The sCIfEr (∅)

“sCIfEr” is pronouced “cipher”.

The interunion operation, \( s - f = c = r = ↑; f = i·e; [1; 2, 3, ...] = 1+\frac{1}{2+\frac{1}{3+⋱}} (⋱\ddots, ·\cdot) \)
metallic ratios: golden \( φ = φ_0 \), silver \( φ_1 \), bronze \( φ_2 \), ... φ2 
s =  f  + c
  = i·e + r
  = i·e + s'
  = Σ(i·e)  <-- clear cut addition => free form (mixed radices: 60 secs × 60 mins × 24 hours × 365 days)
  c/i  c'/i'
   e + r e' + r'

  c/i/c'/i' <-- interleaving inter-linked => emergent form
   e e1 e2
  s0/s1/s2/s3
    e0 e1 e2  = [e0;e1,e2]

radix system:
- form: s = Σ(i·e); i_{n+1} = b·i_n
- content: e = [0..b]

interunion with metallic ratios:
- form: s_{n+1} = e_n·s_n + s_{n-1}; e = b <=> s_{∞+1}/s_∞ = φ_b
- content: extension of s_{∞+1}⋇s_∞

Content arrow c = i0·e0 ranging on screen i:
c =    i·e    + r
  =    tail   + head
  = --------- + >
  =    body   + head
  =     🌀    + →
- Head is the higher order arrow with finer step/intent to range the broader extent (more steps) on the screen i:
  Extent = ext(body) × i/head
  E      =      e0   × i/r
  E is then projected onto the storage/memory s:
  + s = i: ext(body) = i0·e0/i.
  + s = 𝚷(i): ext(body) = i0·e0...

While the three components of the Trinion (○, ↑, =) show the objective and qualitative structure of the Universe, the Trinion itself observes the Universe via the subjective and quantitative observer-operator(obop) of the FoC. The obop being (◉) works with the following three components:

Apendix

A. About the symbol “Ψ”