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