Null Well Formalism: Modified Constants and Merger Origins

This chapter is the formal companion to Chapter 2. Chapter 2 sets out the physical picture of Wells, Density, and Mass; here we give the mathematics behind it: the Planck Pulse architecture, density-modified constants, the Null Mass integral, boundary encoding at the computational event horizon, and the compression factor and spin inheritance of merger-origin Universes.

~ Key Math ~

Dimensional Consistency Constraint

α²·β⁵ = γ·δ

Dimensional analysis:
[∅] × [∅] = [∅]
[∅] × [∅] = [∅]
[∅] = [∅] ✓ Valid PulseCore Verified ✓

A child universe’s Planck time, light speed, gravity and quantum of action change together, so its Planck time is still √(ℏG/c⁵).

Inherited Planck Time

①⥂⧗'⌂ = ①⥂⧗⌂ × (M∅ / M_P)^(1/2)

Dimensional analysis:
[𝕋]
[𝕋] × ([𝕄] ÷ [𝕄])^([∅] ÷ [∅]) = [𝕋] × ([𝕄] ÷ [𝕄])^([∅]) = [𝕋] × [∅]^([∅]) = [𝕋] × [∅] = [𝕋]
[𝕋] = [𝕋] ✓ Valid PulseCore Verified ✓

A child universe’s Planck time is set by the Null Mass of the collapse that made it.

Time Dilation as Pulse Tempo

dt'/dt = ①⥂⧗'⌂/①⥂⧗⌂ = sqrt(ρ_P/ρ⌂)

Dimensional analysis:
Read dimensionally: (t'/t) = ①⥂⧗'⌂/①⥂⧗⌂ = sqrt(ρ_P/ρ⌂)
([𝕋] ÷ [𝕋]) = [∅]
[𝕋] ÷ [𝕋] = [∅]
sqrt([𝕄·𝕃⁻³] ÷ [𝕄·𝕃⁻³]) = sqrt([∅]) = [∅]
[∅] = [∅] = [∅] ✓ Valid PulseCore Verified ✓

Gravitational time dilation as a change in the local Pulse Tempo, set by local density against the Planck density.

Inherited Spin in Quanta

N↻ = J_f / ℨ↻ = 2·a_f·G·M_f² / (𝒞→·ℏ)

Dimensional analysis:
[∅]
[𝕄·𝕃²·𝕋⁻¹] ÷ [𝕄·𝕃²·𝕋⁻¹] = [∅]
[∅] × [∅] × [𝕄⁻¹·𝕃³·𝕋⁻²] × [𝕄²] ÷ ([𝕃·𝕋⁻¹] × [𝕄·𝕃²·𝕋⁻¹]) = [∅] × [𝕄⁻¹·𝕃³·𝕋⁻²] × [𝕄²] ÷ ([𝕃·𝕋⁻¹] × [𝕄·𝕃²·𝕋⁻¹]) = [𝕄⁻¹·𝕃³·𝕋⁻²] × [𝕄²] ÷ ([𝕃·𝕋⁻¹] × [𝕄·𝕃²·𝕋⁻¹]) = [𝕄·𝕃³·𝕋⁻²] ÷ ([𝕃·𝕋⁻¹] × [𝕄·𝕃²·𝕋⁻¹]) = [𝕄·𝕃³·𝕋⁻²] ÷ [𝕄·𝕃³·𝕋⁻²] = [∅]
[∅] = [∅] = [∅] ✓ Valid PulseCore Verified ✓

The spin a child universe inherits from the merger that made it, counted in spin quanta.