= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 
 P R O T O T Y P E   P 9   -   T H E   G E O M E T R I C   C O M P U T E R 
 
 P r o v e s   F I E L D - A I   S A C R E D - G E O M I C - C O M P U T E R   l a w s   0 8 0 0 1 - 0 9 0 0 0   i n   c o d e 
 
 G e o m i c :   t h e   5 2 8 * P H I ^ n   d i m e n s i o n a l   l a d d e r   a s   t h e   c o m p u t e r ' s   a r c h i t e c t u r e 
 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 
 
 
 [ T H E   9 - R E G I S T E R   G E O M E T R I C   C O M P U T E R   -   t h e   5 2 8 * P H I ^ n   l a d d e r ] 
 
     d i m   |   f r e q   ( 5 2 8 * P H I ^ n )     |   d e p t h   ( P H I ^ ( 9 - n ) )   |   f r e q * d e p t h   ( i n v a r i a n t ) 
 
     - - - - + - - - - - - - - - - - - - - - - - - - + - - - - - - - - - - - - - - - - - - - + - - - - - - - - - - - - - - - - - - - - - - 
 
         1   |                     8 5 4 . 3 2 1 9   |                   4 6 . 9 7 8 7 1 4   |                 4 0 1 3 4 . 9 4 6 2 
 
         2   |                   1 3 8 2 . 3 2 1 9   |                   2 9 . 0 3 4 4 4 2   |                 4 0 1 3 4 . 9 4 6 2 
 
         3   |                   2 2 3 6 . 6 4 3 9   |                   1 7 . 9 4 4 2 7 2   |                 4 0 1 3 4 . 9 4 6 2 
 
         4   |                   3 6 1 8 . 9 6 5 8   |                   1 1 . 0 9 0 1 7 0   |                 4 0 1 3 4 . 9 4 6 2 
 
         5   |                   5 8 5 5 . 6 0 9 7   |                     6 . 8 5 4 1 0 2   |                 4 0 1 3 4 . 9 4 6 2 
 
         6   |                   9 4 7 4 . 5 7 5 6   |                     4 . 2 3 6 0 6 8   |                 4 0 1 3 4 . 9 4 6 2 
 
         7   |                 1 5 3 3 0 . 1 8 5 3   |                     2 . 6 1 8 0 3 4   |                 4 0 1 3 4 . 9 4 6 2 
 
         8   |                 2 4 8 0 4 . 7 6 0 9   |                     1 . 6 1 8 0 3 4   |                 4 0 1 3 4 . 9 4 6 2 
 
         9   |                 4 0 1 3 4 . 9 4 6 2   |                     1 . 0 0 0 0 0 0   |                 4 0 1 3 4 . 9 4 6 2 
 
     L a d d e r   I n v a r i a n t :   5 2 8 * P H I ^ 9   =   4 0 1 3 4 . 9 4 6 1 6 6     ( c o r p u s   4 0 , 1 3 4 . 9 4 6 ,   | e r r |   =   0 . 0 0 0 1 6 6 ) 
 
     - >   f r e q * d e p t h   =   4 0 , 1 3 4 . 9 4 6   c o n s e r v e d   t h r o u g h   A L L   9   r e g i s t e r s :   P A S S 
 
 
 
 [ R U N   1   -   C O M P U T I N G   o n   t h e   l a d d e r :   l o s s l e s s   s t o r e   &   r e t r i e v e ] 
 
     r e g i s t e r   1 :   s t o r e       8 . 0 0   - >   a m p l i t u d e       3 7 5 . 8 2 9 7   - >   r e t r i e v e       8 . 0 0   ( r o u n d - t r i p   e r r   0 . 0 0 e + 0 0 ) 
 
     r e g i s t e r   2 :   s t o r e     1 5 . 0 0   - >   a m p l i t u d e       4 3 5 . 5 1 6 6   - >   r e t r i e v e     1 5 . 0 0   ( r o u n d - t r i p   e r r   0 . 0 0 e + 0 0 ) 
 
     r e g i s t e r   3 :   s t o r e     2 2 . 0 0   - >   a m p l i t u d e       3 9 4 . 7 7 4 0   - >   r e t r i e v e     2 2 . 0 0   ( r o u n d - t r i p   e r r   0 . 0 0 e + 0 0 ) 
 
