Bifold Containment Law

The Bifold Containment Law says a Pulsecore holds while the Bifold, its skin, can record what it contains, and gives way when what it contains exceeds the Bifold's holographic capacity χ_∂: to its null first, at the Null Nova, when data and null together fill the record, and to its data, at the Data Nova, when the data alone exceeds it. The Containment Force Balance (Part 4.3) sets the skin's tension over its area against the internal pressure through its volume, F = σA − PV. A bubble stands where that balance is stationary in its radius, which is Laplace's law of a bubble, P = 2σ/R. The skin's capacity is its horizon count, one bit for every 4·ln2 Planck areas (Bekenstein, Hawking). With the data's pressure P = N·k_B·T/(3V), the two conditions are one when the skin's tension is σ_∂ = k_B·T/(8·ln2·ℓ_p²): the temperature then cancels, and the bubble bursts exactly when N exceeds χ_∂, whatever its heat. Heating the Pulsecore brings it no nearer the burst; only more data does, which is why the Data Nova comes at a definite count. χ_∂ is the containment threshold of the Nova Threshold Law, the Bifold for the Pulsecore's two Novas and the torus's for each Nova after it; at the Data Nova the bubble turns inside out and the emptied Pulsecore becomes the Hollow, the torus's hole. Formally, P_∂ ≤ 2σ_∂/R, χ_∂ = A/(4·ln2·ℓ_p²) and σ_∂ = k_B·T/(8·ln2·ℓ_p²), where P_∂ is the pressure of the data within [𝕄·𝕃⁻¹·𝕋⁻²], σ_∂ the skin's tension, the dimensional boundary tension for the Bifold [𝕄·𝕋⁻²], R the Pulsecore's radius [𝕃], A = 4πR² its skin's area [𝕃²], χ_∂ the skin's holographic capacity [1ᵇ], N the data within [1ᵇ], ℓ_p the local Planck length of the universe the Pulsecore begins [𝕃], k_B the Boltzmann constant, T the Pulsecore's temperature [Θ] and ln2 the natural logarithm of 2 [∅]: [𝕄·𝕃⁻¹·𝕋⁻²] = [𝕄·𝕋⁻²]/[𝕃], [1ᵇ] = [𝕃²]/[𝕃²], [𝕄·𝕋⁻²] = [𝕄·𝕃²·𝕋⁻²·Θ⁻¹]·[Θ]/[𝕃²]. It connects to Containment Threshold, The UniSpheral Data Nova Threshold Law, Containment Force Balance, Bifold, Pulsecore Data Radiance, Bifold Record Law, Null Nova Condition and Data Nova.

Category: Manuscript

Chapter: Chapter 3

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