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