Pulse Core Lexicon

UniSpheral Collapse Scaling Relations

Definition

The UniSpheral Collapse Scaling Relations describe how four fundamental quantities, the pulse tempo, the light speed, the gravitational constant and the Planck constant, are rescaled during Null Well collapse, each by a dimensionless function of one collapse parameter. Child universes inherit constants set by the collapse of the Null Well that formed them, so physics becomes domain-specific rather than universal. The collapse density rescales the pulse tempo, the boundary information rescales the light speed, the boundary tension rescales the gravitational constant, and the entropy change rescales the Planck constant. The book stresses that these constants are not separate entities needing a bridge between computation and physics but unified structures spanning the Data-Physical architecture, so a collapse that starts in the computational substrate alters the temporal, propagation, curvature and quantum parameters of both domains at once. The book writes ⧗'(ℨ) = α(ↁρ⟫,ℨ) · ⧗(ℨ), 𝒞→'(ℨ) = β(ↁℹ∂,ℨ) · 𝒞→(ℨ), 𝒢'(ℨ) = γ(⋈∂,ℨ) · 𝒢(ℨ) and ℏ'(ℨ) = δ(S∅,ℨ) · ℏ(ℨ), where primes mark the modified values [𝕋], [𝕃·𝕋⁻¹], [𝕄⁻¹·𝕃³·𝕋⁻²], [𝕄·𝕃²·𝕋⁻¹]; α, β, γ, δ are the dimensionless scaling functions; ↁρ⟫ is the data collapse density, ↁℹ∂ the boundary information, ⋈∂ the boundary tension and S∅ the entropy parameter, all [∅]; and ℨ is the Zinf unit, the primordial temporal atom [ℨ]. It connects to UniSpheral Explicit Scaling Functions, Universe Parameter Inheritance Framework, UniSpheral Universe Consistency Equations, Collapse Density Scaling Function and Entropy Scaling Function.

Mathematical Expression

From the book · Chapter 2 · Null Wells (Black Holes) and the Birth of New Universes · Modified Pulse Tempo

⧗'(ℨ) = α(ↁρ⟫,ℨ) · ⧗(ℨ)

Dimensional analysis:
Where (from the book): ⧗'(ℨ) [𝕋], 𝒞→'(ℨ) [𝕃·𝕋⁻¹], 𝒢'(ℨ) [𝕄⁻¹·𝕃³·𝕋⁻²], ℏ'(ℨ) [𝕄·𝕃²·𝕋⁻¹], α(ↁρ⟫,ℨ) [∅], β(ↁℹ∂,ℨ) [∅], γ(⋈∂,ℨ) [∅], δ(S∅,ℨ) [∅], ⧗(ℨ) [𝕋], 𝒢(ℨ) [𝕄⁻¹·𝕃³·𝕋⁻²], ↁρ⟫ [𝕃⁻³·𝕋⁻¹], ↁℹ∂ [∅], ⋈∂ [∅], ℨ [ℨ]
[𝕋]
[∅] × [𝕋] = [𝕋]
[𝕋] = [𝕋] ✓ Valid PulseCore Verified ✓

Pulse temporal duration scaling with collapse density

From the book · Chapter 2 · Null Wells (Black Holes) and the Birth of New Universes · Altered Light Speed

𝒞→'(ℨ) = β(ↁℹ∂,ℨ) · 𝒞→(ℨ)

Dimensional analysis:
Where (from the book): ⧗'(ℨ) [𝕋], 𝒞→'(ℨ) [𝕃·𝕋⁻¹], 𝒢'(ℨ) [𝕄⁻¹·𝕃³·𝕋⁻²], ℏ'(ℨ) [𝕄·𝕃²·𝕋⁻¹], α(ↁρ⟫,ℨ) [∅], β(ↁℹ∂,ℨ) [∅], γ(⋈∂,ℨ) [∅], δ(S∅,ℨ) [∅], ⧗(ℨ) [𝕋], 𝒢(ℨ) [𝕄⁻¹·𝕃³·𝕋⁻²], ↁρ⟫ [𝕃⁻³·𝕋⁻¹], ↁℹ∂ [∅], ⋈∂ [∅], ℨ [ℨ]
[𝕃·𝕋⁻¹]
[∅] × [𝕃·𝕋⁻¹] = [𝕃·𝕋⁻¹]
[𝕃·𝕋⁻¹] = [𝕃·𝕋⁻¹] ✓ Valid PulseCore Verified ✓

Data Information propagation rate modification with boundary information

From the book · Chapter 2 · Null Wells (Black Holes) and the Birth of New Universes · Modified Gravitational Constant

𝒢'(ℨ) = γ(⋈∂,ℨ) · 𝒢(ℨ)

