Roof — Speculative Extension
Version 11.2 | Originally March 1, 2026; nav updated April 6, 2026 | John Pepin
⚠️ Ongoing research project — SPECULATIVE. This idea emerged on March 1, 2026. The literature search was conducted after the insight, which is confirmation bias territory. What makes it worth investigating is described below. Not destruction-tested.
What if W isn't just "fraction of paths non-operational" — what if it's measuring effective dimensionality?
| W value | deff = 7W | Physical interpretation | Connection |
|---|---|---|---|
| 1 | 7 | Full quantum state space | S⁷, octonions, M-theory |
| 6/7 | 6 | Six active dimensions | Calabi-Yau (string theory) |
| 4/7 | 4 | Spacetime | General relativity |
| 3/7 | 3 | Spatial dimensions | Classical space |
| pc | ≈ 2.18 | Fractal, critical | Percolation at criticality |
| 2/7 | 2 | Holographic floor | Holographic principle, QG universal |
For different lattice dimensions, Z × pc gives:
| Lattice dimension | Z × pc | Result |
|---|---|---|
| d = 2 | 7 × 0.5927 = 4.15 | Too high |
| d = 3 | 7 × 0.3116 = 2.18 | ≈ 2 (holographic floor) |
| d = 4 | 7 × 0.197 = 1.38 | Below 2 |
| d = 5 | 7 × 0.141 = 0.99 | Below 2 |
Only for 3D lattices does Z × pc ≈ 2. Not tuned. Falls directly from percolation mathematics. This is independent support for the 3D-space anchor that gives the Z = 7 path count (6 cardinal directions in 3D + stay = 7) on the foundation page.
Several independent quantum gravity programs find deff → 2 at the Planck scale:
| Program | Method | Floor | Year |
|---|---|---|---|
| Ambjørn, Jurkiewicz, Loll | Causal Dynamical Triangulations | d → ~2 | 2005 |
| Modesto | Loop quantum gravity | d → 2 | 2009 |
| Hořava | Lifshitz gravity | d → 2 | 2009 |
| Padmanabhan et al. | Zero-point length geometry | d → 2 | 2016 |
| Carlip (review) | Survey of 6+ approaches | d → 2 (universal) | 2017 |
| TSO | Percolation geometry | deff = 2 from W=2/7 | 2024–2025 |
Carlip S. (2017) Class. Quantum Grav. 34, 193001. arXiv: 1705.05417. Added to references page.
QG convergence on d → 2 is real, robust, and independent
"Only d=3 gives Z·pc ≈ 2" result is not tuned — falls from percolation math
Supports the 3D geometric anchor for Z = 7
Literature found post-hoc
CDT comparison qualitative only
Integers at every 1/7 are mathematically trivial
Not destruction-tested