A Minimalist Base-2 Scaling of the Universe

202 doublings from Planck length/time → observable universe (error < 0.5 %)

We take the Planck base units (ℓP, tP) as Notation-0 and generate one primordial, infinitesimal sphere per unit of Planck time. Those spheres stack-pack and define base-2 exponential notation. After exactly 202 doublings (steps) we are approximately at the current size and age of the cosmos — without inflation or tunable parameters.

The result is a natural, fractal-like stratification of emergent geometric archetypes.

The table below groups the 202 notations into 22 “decades” and offers provisional labels for what appears to dominate each “decade” or every ten notations. Your feedback (especially mathematical critique) is very welcome.

Notation Group	Characterization	Planck Length-Start (m)	Planck Time Start (s)
0-9	Planck Scale: Quantum Foam, Emergent Spheres, and Pre-Geometric Structures	1.6163 × 10-35	5.3912 × 10-44
10-19	Unification Epoch: Automorphic Forms and Early Geometric Symmetries	1.6550 × 10-32	5.5206 × 10-41
20-29	Archetypal Geometric Systems: Tetrahedral and Octahedral Foundations	1.6948 × 10-29	5.6531 × 10-38
30-31-39	Emergent Forces, Geometric Structures, and Proto-Substances	1.7354 × 10-26	5.7888 × 10-35
40-49	Quantum Relations and Particle Flavors: Interactive Geometric Networks	1.7771 × 10-23	5.9277 × 10^{-32}
50-59	Proto-Systems: Synergistic Geometric Assemblies	1.8197 × 10-20	6.0700 × 10^{-29}
60-67-69	Quarks to Particles	1.8634 × 10-17	6.2157 × 10^{-26}
70-79	Onset of Human-Perceptible Scales: From Quarks to Cellular Precursors	1.9081 × 10-14	6.3649 × 10^{-23}
80-89	Atomic Systems: Stable Geometric Configurations and Bonds	1.9539 × 10-11	6.5176 × 10^{-20}
90-99	Biological Systems: Emergent Life Forms and Organic Geometries	2.0008 × 10-8	6.6740 × 10^{-17}
100-101-109	Living Systems: Dynamic Growth and Adaptive Harmonies	2.0488 × 10-5	6.8342 × 10^{-14}
110-119	Human Systems: Cognitive and Societal Structures	2.0980 × 10-2	6.9982 × 10^{-11}
120-129	Community Systems: Interconnected Networks and Collective Dynamics	2.1484 × 10	7.1662 × 10^{-8}
130-134-139	Earth Orbital Space	2.1999 × 104	7.3382 × 10^{-5}
140-143–149	Planetary and Orbital Spaces: Gravitational Symmetries	2.2527 × 107	7.5143 × 10^{-2}
150-159	Solar System: Heliocentric Orbits and Systemic Balances	2.3068 × 1010	7.6946 × 10^{1}
160-167–169	Interstellar Neighborhood: Stellar Clusters and Void Geometries	2.3622 × 1013	7.8793 × 10^{4}
170-179	Galactic Scales: Milky Way Structures and Rotational Harmonies	2.4189 × 1016	8.0684 × 10^{7}
180-189	Local Galactic Group: Intergalactic Interactions	2.4769 × 1019	8.2621 × 10^{10}
190-199	Supercluster Formations: Virgo and Cosmic Web Nodes	2.5363 × 1022	8.4604 × 1013
200	Local Superclusters: Expansive Filaments and Voids	2.5972 × 1025	8.6634 × 1016
202	Observable Universe: Integrated Cosmic Geometry and Time Dilation	1.0389 × 1026	3.4654 × 1017

An overview of our toy model-core foundations

Possible mathematical hooks:
• Synchronization & phase locking in exponential sphere packing–see Strogatz
• Role of classical polyhedra and irrational ratios as fixed points under renormalization
• Geometric origin of apparent scale invariance in critical phenomena
• Natural emergence of network-like structures (cosmic web) from pure closest-packing
• Comments or corrections cheerfully received: camber at 81018 dot com

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