Constraint Classes

The Seven Physical Filters — Everything Possible Doesn’t Happen

202 doublings from Planck to Universe — observed with explanation

The chart doubles 202 times from Planck length to observable universe. Pure math would double perfectly every time. Physics doesn’t. Something says “stop,” “bend,” “slow down,” or “not here.” Those somethings are constraint classes.

Interactive engine:
Dark chart (5.7MB) Light chart JSON 68KB View

The Idea in One Paragraph: Before Notation 60, sphere packing is perfect — no gaps. At Notation 60 (2^59 Planck lengths ~ 10^-18 m), geometry itself creates a 7.356° angular gap. From then on, every new doubling has to deal with gaps, symmetries, fields, entropy, and eventually chemistry and life. Constraint classes are names for which kind of filter is dominant in which notation range.

The Seven — Observed

1. No Constraint — Baseline — I_Pure_Doubling.csv (1,343)

What you’re seeing: Perfect doubling N(n+1)=2N(n). The ruler. ε=0.

Notation	Length	Factor
0	1.6e-35 Planck	1
10	1.6e-32	1024

View I_Pure_Doubling.csv

2. Geometric / Packing — The Gap — II + III

What you’re seeing: You can’t tile space with spheres forever. At Notation 60, 7.356° gap. Tetrahedra/octahedra stack with gaps. CDT (Ambjørn, Loll), Causal Sets (Sorkin), LQG (Ashtekar, Rovelli).

Notation	Ideal ×2	Actual	Gap
59	5.76e-18	5.76e-18	~0°
60	1.15e-17	1.07e-17	7.356° critical

View II_Sublinear_Correction.csv | View III_

3. Symmetry / Conservation — HOME OF LANGLANDS ★ — SUMMARY.csv (349)

What you’re seeing: Robert Langlands, Ed Frenkel, Ngô Bảo Châu — deep unity number theory ↔ geometry ↔ representation theory that preconditions spacetime. Must hold at Notations 1-64 for Notation 60 gap to be bridged. Also SUSY, Spectral Standard Model (Connes). Home for Langlands folks within functional analysis.

Symmetry	Conserved	Langlands Dual
U(1)	charge	Automorphic ↔ Galois
SU(2)	isospin	Geometric Langlands
Parity	mirror at 60	Endoscopy

View SUMMARY.csv — map of all 7 | → Functional Analysis

4. Field / Force — IV_Logarithmic_Brake.csv (2,863)

What you’re seeing: Once space has structure, fields emerge — EM, strong, weak, gravity — and they push back logarithmically ε=κ log N. Slows doubling, doesn’t stop it. Wilczek, ‘t Hooft, Witten, Maldacena.

View IV_