================================================================================ RADIAL DIMENSIONAL MAP — DATA COMPILATION ================================================================================ Date: 2026-03-21 Purpose: Compile ALL available data onto the radial coordinate system. Sources: TLT verified data, periodic table, cosmic structure surveys, engine data, dimensional formula. Status: Data compilation — mapping is proposed, not yet independently tested. ================================================================================ 1. THE C_POTENTIAL WELL AS RADIAL PROFILE ================================================================================ The C_potential well maps INVERSELY to the radial coordinate: Deepest point (max potential) = 1D center = highest frequency Well rim = 3D/4D boundary = lower frequency Beyond rim = 4D frontier = expanding space Well depth proportional to dimensional formula: d=1: a=1.000 (well bottom — singularity, max confinement) d=2: a=1.500 (geometry forms, potential releasing) d=3: a=1.618 (phi — topology, well structured) d=4: a=1.667 (peak room — frontier, well nearly flat) d=5: a=1.334 (declining — well curves back up) The C_potential (verified through 133 elements) IS the radial coordinate expressed as a potential energy landscape. 2. THE 0.5 DECOHERENCE BARRIER AT RING BOUNDARIES ================================================================================ Helium (Z=2): nu = 9.016e23 Hz — 1D/2D boundary First element to fill 1s^2. Noble gas, inert, spherical. Its inertness IS the boundary expression. Mercury (Z=80): nu = 4.518e25 Hz — 3D/4D boundary Anomalous structure (rhombohedral). Liquid at RT. Its anomalies ARE the boundary effects. TLT-019 verified: collapse at t/T = 0.5 (exact). B.6.8 verified: dimensional overflow at r = 0.5. The 0.5 barrier operates at EVERY ring boundary. Each overflow creates the next dimension. 3. FREQUENCY -> RING MAPPING ================================================================================ Particles (innermost — near 1D center): Planck: 1.855e43 Hz (1D absolute limit) Top quark: 4.183e25 Hz Higgs: 3.025e25 Hz EW VEV: 5.954e25 Hz W/Z bosons: 1.944-2.205e25 Hz Bottom quark: 1.011e24 Hz Tau: 4.296e23 Hz Proton: 2.269e23 Hz Electron: 1.236e20 Hz Elements (rings 1-3): Hydrogen: 2.270e23 Hz (lightest, inner ring) Helium: 9.016e23 Hz (1D/2D boundary marker) Carbon: 2.705e24 Hz (mid 3D ring) Iron: 1.258e25 Hz (3D active zone) Mercury: 4.518e25 Hz (3D/4D boundary marker) Oganesson: 6.622e25 Hz (deep into 4D frontier) Cosmic objects (outermost): Sun: 2.698e80 Hz (stellar scale, 3D ring) SMBH SgrA*: 1.08e87 Hz (galactic center) Milky Way: 2.7e92 Hz (galactic scale) 4. COSMIC WEB = RADIAL MAP AT LARGEST SCALE ================================================================================ Structure Geometry Dimension Volume% Mass% ------------------------------------------------------- Filaments Cylindrical 1D-like 5-8% 40-50% Walls/sheets Planar 2D-like 10-15% -- Voids Spherical 3D-like 77-80% 15% Nodes/clusters Concentrated 3D/4D 1-2% significant The cosmic web recapitulates the dimensional progression: 1D filaments -> 2D walls -> 3D voids -> 4D frontier nodes Void fraction 77-80% = the 3D ring dominates by volume (theory.txt predicts ~77%) Filaments + walls (~20%) = the 1D + 2D inner rings 5. {2,3} CONNECTIVITY AT EVERY SCALE ================================================================================ STELLAR: 33% binary({2}), 8% triple({3}) ORBITAL: Lagrange L4/L5 at {3} geometry (equilateral triangle) Kirkwood resonances: 2:1, 3:1, 5:2 GALACTIC: 2-arm spirals (30%), 3-4 arm (32%) Connectivity: 3-6 filaments per node COSMIC: {5} becomes structural at cosmic scale (approaching 4D frontier where {5} bridges) 6. THE DIMENSIONAL OVERFLOW -> EXPANSION CHAIN ================================================================================ Verified data points supporting the chain: a. 1D pulse creates radial propagation (TLT foundational, theory.txt) b. 2D geometry from interference (verified: B.6.2, k=9 invariant) c. 3D topology from phi folding (verified: 133 elements, cipher) d. Overflow at r=0.5 creates 5-fold symmetry (verified: B.6.8) e. Heavy elements show 4D boundary effects (verified: SO coupling, 9 elements corrected, 96.9% accuracy with spiral coordinate) f. Engine shows 3D/4D resonance (engine data: c=1.700, 1.732) g. Cosmic web structure matches ring volume fractions (published data) The overflow mechanism (d) operates at each ring boundary. Helium at 1D/2D boundary. Mercury at 3D/4D boundary. The overflow creates the next ring = expansion of dimensional space. UNTESTED: Whether the current expansion rate (Hubble constant) derives quantitatively from the 3D ring overflow rate. 7. BLACK HOLES AS 1D RETURN ================================================================================ A black hole is a system that has returned to the center of the radial map. Maximum confinement, maximum potential, zero geometry. The singularity IS 1D — pure f|t without dimensional room. This is consistent with: - Information paradox: 1D has no geometric structure to encode information in the 2D/3D sense. Information doesn't "disappear" — it returns to the 1D frequency domain where geometry hasn't formed yet. - Hawking radiation: the 1D center still pulses (f|t never stops). The radiation is the pulse leaking back outward through the ring boundaries. - Event horizon: the boundary where the C_potential well becomes too deep for 3D geometry to persist. Below the horizon, the system is in the 1D/2D regime. STATUS: SPECULATIVE interpretation of the radial map. Consistent with the framework but no quantitative test. ================================================================================ PROVENANCE: Jonathan Shelton, session 2026-03-21. Data from: TLT verified items, STRUCTURAL_FREQUENCY_MAP.txt, cosmic_frequency_map_research.txt, cosmological_geometry_research.txt, formula.txt, 4D engine results. ================================================================================