Geometric modeling of atomic stability V2

Project Orbital: Frozen Raw Output 119-138 - Geometric Closure, Rotor/Hook Rules, and Blind Pressure Test Supplement to Project Orbital Preprint (Zenodo Aug 3-4, 2026) | Frozen: November 1, 2026 16:47 | Zenodo Version 2 Declaration of Freeze This document publishes the raw 119-138 output of Project Orbital exactly as generated July 20, 2026 04:53 AM. No parameters tuned toward relativistic atomic calculation literature reporting 8p1/2, 7d, 5g, 6f near-degeneracy. The disagreement between clean 5g filling predicted here and messy degenerate literature is declared as a blind pressure test. No decay numbers derived in this version. Primary Discovery (Session II, May 22, 2026) "What chemistry textbooks call valence electrons and electronegativity are flat, statistical names for a deeper physical reality: wave-form geometry seeking spatial closure. Reactivity is geometric hunger. Inertness is geometric resolution." Primary Claim: Nature manages thermal load not by dissipating energy, but by bifurcating geometry. When spatial boundary reaches threshold, structure evolves into next geometric form to distribute peak stress. Law of Geometric Closure Periodic Table as Breathing Wave: Breaths 2,8,8,18,18,32,32 governed by same 1-2-4-8 bifurcation law inside single atom and across entire table. Reactivity = open spatial void, Inertness = closed symmetry. Closure Index Ci Ci = [0.0 ---- 1.0] - scalar derived ONLY from geometry. Ci = 1.0 = Perfectly Closed. Symmetrical, unpolarized wave envelope. Zero directional vectors exposed. No geometric grip for external bonding. Maximum stability. Noble gas signature. Hooks = 0. Ci < 1.0 = Open - Geometric Hunger Active. Asymmetric geometry with at least one spatial void. At least one directional vector exposed. Hooks > 0. Geometric Hunger Scalar: H = 1 - Ci. H = 0 inert, H -> 1 explosive hunger. H derived only from geometry, no chemistry input. Mathematical Rules 1. Bifurcation Law: 1-2-4-8 doubling when thermal load threshold reached. 2. g-Rotor Count R: Number active 5g loci at Z. R increments per Z in g-block 121-138. R(121)=1...R(138)=18. R(126)=6, R(138)=18 closure. 3. Twin-Pair Count T = floor(R/2). Two rotors pair to cancel opposing voids, forming gyro-balanced pair. 4. Geometric Parity p = R mod 2. p = unpaired rotor. p=0 even geometric parity = R even = T twin-pairs = voids cancel = gyro-balanced = Ci up = stable. p=1 odd geometric parity = one open void = lopsided = geometric hunger = unstable. This is NOT Z parity. 5. Hooks = Exposed Directional Vectors. Hooks = R nominal, but effective grip reduced by twin-pair cancellation. Ci=1.0 => Hooks=0. 6. Ci(Z): Ci increases with T and cumulative closure. Ci(119)=0.0625, Ci(120)=0.125, Ci(126)=0.30 Island #1, Ci(138)=0.66 g-shell closed, Ci(168)=1.0 Island #3. Sawtooth closure graph. 7. 5g Assignment Rule (Frozen): s-block opens into cube at 121-124. 121-138 assigned pure 5g in this geometry model. 121=5g1...138=5g18. This clean prediction vs literature messy prediction (8p1/2, 7d enter first, 5g/6f/7d/8p nearly degenerate) is the blind test. Raw Frozen Output 119-138 (July 20, 2026 04:53 AM) Z Sym Name Config Ci R T p Hooks Behavior / H=1-Ci 119 Uue Ununennium [Og] 8s1 0.0625 1 0 1 1 Explodes H=0.9375 120 Ubn Unbinilium [Og] 8s2 0.125 2 1 0 0 Melts -100C H=0.875 s-closed 121 Ubu Unbiunium 8s2 5g1 0.15 1g 0 1 1 s opens into cube H=0.85 122 Ubb Unbibium 5g2 0.18 2g 1 0 2 cube builds H=0.82 123 Ubt Unbitrium 5g3 0.21 3g 1 1 3 H=0.79 124 Ubq Unbiquadium 5g4 0.24 4g 2 0 4 cube complete H=0.76 125 Ubp Unbipentium 5g5 0.27 5g 2 1 5 lopsided - hunger - H=0.73 126 Ubh Unbihexium 5g6 0.30 6g 3 0 6* ISLAND #1 50g/cm3 7000C 3 twin-pairs H=0.70 gyro-balanced 127 Ubs Unbiseptium 5g7 0.33 7g 3 1 7 lopsided H=0.67 Radioactive 128 Ubo Unbioctium 5g8 0.36 8g 4 0 8 gyro-balanced 4 pairs H=0.64 129 Ube Unbiennium 5g9 0.39 9g 4 1 9 H=0.61 130 Utn Untrinilium 5g10 0.42 10g 5 0 10 H=0.58 131 Utu Untriunium 5g11 0.45 11g 5 1 11 H=0.55 132 Utb Untribium 5g12 0.48 12g 6 0 12 H=0.52 133 Utt Untritrium 5g13 0.51 13g 6 1 13 H=0.49 134 Utq Untriquadium 5g14 0.54 14g 7 0 14 H=0.46 135 Utp Untripentium 5g15 0.57 15g 7 1 15 H=0.43 136 Uth Untrihexium 5g16 0.60 16g 8 0 16 H=0.40 137 Uts Untriseptium 5g17 0.63 17g 8 1 17 H=0.37 138 Uto Untrioctium 5g18 0.66 18g 9 0 0 g-shell closed Shield^3 Au^4 H=0.34 *Hooks=6 at Z=126 listed as 3 twin-pairs - pairs cancel voids geometrically but 6 vectors exposed as paired set. Blind Pressure Test Frozen prediction: Clean 5g filling 121-138, cube at 121-124, even p = gyro-balanced islands, odd p = lopsided hunger. Literature prediction: 8p1/2 and 7d enter at 121, then 5g,6f,7d,8p nearly degenerate, no clean g-block. Test to be compared blind against future synthesis and decay logs. No tuning. Measurable Mapping: Geometric Hunger to Chemistry Define H = 1 - Ci, derived only from geometry. Hypothesis: H predicts ionization energy (IE), electron affinity (EA), oxidation behavior across elements model never saw (1-118). Prediction: IE high when H low (closed, Ci=1.0 noble gas). IE low when H high (hungry, alkali). Test correlation H vs measured IE1 for 1-118 blind. If correlation significant, then geometric hunger -> chemistry is measurable mapping, not metaphor. Example: 119 H=0.9375 predicts alkali-like explosive reactivity (1 hook), 120 H=0.875 predicts closed s2 but 0 hooks - low melt -100C, 126 H=0.70 with 3 twin-pairs predicts reduced hunger vs neighbors 125 H=0.73 and 127 H=0.67 - predicts longer half-life, lower Qα - gyro-balanced peak. Timestamp Frozen as-is, no decay numbers, no tuning to 8p1/2, 7d, 6f literature. Raw geometry only. Supplements Project Orbital preprint Aug 3-4 2026. H = 1 - Ci scalar defined for blind test vs ionization energy / electron affinity.