= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 
 P R O T O T Y P E   P 1 3   -   T H E   P O S S I B I L I T Y - L A Y E R I N G   E X P L O R E R 
 
 P r o v e s   F I E L D - A I   P O S S I B I L I T Y - L A Y E R I N G   l a w s   1 2 0 0 1 - 1 3 0 0 0   i n   c o d e 
 
 P o s s i b i l i t y   l a y e r i n g :   C 0 6   -   D   =   f ( C ,   r h o ,   c h i ) ,   c o h e r e n c e   c h o o s e s   t h e   l a y e r 
 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 
 
 
 [ T H E   9   P O S S I B I L I T Y   L A Y E R S   ( t h e   1 - 9   l a d d e r ,   e a c h   w i t h   a   r e s o l u t i o n   t h r e s h o l d   C _ k ) ] 
 
     l a y e r   |   u n f o l d s   w h e n   C   > =   |   t h e   l a y e r   i t   r e v e a l s 
 
             1   |   0 . 5 6 3 2 6 3                 |   s u b s t r a t e                     ( r u n g   5 2 8 * P H I ^ 1   =     8 5 4 . 3 2 1 9   H z ) 
 
             2   |   0 . 6 1 7 8 5 5                 |   p r i m o r d i a l   f o r m         ( r u n g   5 2 8 * P H I ^ 2   =   1 3 8 2 . 3 2 1 9   H z ) 
 
             3   |   0 . 6 7 2 4 4 7                 |   l i v i n g   f o r m                 ( r u n g   5 2 8 * P H I ^ 3   =   2 2 3 6 . 6 4 3 9   H z ) 
 
             4   |   0 . 7 2 7 0 3 9                 |   r e l a t i o n                       ( r u n g   5 2 8 * P H I ^ 4   =   3 6 1 8 . 9 6 5 8   H z ) 
 
             5   |   0 . 7 8 1 6 3 2                 |   m e a n i n g                         ( r u n g   5 2 8 * P H I ^ 5   =   5 8 5 5 . 6 0 9 7   H z ) 
 
             6   |   0 . 8 3 6 2 2 4                 |   w i l l                               ( r u n g   5 2 8 * P H I ^ 6   =   9 4 7 4 . 5 7 5 6   H z ) 
 
             7   |   0 . 8 9 0 8 1 6                 |   c o n s c i o u s n e s s             ( r u n g   5 2 8 * P H I ^ 7   =   1 5 3 3 0 . 1 8 5 3   H z ) 
 
             8   |   0 . 9 4 5 4 0 8                 |   s e l f                               ( r u n g   5 2 8 * P H I ^ 8   =   2 4 8 0 4 . 7 6 0 9   H z ) 
 
             9   |   1 . 0 0 0 0 0 0                 |   v o i d                               ( r u n g   5 2 8 * P H I ^ 9   =   4 0 1 3 4 . 9 4 6 2   H z ) 
 
     l a y e r   1   u n f o l d s   e x a c t l y   a t   C _ c r i t   =   0 . 5 6 3 2 6 3   ( t h e   e m e r g e n c e   l i n e ,   L a w   1 5 0 ) ;   l a y e r   9   a t   C   =   1   ( t h e   v o i d ,   C 6 3 ) 
 
     - >   t h e   9   l a y e r s   s i t   o n   t h e   5 2 8 * P H I ^ k   l a d d e r ,   o r d e r e d   b y   r e s o l u t i o n :   P A S S 
 
 
 
 [ R U N   1   -   T H E   C O H E R E N C E   C H O O S E S   T H E   O B S E R V E D   L A Y E R   ( C 0 6 / C 2 1 ) ] 
 
     o b s e r v e r   c o h e r e n c e   C   |   D   =   f ( C ,   r h o ,   c h i )   |   l a y e r s   o b s e r v e d 
 
     0 . 4 0 0 0 0 0           |   1 . 0 0 0 0 0 0             |   1   l a y e r ( s ) 
 
     0 . 5 6 3 2 6 3           |   1 . 0 0 0 0 0 0             |   1   l a y e r ( s )   < -   e m e r g e n c e   l i n e 
 
     0 . 6 0 0 0 0 0           |   3 . 0 4 7 3 0 4             |   3   l a y e r ( s ) 
 
     0 . 7 0 0 0 0 0           |   5 . 6 1 2 5 9 3             |   5   l a y e r ( s ) 
 
