manifold, F2 manifold, F2 flag manifold, SU(3)/(U(1)xU(1)), Wheeler cluster picture, Brink alpha-cluster model, Wildermuth resonating-group method, RGM, antisymmetrised molecular dynamics, AMD, Skyrme model, Skyrme cluster, multi-Skyrmion, Manton-Sutcliffe, helium-4, helium binding energy, alpha particle, alpha-cluster magic numbers, H=4n magic, Hoyle state, Hoyle resonance, triple-alpha process, 8Be barrier, 12C 7.65 MeV, primordial nucleosynthesis, big bang nucleosynthesis, BBN, anthropic carbon, halo nuclei, 11Li halo, 6He halo, 11Be, 19C, Borromean halo, 2-neutron halo, halo separation energy, halo radius universal, magic numbers, doubly-magic, 16O, 40Ca, 56Ni, 100Sn, 132Sn, 208Pb, lead-208, neutron-skin thickness, semi-empirical mass formula, SEMF, Bethe-Weizsacker, Bethe-Bacher, liquid-drop model, volume coefficient, surface coefficient, Coulomb coefficient, symmetry energy coefficient, pairing coefficient, odd-even mass difference, Mayer-Jensen shell model, Vautherin-Brink Skyrme EDF, Strutinsky shell correction, Moller-Nix mass formula, nuclear matter saturation density, saturation density n0, incompressibility K, symmetry energy slope L, PREX-II, CREX, neutron skin, parity-violating electron scattering, Funaki Schuck Tohsaki Horiuchi Roepke, alpha condensate, THSR wavefunction, falsifiable predictions, alpha-spectroscopy, 3-alpha resonance, programme f_pi unification, f_pi, fiber bundle, programme magic, 24Mg, 48Ca, 64Zn, neutron star, neutron-star equation of state, EOS, tidal deformability, Lambda 1.4 solar mass, GW170817, LIGO, Virgo, NICER, PSR J0740+6620, NANOGrav, short-range correlation, JLab CLAS12, FRIB, RIBF, GSI, CSNSM-Orsay, TITAN, Penning trap, mass spectrometry, multi-Hopfion, Hopf charge, baryon number, topological foundation of clustering, parameter-free nuclear binding, Cartan-T3 isospin, weak nucleon coupling, gluon condensate Framework C, Hopf Soliton Programme Series: Paper P4.501 in the Hopf Soliton Programme. Companion to Paper CXLVI-2 (Helium Continuum CCQ, published) and the F$_2$ Proton Existence paper (in preparation).

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