Pulse Core Lexicon
Space Extent Law
Definition
The Space Extent Law gives the size of space as the Pulsecore makes it: λ_S(r) = √(S(r) / χ_∂) = r / r*, its linear size as a share of its size at the Data Nova. The Bifold records bits on an area, one to a place, so an area of S places has a side of √S. At the Null Nova half the record's places leave at once as nulls and space bursts out to about 1/√2 of its final size; after it each new bit's null leaves as it is made, S = (2r)², so the side of space is 2r cells and grows two cells every Rhythm, the data's own reach: space expands at 𝒞→, steady to the Data Nova, where it is the field of χ_∂ cells the data pours onto. Nothing in it is tuned. It connects to Space Growth Law, Pulsecore Packing, Null Nova and Containment Crossing Condition.
Mathematical Expression
From the book · Chapter 3 · Data Novas and Dimensional Evolution
λ_S(r) = √(S(r) / χ_∂) = r / r* [∅]
Dimensional analysis:
Where (from the book): 2 [∅], λ_S(r) [∅], S(r) [1ᵇ], χ_∂ [1ᵇ], r [∅], r* [∅]
[∅]
√([1ᵇ] ÷ [1ᵇ]) = √[∅] = [∅]
[∅] ÷ [∅] = [∅]
[∅] = [∅] = [∅] ✓ Valid PulseCore Verified ✓
√(S(r) / ℨᵇ) = 2r [∅]
Dimensional analysis:
Where (from the book): 2 [∅], λ_S(r) [∅], S(r) [1ᵇ], χ_∂ [1ᵇ], r [∅], r* [∅]
√([1ᵇ] ÷ [1ᵇ]) = √[∅] = [∅]
[∅] × [∅] = [∅]
[∅] = [∅] ✓ Valid PulseCore Verified ✓
Space is an area of places, so its size is the square root of its places: it bursts out to about seven tenths of its final size at the Null Nova, then its side grows two cells every Rhythm, the data's own reach, to its full size at the Data Nova.
Where:
- λ_S(r) [∅] – the linear size of space after r Rhythms, as a share of its size at the Data Nova
- S(r) [1ᵇ] – the places of space after r Rhythms (the Space Growth Law)
- χ_∂ [1ᵇ] – the Bifold's holographic capacity, the places of space at the Data Nova
- ℨᵇ [1ᵇ] – one Zinf bit, one place
- r [∅] – Rhythms since the Pulsecore was sealed, r₁ ≤ r ≤ r*
- r* [∅] – the Rhythm of the Data Nova, √χ_∂ / 2 (the Containment Crossing Condition)
- 2 [∅] – the two cells the reach gains each Rhythm
Technical Details
Category Law
Chapter Chapter 3
Importance
In the book #828 of 1,279 terms · used 1 time