PIST EXTENDED ENCODING WORKFLOW
Deterministic maps from natural numbers to structured tuples
Encoding Pipeline
Decoding Pipeline
Basis Operations
Coordinate Mapping
Input Layer
Raw Bytes
b ∈ [0, 255]
Byte Histogram
Top-16 Basis
Coordinate Mapping
PIST Decompose
n = k² + t
k = ⌊√n⌋
Tree Address
Base-20 Path
depth = 3
Surface Coord
y = 1/x
θ = n·Φ mod 2π
Torus Angles
(θ, φ, ψ)
Φ, Φ², Φ³ mod 2π
Composite Address
9D+ Tuple
O(1) per position
Basis Operations
Basis Fusion
A ∩ B = Intersection
Bilinear Operators
Adaptive Selection
Compatibility Metric
Pool Exchange
Basis Expansion
Unfold → Extract →
Reduce
Mutual Simulation
Iterative Convergence
Shared Basis
Substrate Basis
Symbol Remapping
O-AVMR Preserve
Shifter Pipeline
ConstraintBlock
Shell Constraints
AdaptiveBasis
Pool + Screening
BasisFusion
Set + Bilinear
CompositeCoord
9D+ Address
Programmable
Data = Program
Compressed
Basis + Program
Input: Compressed Stream
Compressed Stream
Basis + Program
Parse Basis
Initial State
Init Registers
pc = 0, sp = 0
Execution Loop (per byte)
FETCH
b = program[pc]
DECODE
(op, arg) = split(b)
ADDRESS
composite(pc)
EXECUTE
Apply operation
EMIT?
should_emit()
LOOP
pc < len
Instruction Set:
0=NOOP 1=LOAD 2=STORE 3=ADD 4=XOR 5=BRANCH 6=FUSE 7=HALT
NOOP
LOAD
STORE
ADD
XOR
BRANCH
FUSE
HALT
Output
Reconstructed Bytes
Deterministic Output
BASIS OPERATIONS DETAIL
Basis Fusion
Basis A
Basis B
A ∩ B
Bilinear Map
Fused Basis
16 vectors
Adaptive Basis Selection
Candidate a
Compatibility
Memory Buffer
Fitness Screen
Integrate
Basis Expansion
1. Unfold
2. Extract
3. Reduce
Reduced
Basis + Residuals
COORDINATE MAPPING DETAIL
Position n ∈ ℕ
PIST Decomposition
k = ⌊√n⌋
t = n - k²
mass(k,t)
Information Weight
mirror(k,t)
t ↦ 2k+1-t
Tree Address
Level 0: n%20
n ← n//20
Level 1: n%20
Level 2: n%20
Surface Coordinates
x = 1 + n%255
y = 1/x
θ = n·Φ mod 2π
Irrational
Torus Angles
θ = n·Φ
φ = n·Φ²
ψ = n·Φ³
mod 2π
Dense in T³
Unique per n
Composite Address(n)
(tree_path, surface_coord, torus_angles, pist_shell)
Input/Output
Coordinate Mapping
Basis Operations
Shifter Pipeline
Compressed Data
Composite Structure
Node Info
Hover over a node to see details.