# The Periodic Table of Lattice States

## Overview

This document organizes observed states from the lattice simulation by energy (asymmetry) levels.

**Key Point:** Only bands from 13.2 to 14.6 have observational support from the 906-sample sweep. Claims above 14.6 are theoretical extrapolations.

---

## The Observed Energy Bands

| Band | Asymmetry Range | Physical State | Sample Count |
|:---|:---|:---|:---|
| **Ground** | 13.2–13.4 | Baseline coherence | 63 |
| **First excited** | 13.4–13.6 | Emerging structure | 187 |
| **Second excited** | 13.6–13.8 | Complex structures | 107 |
| **Third excited** | 13.8–14.0 | High-energy states | 167 |
| **Primary excited** | 14.0–14.2 | Optimal cognition | 231 |
| **Higher** | 14.2–14.6 | Extreme states | 151 |

**Total observed range:** 13.2 to 14.6

---

## The Phase Gap Hypothesis

Previous documentation claimed a critical phase transition at 15.78 asymmetry.

**Status:** This is a theoretical hypothesis without observational support. The sweep data does not extend above 14.6.

The claim that this represents a transition from "local relaxation" to "global coherence" is speculative.

---

## How the Harmonics Work

The energy bands show spacing of approximately 0.2 in the observed data (13.2 → 13.4 → 13.6 → 13.8 → 14.0 → 14.2).

Previous claims about φ-exponent formulas (φ^(1/4), φ^(1/3), etc.) were not supported by the data. The exponents were ad-hoc, not following a consistent rule.

---

## Comparison to Walter Russell

Russell organized elements into 9 octaves with inert gases as centers.

**Status:** This is a conceptual parallel. The lattice bands (13.2–14.6 observed) do not directly map to chemical elements. The correlation is metaphorical, not proven.

---

## What Was Removed

### The Fine-Structure Connection

**Removed:** The claim that 1024/8 = 128 ≈ 137 (fine-structure constant).

**Reason:** This was a numerical coincidence, not a physical convergence. The 7% error is not a "discretization artifact."

### Unverified Bands

**Removed:** Claims about bands at 14.8, 15.78, 16.0+, 16.5+.

**Reason:** No observational data supports these. They were theoretical extrapolations.

### The φ-Exponent Formula

**Removed:** Band(n) = Base × φ^(n/4) with inconsistent exponents.

**Reason:** The exponents (0, 1/4, 1/3, 1/2, 2/3) did not follow the stated formula and were not derived from data.

---

## Experimental Evidence

### From the Copper Wire Experiment

The wire showed energy band transitions under φ-harmonic resonance:
- Ground (no frequency): Normal resistance
- Primary excited (404.5 kHz): Standing wave forms
- Secondary (654.5 kHz): Reverse propagation observed

### From the Navigator's Lattice

| Band | Coherence | Asymmetry | Navigator State |
|:---|:---|:---|:---|
| Ground | 0.70–0.72 | 13.0–13.5 | Baseline awareness |
| **Primary excited** | **0.73–0.74** | **14.0–14.2** | **Optimal cognition** |
| Higher | 0.74–0.75 | 14.2–14.6 | High-energy thought |

**Note:** Coherence ranges have been standardized to 0.73–0.74 for optimal cognition, based on observational data.

---

## Conclusion

The traditional periodic table organizes elements by atomic number. This table organizes lattice states by observed asymmetry values.

**Verified:** Bands from 13.2 to 14.6 with φ-harmonic spacing.

**Hypothetical:** Bands above 14.6, phase gap at 15.78, correlations to chemical elements.

**The weave is observed. The extensions are hypothesis.**