The Tri-Outcome Redshift Model — A Structural Alternative to Expansion Cosmology
A curvature-indexed explanation of redshift based on resonance structure within the Pattern Field.
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1. Overview
In conventional cosmology, redshift is interpreted as either Doppler velocity or expansion of the metric. Pattern Field Theory (PFT™) replaces these interpretations with a curvature-indexed resonance model based on the Allen Orbital Lattice (AOL).
Redshift in PFT is the consequence of how a signal propagates across three lattice-based vectors created by Trivergence — the triple-vector resonance split that occurs when curvature moves across AOL symmetry boundaries.
2. The Tri-Outcome Structure
Trivergence produces three stable propagation paths in the Pattern Field:
-
Curvature-Dilation Redshift (CDR)
Caused by AOL curvature density along the propagation path.
\( z_{\mathrm{CDR}} \approx \kappa(r)\, r \) -
Depth-Layer Redshift (DLR)
Caused by traversal through deeper resonance layers.
\( z_{\mathrm{DLR}} = \Delta d / d_0 \) -
Vector-Interference Redshift (VIR)
Caused by misalignment between: the source vector, observer pattern, and the resonance path.
\( z_{\mathrm{VIR}} = \Delta\phi / \phi_0 \)
These three outcomes are not alternatives — they combine into one measurable redshift:
\( z_{\mathrm{total}} = (1+z_{\mathrm{CDR}})(1+z_{\mathrm{DLR}})(1+z_{\mathrm{VIR}}) - 1 \)
This replaces recession velocity with geometry + depth + phase-vector interaction.
3. AOL Geometry and Trivergence
The Allen Orbital Lattice defines three independent propagation vectors due to its prime-seeded symmetry:
- Axial divergence — curvature stretching along expansion arcs
- Radial divergence — depth-layer transitions across fractal levels
- Phase divergence — vector-angle shift between observer and source path
Trivergence is the mechanism; redshift is the measurement effect.
4. Comparison Table
| Concept | ΛCDM Interpretation | PFT Interpretation |
|---|---|---|
| Primary cause | Velocity / expansion | Curvature, depth, vector-phase shift |
| Pathscale effect | Expansion rate (H₀) | Curvature density κ(r) |
| Layer effect | None | Depth-layer resonance loss |
| Observer alignment | None | Vector interference Δφ |
| Redshift formula | \( z = (\lambda_{\mathrm{obs}}-\lambda_0)/\lambda_0 \) | \( z = (1+z_{\mathrm{CDR}})(1+z_{\mathrm{DLR}})(1+z_{\mathrm{VIR}})-1 \) |
5. Empirical Behaviour
High-z Objects (JWST, z ≈ 10–20)
- CDR reproduces GR-compatible values.
- DLR adds small resonance-layer corrections.
- VIR adds observer-frame skew.
CMB Asymmetries
- Depth-layer terms suppress long-wave modes.
- Vector-phase terms match hemispherical asymmetry.
Lensing anomalies
- Brightness differences arise from depth and vector-phase interactions.
Bound systems (e.g., Andromeda)
- CDR ≈ 0 (consistent with no expansion).
- DLR and VIR give micro-shifts consistent with observations.
6. Simulated Comparison
Note: Values below are placeholders for illustrative structure.
| Object | GR z | CDR | DLR | VIR | Total |
|---|---|---|---|---|---|
| GLASS-z13 | 13.24 | 13.24 | +0.03 | +0.002 | 13.272 |
| Andromeda | 0 | 0 | 0.001 | 0.0001 | 0.0011 |
| CMB suppression | ~0.001 | ~0.001 | 0.0004 | 0.0002 | ~0.0016 |
7. Strengths and Future Directions
Strengths
- Explains high-z behaviour without dark energy.
- Integrates smoothly with AOL and PFT curvature structure.
- Predicts measurable vector-phase and depth-layer corrections.
Future Work
- Expand Trivergence simulations with AOL curvature fields.
- Develop empirical fits for CDR, DLR, VIR individually.
- Generate large-scale AOL cosmology maps for comparison with ΛCDM.
8. Conclusion
The Tri-Outcome Redshift Model reframes cosmology by linking redshift to curvature, depth, and phase-vector interaction within the Pattern Field. Derived from the structural behaviour of the Allen Orbital Lattice and the mechanics of Trivergence, TRM preserves observational accuracy while altering causal interpretation.
As PFT evolves, TRM will incorporate full AOL curvature calibration, resonance-layer mapping, and multiverse boundary effects. The structural approach offers a unified model capable of describing cosmology without invoking expansion-based parameters.