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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.