; ============================================================================
; HDGL — CROSS-COUPLED DUAL-AXIS SUBSTRATE KERNEL
;
; Trajectories:
; Axis 1 (Forward): (a, b) → (a+b, a)
; Axis 2 (Inverse): (c, d) → (d, c-d)
;
; Non-Linear Coupling:
; The systems inject cross-entropy by XORing their state vectors.
; The mixing matrix is dynamically masked by the parity of Axis 1.
; ============================================================================
BITS 64
section .text
global _start
_start:
; --- INITIALIZE AXIS 1 (Forward) ---
mov r8, 0 ; r8 = a
mov r9, 1 ; r9 = b
; --- INITIALIZE AXIS 2 (Inverse) ---
mov r10, 0 ; r10 = c
mov r11, 1 ; r11 = d
.coupled_loop:
; === 1. STEP BOTH AXES IN PARALLEL ===
; Axis 1 Step
mov rax, r8 ; rax = old_a
add r8, r9 ; r8 = new_a (old_a + old_b)
mov r9, rax ; r9 = new_b (old_a)
; Axis 2 Step
mov rbx, r10 ; rbx = old_c
mov r10, r11 ; r10 = new_c (old_d)
sub rbx, r11 ; rbx = old_c - old_d
mov r11, rbx ; r11 = new_d (old_c - old_d)
; === 2. NON-LINEAR CROSS-COUPLING ===
; We construct a dynamic bitmask based on the parity of Axis 1 (b-coordinate).
; If r9 is odd, mask becomes all 1s (0xFFFFFFFFFFFFFFFF). If even, all 0s.
mov rcx, r9 ; Extract state from Axis 1
and rcx, 1 ; Isolate the lowest bit
neg rcx ; Mathematical mask generation (0 -> 0, 1 -> -1/all 1s)
; Compute the cross-entropy delta between the two internal spaces
mov rdx, r8 ; rdx = Axis 1 (a)
xor rdx, r10 ; rdx = a XOR c
and rdx, rcx ; Apply the dynamic parity mask
; Apply the balanced feedback injection to both systems simultaneously
xor r8, rdx ; Permute Axis 1 (a)
xor r10, rdx ; Permute Axis 2 (c)
; === CYBERNETIC LOCKED STATE ===
; The field norms are no longer cleanly isolated to ±1.
; They are now bound together in a high-entropy, deterministic cycle.
jmp .coupled_loop
