ORT · The Time‑Corridor Formulation — (Formerly Dark Energy)
ORT · The Time‑Corridor Formulation (A Principle Once Known as Dark Energy)

The Time‑Corridor Formulation

A Principle Once Known as Dark Energy

I. Constants and Laws

• Sing Constant

𝓢 = 2^410 ≈ 2.64 × 10^123

Defines the total corridor span of existence — the ratio between every maximum and minimum allowed state in reality.

• Gradient Constant

κ(γ) = 2^(γ√3),   γ ∈ { 1, 1/2, 1/4, 1/8, 0 }

Sets the geometric slope that links each corridor to the next — density, macro, quantum, foam and unity.

• Corridor Law

Q_max / Q_min = 𝓢^γ(Q)

Every measurable quantity expands between its Sing limits following this pure exponential grammar.

• Time‑Progress Variable

y(t) = ln(t / t_min) / ln(t_max / t_min),   0 ≤ y ≤ 1
t_min ≈ 2.2 × 10^−41 s
t_max ≈ 3.65 × 10^13 years (≈ 1.15 × 10^21 s)

II. Independent Corridors — The Core‑8 with Foam

𝓚₈ = { ρ(γ=1), L, M, E, T, v(γ=1/2), Q(γ=1/4), F(γ=1/8) }

Eight irreducible slope channels form the OPS lattice of reality.

  • ρ (γ = 1) → density anchor.
  • {L, M, E, T, v, Θ} (γ = 1/2) → macro corridor.
  • Q (γ = 1/4) → quantum layer.
  • F (γ = 1/8) → sub‑quantum foam.

No extra dimensions — all else is a transient echo within the foam.

III. Time‑Corridor Law (formerly Dark‑Energy Law)

1️⃣ Canonical (Geometric) Form — Timeless ORT Expression

f_t(t) = y(t) / ( 8 − 7y(t) )

This ratio shows how much of the total OPS‑corridor slope is carried by time among the eight fundamental corridors. It depends only on the geometry of existence — no forces, no parameters, no tuning — pure ORT symmetry.

2️⃣ Dynamical (Observable) Form — With Phantom Multiplicities

When the OPS lattice still hosts unresolved multiplicities — the phantoms of early reality — the effective number of active channels becomes:

K_eff(t) = 8 + M_phantom(t)

The observable share is then

F_t^{obs}(t) = y(t) / [ K_eff(t) − ( K_eff(t) − 1 ) · y(t) ]
Early universe → M_phantom ≫ 1 ⇒ K_eff ≫ 8 ⇒ F_t^{obs} ≈ 0
Late universe → M_phantom → 0 ⇒ K_eff → 8 ⇒ F_t^{obs} → f_t
Entire curve arises from 𝓢, κ(γ), OPS grammar — no tuning.

IV. Numerical Anchors (Fixed Epochs)

  • Early epochs: K_eff ≈ 10^3–10^4 → f_t ≈ 0 → Phantom‑dominated, CMB safe.
  • Present: K_eff = 8 → f_t ≈ 0.68 → Perfect observational match.
  • Future: K_eff = 8 (stable Core‑8) → f_t → 1 as t → t_max.

V. The Time‑Corridor Law — Once Called Dark Energy

f_t(t) = y(t) / (8 − 7y(t)),   y(t) = ln(t / t_min) / ln(t_max / t_min)

Core‑8 corridors: { ρ, L, M, E, T, v, Q, F }  ·  Sing Constant 𝓢 = 2^410.

Early phantom multiplicities kept F_t^{obs} ≈ 0 before recombination. As the lattice collapsed to Core‑8, the universe entered its modern slope: f_t(t) ≈ 0.68.

No borrowing. No modification. No tuning. Pure ORT.

Interactive Explorer

Play with cosmic time and phantom multiplicities. This tool computes y(t), the canonical share f_t, and the observable share F_t^{obs}.

© SK · ORT — Time‑Corridor
S = 2^410 · κ(γ)=2^(γ√3)