Roof — Speculative Extension
Version 11.2 | Originally March 2–5, 2026; updated April 6, 2026 | John Pepin
⚠️ Ongoing research project — SPECULATIVE. Passed 14/14 internal consistency checks when originally built. Updated April 6, 2026 to replace the retired δW = 2/77 approximation with the exact form δW = pc − 2/7. Not destruction-tested externally.
Z = 7 is the geometric count of 6 cardinal directions in 3D + "stay" = 7. The five rotatable paths plus two fixed paths split as 2 fixed floor + 3 visible slot + 2 remaining rotatable. S ∈ [2/7, 5/7], W ∈ [2/7, 5/7], S + W = 1 exactly.
| Slot | Paths | Status | Forces | Provides |
|---|---|---|---|---|
| Fixed floor | T, ∅ | Always open (Wfloor = 2/7) | Gravity only | Time, vacuum energy |
| Contested | X1, X2, x, y, z | Rotate under SO(5) | EM, QCD, gravity | Space, non-locality, superposition |
| Fixed ceiling | (Same T, ∅) | Only extreme gravity closes these | Only gravity | Neutron star, BH dynamics |
Position and momentum compete for the same 3 contested slots. Defining position crystallizes a dimension and forces the conjugate into the undefined zone. ΔxΔp ≥ ℏ/2 is a geometric statement about 3 contested dimensions.
If all dimensions were defined, the universe would be a frozen crystal. The 2 always-undefined dimensions (in any given observation) inject irreducible indeterminacy into every interaction.
Z = 9 (the "3-3-3" alternative) is ruled out by five independent anchors:
| Anchor | 2-3-2 (Z=7) | 3-3-3 (Z=9) |
|---|---|---|
| Ωm = 0.315 | pc = 0.3116 ✓ (1.2% off) | pc ≈ 0.242 (23% off) |
| δW ≈ kBT at 300 K | δW = pc − 2/7 ≈ 0.0259 ✓ (0.15% off) | wrong sign |
| Z × pc ≈ 2 (holographic floor) | 7 × 0.3116 = 2.18 ✓ | breaks |
| NN+NNN+4N lattice threshold | 0.2885 ≈ 2/7 ✓ | no match |
| Jaiswal et al. 2025 (independent) | finds pc = 0.3116 ✓ | would need 0.242 |
Update (April 6, 2026): the earlier δW = 2/77 form in this table was retired in v11.0. The exact definition is δW = pc − 2/7 ≈ 0.02589 — the "11" in 77 had no physical meaning. The rest of the table is unaffected by the change since the numerical value is within 0.3% either way.
This table is one of the strongest arguments for Z = 7 on the site — five independent constraints that all fail for Z = 9 simultaneously, combined with the geometric anchor (6 cardinal directions in 3D + stay) on the foundation page.
2-3-2 Causal Structure (7/7 passed)
QPU Ceiling Test (5 predictions) — note: IBM gate-depth sweep is now an active experiment, see prediction 19