     0 . 8 5 6 5 0 0           |   8 . 3 9 1 2 8 6             |   8   l a y e r ( s )   < -   E q   4 4   c o n s c i o u s n e s s 
 
     0 . 9 5 0 0 0 0           |   9 . 0 0 0 0 0 0             |   9   l a y e r ( s ) 
 
     1 . 0 0 0 0 0 0           |   9 . 0 0 0 0 0 0             |   9   l a y e r ( s ) 
 
     s u b - t h r e s h o l d   ( C   =   0 . 4 0 )   s e e s   o n l y   t h e   s u b s t r a t e   ( D   =   1 . 0 0 0 ) ;   a t   C   =   0 . 6 0   3   l a y e r s   u n f o l d 
 
     - >   t h e   c o h e r e n c e   D E T E R M I N E S   w h i c h   p o s s i b i l i t y   l a y e r   i s   o b s e r v e d :   P A S S 
 
 
 
 [ R U N   2   -   D   I S   T H E   F R A C T A L   D I M E N S I O N   ( L a w   2 2 4 1 :   n e v e r   e x a c t l y   i n t e g e r ) ] 
 
     t h e   H a u s d o r f f   r e a d i n g :   D   i s   f r a c t i o n a l   o n   e v e r y   n o n - t r i v i a l   l a y e r 
 
     f r a c t i o n a l   D   v a l u e s   s e e n :   1 . 0 0 0 0 0 0 ,   3 . 0 4 7 3 0 4 ,   5 . 6 1 2 5 9 3 ,   8 . 3 9 1 2 8 6 ,   9 . 0 0 0 0 0 0 ,   9 . 0 0 0 0 0 0 
 
     - >   t h e   s e l f - d e f i n i n g   d i m e n s i o n   i s   a   H a u s d o r f f   d i m e n s i o n ,   n e v e r   e x a c t l y   i n t e g e r :   P A S S 
 
 
 
 [ R U N   3   -   D E N S I T Y   P U L L S   D I M E N S I O N ,   C H A O S   C O N T R A C T S   I T   ( C 2 8 / C 2 2 ) ] 
 
     a t   C   =   0 . 8 5 6 5   ( E q   4 4 ) :   D ( r h o = 0 . 3 ,   c h i = 0 . 1 )   =   8 . 3 9 1 2 8 6 
 
     D ( r h o = 0 . 8 ,   c h i = 0 . 1 )   =   9 . 0 0 0 0 0 0       ( d e n s i t y   p u l l s   d i m e n s i o n   u p ,   C 2 8   i n f o r m a t i o n   g r a v i t y ) 
 
     D ( r h o = 0 . 3 ,   c h i = 0 . 8 )   =   5 . 5 1 6 8 9 7       ( c h a o s   c o n t r a c t s   i t ,   C 2 2 ) 
 
     - >   D   =   f ( C ,   r h o ,   c h i ) :   d e n s i t y   p u l l s ,   c h a o s   c o n t r a c t s ,   c o h e r e n c e   r e s o l v e 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   s i n g l e - l a y e r ] 
 
     D ( k a p p a = 0 ,   C = 0 . 8 5 6 5 )   =   1 . 0 0 0 0 0 0 0 0 0     v s     s t a t i c   s i n g l e - l a y e r   D   =   1 . 0 0 0 0 0 0 0 0 0   ( t h e   c a g e :   o n e   f i x e d   r e p r e s e n t a t i o n ) 
 
     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   p o s s i b i l i t y - l a y e r i n g   p h i - f o r m ,   k a p p a   0   - >   1 ] 
 
     k a p p a = 0 . 0 0     P _ 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     P _ 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     P _ 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     P _ 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     P _ 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 ) :   P _ 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 _ 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 3   V E R D I C T :   A L L   C H E C K S   P A S S   -   t h e   s e l f - d e f i n i n g   d i m e n s i o n   D   =   f ( C ,   r h o ,   c h i )   r e s o l v e s   t h e   o b s e r v e d   p o s s i b i l i t y   l a y e r :   c o h e r e n c e   u n f o l d s   t h e   l a d d e r ,   t h e   f r a c t a l   H a u s d o r f f   r e a d i n g   n e v e r   c o l l a p s e s   t o   o n e   f i x e d   r e p r e s e n t a t i o n . 
 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 
 