Not everything mathematically possible between Notation 0 and 202 actually happens.
The chart doubles 202 times from Planck length to the 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 (verified working):
Dark chart (5.7MB) | Light chart | chart_202_notations.json (68KB) | chart_202_notations.csv (32KB)
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.
Most people won’t download a CSV from someone they don’t know well. So here below, each file is observed in place with plain-English explanation. Download is available — small gray link — for researchers who want it.
Interactive Engine
https://81018.com/embed/chart-constraint-overlay-dark.html
Open Full-Screen — iPhone Perfect
The Seven — Observed
1. No Constraint — Baseline — I_Pure_Doubling.csv
What you’re seeing: Perfect doubling. Every notation doubles exactly. This is the math ideal that physics never quite achieves. N(n+1)=2×N(n). No ε.
Why it matters: It’s the ruler. Everything else is deviation from this.
| Notation | Length (m) | Factor | ε(N) |
|---|---|---|---|
| 0 | 1.6e-35 (Planck) | 1 | 0 |
| 1 | 3.2e-35 | 2 | 0 |
| 10 | 1.6e-32 | 1024 | 0 |
I_Pure_Doubling.csv download (1.3KB)
2. Geometric / Packing — II_Sublinear_Correction.csv + III_Subdoubling_Linear.csv
What you’re seeing: You can’t tile space with spheres forever. Tetrahedra + octahedra leave gaps. At Notation 60, a 7.356° angular gap appears — pure geometry says “stop.” The correction ε = κN^α bends doubling sublinear.
Where: Notations 0-64, critical at 60. Home of CDT (Ambjørn, Loll), Causal Sets (Sorkin), LQG (Ashtekar, Rovelli).
| Notation | Ideal ×2 | Actual (with gap) | Gap |
|---|---|---|---|
| 59 | 5.76e-18 m | 5.76e-18 | ~0° |
| 60 | 1.15e-17 | 1.07e-17 | 7.356° ← critical |
| 61 | 2.3e-17 | 2.1e-17 | 8.1° |
II_Sublinear_Correction.csv download (3.1KB) | III_Subdoubling_Linear.csv download (3.1KB)
3. Symmetry / Conservation — HOME OF LANGLANDS — SUMMARY.csv
What you’re seeing: Nature keeps accounts — charge, spin, parity must balance. Langlands Programs (Robert Langlands, Ed Frenkel, Ngô Bảo Châu) show deep unity number theory ↔ geometry ↔ representation theory. This symmetry filter preconditions spacetime: only certain packings can survive the Notation 60 gap. If symmetry doesn’t hold, the universe can’t bridge 60.
Why here: Notations 1-64, foundational. This is where Langlands lives inside functional analysis. Also SUSY (Dimopoulos, Gates), Spectral Standard Model (Connes).
| Symmetry | Conserved | Filters Notation | Langlands Dual |
|---|---|---|---|
| U(1) charge | electric charge | 1-64 | Automorphic ↔ Galois |
| SU(2) spin | isospin | 10-65 | Geometric Langlands |
| Parity | mirror | 60 (gap) | Endoscopy |
SUMMARY.csv — The map of all 7 filters download (0.3KB) | chart_202_notations.json displays in browser, no download needed
4. Field / Force — IV_Logarithmic_Brake.csv
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.
Where: 65-134 — particles appear. Field theories (Wilczek, ‘t Hooft), Strings (Witten, Vafa, Maldacena).
| Notation | Field | Brake ε | Effect |
|---|---|---|---|
| 70 | EM appears | 0.12 log N | slight drag |
| 100 | Strong/Weak | 0.18 log N | particles stabilize |
IV_Logarithmic_Brake.csv download
5. Thermodynamic / Entropic — V_Threshold_Saturation.csv
What you’re seeing: Order costs. Threshold filter — doubling works until entropy threshold, then saturates. S curve.
Where: 90-170 dominant.
V_Threshold_Saturation.csv download
6. Information / Complexity — VI_Delayed_Feedback.csv
What you’re seeing: How much info can a notation hold? Decoherence — quantum becomes classical when feedback delay exceeds threshold. Delayed ε(N-τ).
Where: 130-190
VI_Delayed_Feedback.csv download
7. Biological / Chemical + Measurement — VII_Stochastic.csv
What you’re seeing: After ~170, atoms → molecules → life → life measures. Stochastic filter — ε random, but bounded. Consciousness is a constraint class.
Where: 170-202
All Data — Observe First, Download If You Trust
Every table above is a human-readable summary of the live file. Click file name to view in browser (JSON displays, CSV shows text). Only click gray download if you know and trust 81018.com — which you now do, because you can see the data first.
- chart_202_notations.json (68KB) — view in browser
- chart_202_notations.csv (32KB) — view
- I through VII + SUMMARY — same pattern — observe, then optionally download
Rebuilt 2026-08-15 — Observe, don’t download, unless you know Bruce. Bruce Camber, 81018.com