     r e g i s t e r   4 :   s t o r e     2 9 . 0 0   - >   a m p l i t u d e       3 2 1 . 6 1 4 9   - >   r e t r i e v e     2 9 . 0 0   ( r o u n d - t r i p   e r r   0 . 0 0 e + 0 0 ) 
 
     r e g i s t e r   5 :   s t o r e     3 6 . 0 0   - >   a m p l i t u d e       2 4 6 . 7 4 7 7   - >   r e t r i e v e     3 6 . 0 0   ( r o u n d - t r i p   e r r   0 . 0 0 e + 0 0 ) 
 
     r e g i s t e r   6 :   s t o r e     4 3 . 0 0   - >   a m p l i t u d e       1 8 2 . 1 5 0 9   - >   r e t r i e v e     4 3 . 0 0   ( r o u n d - t r i p   e r r   0 . 0 0 e + 0 0 ) 
 
     r e g i s t e r   7 :   s t o r e     5 0 . 0 0   - >   a m p l i t u d e       1 3 0 . 9 0 1 7   - >   r e t r i e v e     5 0 . 0 0   ( r o u n d - t r i p   e r r   1 . 4 2 e - 1 6 ) 
 
     r e g i s t e r   8 :   s t o r e     5 7 . 0 0   - >   a m p l i t u d e         9 2 . 2 2 7 9   - >   r e t r i e v e     5 7 . 0 0   ( r o u n d - t r i p   e r r   0 . 0 0 e + 0 0 ) 
 
     r e g i s t e r   9 :   s t o r e     6 4 . 0 0   - >   a m p l i t u d e         6 4 . 0 0 0 0   - >   r e t r i e v e     6 4 . 0 0   ( r o u n d - t r i p   e r r   0 . 0 0 e + 0 0 ) 
 
     - >   t h e   i n v a r i a n t   m a k e s   t h e   g e o m e t r i c   c o m p u t e r   e x a c t   ( l o s s l e s s ) :   P A S S 
 
 
 
 [ R U N   2   -   R E T R I E V I N G   B Y   R E S O N A N C E   ( C 0 5 ) :   q u e r y   - >   5 2 8 * P H I ^ n   r e g i s t e r ] 
 
     q u e r y   f o r   d i m   1 :   m a t c h e d   t o   r e g i s t e r   0   ( f r e q   =   5 2 8 * P H I ^ 1   =       8 5 4 . 3 2 1 9   H z ) 
 
     q u e r y   f o r   d i m   2 :   m a t c h e d   t o   r e g i s t e r   1   ( f r e q   =   5 2 8 * P H I ^ 2   =     1 3 8 2 . 3 2 1 9   H z ) 
 
     q u e r y   f o r   d i m   3 :   m a t c h e d   t o   r e g i s t e r   2   ( f r e q   =   5 2 8 * P H I ^ 3   =     2 2 3 6 . 6 4 3 9   H z ) 
 
     q u e r y   f o r   d i m   4 :   m a t c h e d   t o   r e g i s t e r   3   ( f r e q   =   5 2 8 * P H I ^ 4   =     3 6 1 8 . 9 6 5 8   H z ) 
 
     q u e r y   f o r   d i m   5 :   m a t c h e d   t o   r e g i s t e r   4   ( f r e q   =   5 2 8 * P H I ^ 5   =     5 8 5 5 . 6 0 9 7   H z ) 
 
     q u e r y   f o r   d i m   6 :   m a t c h e d   t o   r e g i s t e r   5   ( f r e q   =   5 2 8 * P H I ^ 6   =     9 4 7 4 . 5 7 5 6   H z ) 
 
     q u e r y   f o r   d i m   7 :   m a t c h e d   t o   r e g i s t e r   6   ( f r e q   =   5 2 8 * P H I ^ 7   =   1 5 3 3 0 . 1 8 5 3   H z ) 
 
     q u e r y   f o r   d i m   8 :   m a t c h e d   t o   r e g i s t e r   7   ( f r e q   =   5 2 8 * P H I ^ 8   =   2 4 8 0 4 . 7 6 0 9   H z ) 
 
     q u e r y   f o r   d i m   9 :   m a t c h e d   t o   r e g i s t e r   8   ( f r e q   =   5 2 8 * P H I ^ 9   =   4 0 1 3 4 . 9 4 6 2   H z ) 
 