Dimensional analysis:
Where (from the book): ⧗'(ℨ) [𝕋], 𝒞→'(ℨ) [𝕃·𝕋⁻¹], 𝒢'(ℨ) [𝕄⁻¹·𝕃³·𝕋⁻²], ℏ'(ℨ) [𝕄·𝕃²·𝕋⁻¹], α(ↁρ⟫,ℨ) [∅], β(ↁℹ∂,ℨ) [∅], γ(⋈∂,ℨ) [∅], δ(S∅,ℨ) [∅], ⧗(ℨ) [𝕋], 𝒢(ℨ) [𝕄⁻¹·𝕃³·𝕋⁻²], ↁρ⟫ [𝕃⁻³·𝕋⁻¹], ↁℹ∂ [∅], ⋈∂ [∅], ℨ [ℨ]
[𝕄⁻¹·𝕃³·𝕋⁻²]
[∅] × [𝕄⁻¹·𝕃³·𝕋⁻²] = [𝕄⁻¹·𝕃³·𝕋⁻²]
[𝕄⁻¹·𝕃³·𝕋⁻²] = [𝕄⁻¹·𝕃³·𝕋⁻²] ✓ Valid PulseCore Verified ✓

Spacetime curvature parameter scaling with boundary tension

From the book · Chapter 2 · Null Wells (Black Holes) and the Birth of New Universes · Scaled Planck Constant

ℏ'(ℨ) = δ(S∅,ℨ) · ℏ(ℨ)

Dimensional analysis:
Where (from the book): ⧗'(ℨ) [𝕋], 𝒞→'(ℨ) [𝕃·𝕋⁻¹], 𝒢'(ℨ) [𝕄⁻¹·𝕃³·𝕋⁻²], ℏ'(ℨ) [𝕄·𝕃²·𝕋⁻¹], α(ↁρ⟫,ℨ) [∅], β(ↁℹ∂,ℨ) [∅], γ(⋈∂,ℨ) [∅], δ(S∅,ℨ) [∅], ⧗(ℨ) [𝕋], 𝒢(ℨ) [𝕄⁻¹·𝕃³·𝕋⁻²], ↁρ⟫ [𝕃⁻³·𝕋⁻¹], ↁℹ∂ [∅], ⋈∂ [∅], ℨ [ℨ]
[𝕄·𝕃²·𝕋⁻¹]
[∅] × [𝕄·𝕃²·𝕋⁻¹] = [𝕄·𝕃²·𝕋⁻¹]
[𝕄·𝕃²·𝕋⁻¹] = [𝕄·𝕃²·𝕋⁻¹] ✓ Valid PulseCore Verified ✓

Quantum action unit modification with entropy changes

Where:

  • ⧗'(ℨ) [𝕋] – Modified unified Pulse Tempo; altered fundamental temporal duration operating simultaneously across Data computational substrate and Physical manifestation layers
  • 𝒞→'(ℨ) [𝕃·𝕋⁻¹] – Modified unified Light Speed; altered information propagation rate affecting both computational processes and physical phenomena
  • 𝒢'(ℨ) [𝕄⁻¹·𝕃³·𝕋⁻²] – Modified unified Gravitational Constant; altered spacetime curvature parameter operating across Data-Physical architecture
  • ℏ'(ℨ) [𝕄·𝕃²·𝕋⁻¹] – Modified unified Planck Constant; altered quantum action unit affecting both computational substrate and physical manifestation
  • α(ↁρ⟫,ℨ) [∅] – Zinf-scaled collapse density scaling function; dimensionless modification based on Data collapse density
  • β(ↁℹ∂,ℨ) [∅] – Zinf-scaled boundary information scaling function; dimensionless modification based on Data boundary information
  • γ(⋈∂,ℨ) [∅] – Zinf-scaled boundary tension scaling function; dimensionless modification based on boundary tension
  • δ(S∅,ℨ) [∅] – Zinf-scaled entropy scaling function; dimensionless modification based on entropy changes
  • ⧗(ℨ) [𝕋] – base unified Pulse Tempo; fundamental temporal duration operating across Data-Physical architecture
  • 𝒞→(ℨ) [𝕃·𝕋⁻¹] – base unified Light Speed; fundamental information propagation rate across computational and physical domains
  • 𝒢(ℨ) [𝕄⁻¹·𝕃³·𝕋⁻²] – base unified Gravitational Constant; fundamental spacetime curvature parameter
  • ℏ(ℨ) [𝕄·𝕃²·𝕋⁻¹] – base unified Planck Constant; fundamental quantum action unit
  • ↁρ⟫ [𝕃⁻³·𝕋⁻¹] – Data collapse density parameter; computational density during null well formation
  • ↁℹ∂ [∅] – Data boundary information parameter; information content at null well boundaries
  • ⋈∂ [∅] – boundary tension parameter; stress accumulation at null well interfaces
  • S∅ [∅] – entropy parameter; disorder measure during collapse processes
  • ℨ [ℨ] – Zinf Unit; primordial temporal atom determining scaling

Technical Details

Category Equation

Chapter Chapter 2

Importance

Related Terms