latt-c

LATT-C: a recursive C lattice game using only the digits 1..9.

Idea: - C is the order constant: C = 3. - One local game is a C x C matrix, which has C*C = 9 cells. - Every cell recursively expands into another C x C game. - Therefore depth d produces a matrix of matrices of size C^d x C^d. - Every visible value is wrapped into the digit field {1,2,3,4,5,6,7,8,9}.

Proof sketch of the simulation invariant:
  1. Size invariant:
     depth 0 is a single seed. Each step expands one cell by C rows and C columns.
     By induction, depth d has C^d rows and C^d columns.

  2. Digit closure invariant:
     wrap9(n) = 1 + (n mod 9), normalized to {1..9}.
     Since every generated payoff passes through wrap9, no value can leave {1..9}.

  3. Recursive termination:
     latt_c_at(x, y, depth, parent) calls itself with depth-1.
     Since depth is finite and nonnegative, it reaches depth 0.

  4. Game-theory trace:
     Each local C x C block is a two-strategy-space payoff matrix.
     The r == c branch receives an added +C, marking a Nash-like self-consistent
     diagonal preference inside the lattice. The full diagonal across recursive
     layers is the ascension trace.

:: compile and run ::

gcc -std=c11 -Wall -Wextra -O2 latt-c.c -o latt-c ./latt-c 3

:: compile and run latt-c-2 ::

gcc -std=c11 -Wall -Wextra -O2 latt-c-2.c -o latt-c-2 $(sdl2-config --cflags --libs) -lm