feat: Add prime/dimensional analysis scripts - wave sieve, hypothesis battery (11/12), Fibonacci chain, dimensional modes

2026-03-28 20:36:24 +07:00
parent 9302a86ea8
commit f2f312e18c
4 changed files with 404 additions and 0 deletions
@@ -0,0 +1,117 @@
+#!/usr/bin/env python3
+"""DIMENSIONAL PRIME ANALYSIS — mode counting in 1D/2D/3D/4D.
+Tests whether primes are dimension-dependent.
+Key finding: 2 is structural in dimensions 2 and 3.
+At dimension 4 = 2^2, Lagrange's theorem exhausts 2's power.
+"""
+import math
+from collections import defaultdict
+def is_prime(n):
+    if n<2:return False
+    if n<4:return True
+    if n%2==0 or n%3==0:return False
+    i=5
+    while i*i<=n:
+        if n%i==0 or n%(i+2)==0:return False
+        i+=6
+    return True
+def sieve(n):
+    if n<2:return []
+    ip=[True]*(n+1);ip[0]=ip[1]=False
+    for i in range(2,int(n**0.5)+1):
+        if ip[i]:
+            for j in range(i*i,n+1,i):ip[j]=False
+    return [i for i in range(n+1) if ip[i]]
+def modes_1d(me):
+    c=defaultdict(int);mk=int(me**0.5)+1
+    for k in range(-mk,mk+1):
+        e=k*k
+        if 0<e<=me:c[e]+=1
+    return dict(sorted(c.items()))
+def modes_2d(me):
+    c=defaultdict(int);mk=int(me**0.5)+1
+    for kx in range(-mk,mk+1):
+        for ky in range(-mk,mk+1):
+            e=kx*kx+ky*ky
+            if 0<e<=me:c[e]+=1
+    return dict(sorted(c.items()))
+def modes_3d(me):
+    c=defaultdict(int);mk=int(me**0.5)+1
+    for kx in range(-mk,mk+1):
+        for ky in range(-mk,mk+1):
+            for kz in range(-mk,mk+1):
+                e=kx*kx+ky*ky+kz*kz
+                if 0<e<=me:c[e]+=1
+    return dict(sorted(c.items()))
+def modes_4d(me):
+    c=defaultdict(int);mk=int(me**0.5)+1
+    for k1 in range(-mk,mk+1):
+        for k2 in range(-mk,mk+1):
+            for k3 in range(-mk,mk+1):
+                r2=k1*k1+k2*k2+k3*k3
+                if r2>me:continue
+                for k4 in range(-mk,mk+1):
+                    e=r2+k4*k4
+                    if 0<e<=me:c[e]+=1
+    return dict(sorted(c.items()))
+def main():
+    ME=50
+    print('='*70+'\n  DIMENSIONAL PRIME ANALYSIS\n'+'='*70)
+    print('\n  Computing modes...')
+    m1=modes_1d(ME);m2=modes_2d(ME);m3=modes_3d(ME)
+    print('  Computing 4D...')
+    m4=modes_4d(ME)
+    r1=set(m1.keys());r2=set(m2.keys());r3=set(m3.keys());r4=set(m4.keys())
+    nr3=set(range(1,ME+1))-r3;nr4=set(range(1,ME+1))-r4
+    print(f'\n--- REPRESENTABLE ENERGIES ---')
+    print(f'1D: {len(r1)}/{ME} (perfect squares only)')
+    print(f'2D: {len(r2)}/{ME}')
+    print(f'3D: {len(r3)}/{ME}, NOT rep: {sorted(nr3)}')
+    print(f'4D: {len(r4)}/{ME} (ALL — Lagrange theorem)')
+    print(f'\n--- 3D EXCLUSIONS (4^a * (8b+7)) ---')
+    for n in sorted(nr3):
+        m=n;a=0
+        while m%4==0:m//=4;a+=1
+        print(f'  {n:>4} = 4^{a} x {m} (mod8={m%8}) prime={is_prime(n)}')
+    print(f'\n--- MODE TABLE ---')
+    print(f'{"E":>4} {"1D":>4} {"2D":>5} {"3D":>6} {"4D":>7} {"2Dcum":>6} {"3Dcum":>6}')
+    c2=0;c3=0;nm={2,8,20,28,50,82,126};hm={2,8,20,40,70,112}
+    for e in range(1,ME+1):
+        d1=m1.get(e,0);d2=m2.get(e,0);d3=m3.get(e,0);d4=m4.get(e,0)
+        c2+=d2;c3+=d3
+        mk=[]
+        if c2 in nm:mk.append(f'2D->N:{c2}')
+        if c3 in nm:mk.append(f'3D->N:{c3}')
+        if c2 in hm:mk.append(f'2D->HO:{c2}')
+        if d2>0 or d3>0 or mk:
+            print(f'  {e:>4} {d1:>4} {d2:>5} {d3:>6} {d4:>7} {c2:>6} {c3:>6}  {" ".join(mk)}')
+    print(f'\n--- MAGIC NUMBER SPEED ---')
+    for mg in [2,8,20,28,40,50,70,82,112,126]:
+        c2=0;e2=None
+        for e in sorted(m2.keys()):
+            c2+=m2[e]
+            if c2>=mg and not e2:e2=e
+        c3=0;e3=None
+        for e in sorted(m3.keys()):
+            c3+=m3[e]
+            if c3>=mg and not e3:e3=e
+        print(f'  Magic {mg:>3}: 2D@E={e2}, 3D@E={e3} {"(3D faster)" if e3 and e2 and e3<e2 else ""}')
+    print(f'\n--- COPRIME SIEVE IN 3D ---')
+    p100=set(sieve(100))
+    for wls in [(128,8),(128,8,6),(128,9,5),(127,9,5)]:
+        sv=[n for n in range(2,101) if all(math.gcd(n,w)==1 for w in wls)]
+        cap=p100&set(sv);miss=p100-set(sv)
+        sp=set();
+        for w in wls:
+            n=w;d=2
+            while d*d<=n:
+                while n%d==0:sp.add(d);n//=d
+                d+=1
+            if n>1:sp.add(n)
+        print(f'  WL{wls}: structural={sorted(sp)} prec={100*len(cap)/max(1,len(sv)):.1f}% miss={sorted(miss)}')
+    print(f'\n--- SUMMARY ---')
+    print(f'2 is structural in 2D (mod 4) and 3D (4^a(8b+7)).')
+    print(f'At dim 4 = 2^2, Lagrange exhausts 2. Self-referential.')
+    print(f'Odd primes (3,5,7,11...) are universal across all dimensions.')
+    print(f'In dim D, the first D-1 primes can be made structural.')
+if __name__=='__main__':main()