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