GoldenLanguage Specification (v2.0 – Dynamic Base-∞) 1. Core Data Model 1.1 Vector Primitive Every glyph encodes a triple vector: V = [R, G, B] where R,G,B ∈ [0,1] Inverse operations: V⁻¹ = [1-R, 1-G, 1-B] V± = {V, V⁻¹} Base meaning: semantic, visual, and entropic signal. 2. DNA Layer (Quaternary Logic Overlay) 2.1 Mapping Each vector component → 2-bit symbol: A = 0, C = 1, G = 2, T = 3 Thus, [R,G,B] → DNA triplet sequence. 2.2 Logic Operators Defined on DNA symbols: NOT(x) = (3 - x) ADD(x,y) = (x + y) mod 4 MIN(x,y), MAX(x,y) SHIFT(x) = (x+1) mod 4 DNA sequences act as computational strings. 2.3 Folding Control Symbol C reserved as fold signal (entropy contraction). Folding allows compression, branching, and recursion. 3. Compact Layer (Dynamic Base-∞) 3.1 Canonical Alphabet Generator A deterministic alphabet exists for any base (2 ≤ base ≤ ∞). Generated by φ-seeding: import math def BASE_ALPHABET(base: int) -> str: PHI = (1 + math.sqrt(5)) / 2 alphabet = [] x = PHI for i in range(base): x = (x * PHI) % 1 codepoint = 0x2500 + int(x * 0x0FFF) alphabet.append(chr(codepoint)) return ''.join(alphabet) # Example BASE4096_ALPHABET = BASE_ALPHABET(4096) Always deterministic: same base → same glyph alphabet. 3.2 Packing Rule DNA sequences map into integers. Integers are expressed in chosen base using canonical alphabet. Packing ratio depends on base: n DNA bases → ⌈ log_base(4^n) ⌉ glyphs Examples: Base-64 → 3 DNA bases per glyph. Base-4096 → 6 DNA bases per glyph. Base-∞ → adaptive (entropy-scaled). 3.3 Encoding / Decoding Encoding DNA → glyphs (base N): Map ACGT → 0–3. Accumulate as integer. Express integer in base N with φ-alphabet. Decoding glyphs → DNA: Map φ-alphabet → integer. Expand integer in base-4. Map 0–3 → ACGT. Bijective & reversible at all bases. 4. Glyph Trees (Execution Layer) 4.1 Structure Node = compact glyph (any base). Children = sub-glyphs. Execution = traverse tree, expand glyphs → DNA → vectors. 4.2 Evaluation Order Start at root glyph. Decode glyph → DNA. Apply DNA logic operators. Output → vector [R,G,B]. 4.3 Reversibility Every layer reversible: Vector ⇆ DNA ⇆ Base-N ⇆ Glyph Tree 5. Extensions Float∞: arbitrary precision floats encoded in base-∞ glyphs. Breathing Nodes: adaptive folding/unfolding by entropy flow. Symbolic Decorators: prime, Fibonacci, φ operators attached at glyph level. 6. Summary GoldenLanguage = Core: Vector [R,G,B] + inverse triple. Logic Overlay: DNA quaternary. Compact Layer: Dynamic Base-∞ with φ-seeded alphabet. Structure: Recursive glyph trees. Execution: Bijective, reversible, Turing-complete. This replaces the old Base-4096-only design with a universal compact layer: Base-2 → minimal binary. Base-64 → portable transport. Base-4096 → atomic glyphs. Base-∞ → entropy-adaptive compactness.