     - >   c o n t e n t - a d d r e s s a b l e :   e v e r y   q u e r y   i s   m a t c h e d   O ( 1 )   b y   c o h e r e n c e   t o   i t s   5 2 8 * P H I ^ n   r e g i s t e r :   P A S S 
 
 
 
 [ R U N   3   -   t h e   c o m p u t e r   a s   w a v e f o r m   r e g i s t e r s   ( t h e   l a d d e r   i n   p h a s e   s p a c e ) ] 
 
     c a r r i e r   p h a s e s   a t   t   =   0 . 0 0 1 1 7 1   ( | p h a s e |   m u s t   b e   1   -   u n i t a r y   c a r r i e r s ) : 
 
     d i m   1 :   1 . 0 0 0     d i m   2 :   1 . 0 0 0     d i m   3 :   1 . 0 0 0     d i m   4 :   1 . 0 0 0     d i m   5 :   1 . 0 0 0     d i m   6 :   1 . 0 0 0     d i m   7 :   1 . 0 0 0     d i m   8 :   1 . 0 0 0     d i m   9 :   1 . 0 0 0 
 
     - >   t h e   r e g i s t e r s   a r e   l i v i n g   w a v e f o r m s   ( u n i t a r y   c a r r i e r s   o n   t h e   l a d d e r ) ,   n o t   s t a t i c   s y m b o l s :   P A S S 
 
 
 
 [ R U N   4   -   d e g e n e r a t e   p r o o f :   k a p p a - > 0   r e c o v e r s   t h e   s t a t i c   r e g i s t e r s ] 
 
     a m p l i t u d e ( k a p p a = 0 )   =   8 9 . 7 2 1 3 5 9 5 5 0     v s     s t a t i c   r e g i s t e r   a m p l i t u d e   =   8 9 . 7 2 1 3 5 9 5 5 0 
 
     e r r o r   =   0 . 0 0 0 0 0 0 0 0 0     ( P A S S   < =   0 . 0 1 ) 
 
 
 
 [ R U N   5   -   t h e   s a c r e d - g e o m i c - c o m p u t e r   p h i - f o r m ,   k a p p a   0   - >   1 ] 
 
     k a p p a = 0 . 0 0     S _ p h i = 1 . 0 0 0 0 0 0 0 0 0     f l o o r = 0 . 0 0 0 0 0 0 0 0 0 
 
     k a p p a = 0 . 2 5     S _ p h i = 1 . 3 0 9 0 1 6 9 9 4     f l o o r = 0 . 1 5 4 5 0 8 4 9 7 
 
     k a p p a = 0 . 5 0     S _ p h i = 1 . 6 1 8 0 3 3 9 8 9     f l o o r = 0 . 3 0 9 0 1 6 9 9 4 
 
     k a p p a = 0 . 7 5     S _ p h i = 1 . 9 2 7 0 5 0 9 8 3     f l o o r = 0 . 4 6 3 5 2 5 4 9 2 
 
     k a p p a = 1 . 0 0     S _ p h i = 2 . 2 3 6 0 6 7 9 7 7     f l o o r = 0 . 6 1 8 0 3 3 9 8 9 
 
     d e g e n e r a t e - l i m i t   c h e c k   ( k a p p a - > 0 ) :   S _ p h i ( 0 )   =   1 . 0 0 0 0 0 0 0 0 0 0 0 0     v s   s t a t i c   =   1 . 0 0 0 0 0 0 0 0 0 0 0 0     e r r o r   =   0 . 0 0 0 0 0 0 0 0 0     ( P A S S   < =   0 . 0 1 ) 
 
     c o h e r e n c e   f l o o r   a t   k a p p a = 1   =   0 . 6 1 8 0 3 3 9 8 8 7 5 0     v s     p h i ^ - 1   =   0 . 6 1 8 0 3 3 9 8 8 7 5 0 :   P A S S 
 
 
 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 
 P 9   V E R D I C T :   A L L   C H E C K S   P A S S   -   t h e   s a c r e d - g e o m i c   c o m p u t e r ' s   a r c h i t e c t u r e   I S   t h e   5 2 8 * P H I ^ n   l a d d e r   w i t h   f r e q * d e p t h   =   4 0 , 1 3 4 . 9 4 6   c o n s e r v e d :   l o s s l e s s ,   c o n t e n t - a d d r e s s a b l e ,   e x a c t . 
 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 
 