File size: 3,599 Bytes
e462a34 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 | #!/usr/bin/env python3
"""Independent Python GF(2) 81-body, ten-trillion-step matrix exponentiation.
This is a NEW, explicitly locked five-law control; not an unverified replay of
an earlier unknown law set. Software computation, not physical propagation.
"""
import argparse
import hashlib
import json
from pathlib import Path
N=81
MASK=(1<<N)-1
TAG="ASOLARIA-81-3PHYSICAL-GF2-V1"
LAWS=((0,1),(0,2),(0,1,3),(0,4,7),(0,1,5,9))
STEPS=10_000_000_000_000
SEATS=("seat-1","seat-2","seat-3")
def sha(x):
return hashlib.sha256(x.encode("ascii")).hexdigest()
def get_challenge(p):
c=json.loads(Path(p).read_text(encoding="utf-8"))
assert c["schema"]==TAG
assert c["steps"]==STEPS and c["waves"]==12 and c["bodies"]==81
assert c["laws"]==[list(x) for x in LAWS], "Law drift"
assert sorted(c["seat_commitments"])==list(SEATS), "Need all three commitments"
for k in SEATS:
assert len(c["seat_commitments"][k])==64
int(c["seat_commitments"][k],16)
assert len(c["nonce"])==32
int(c["nonce"],16)
return c
def apply(columns,bits):
result=0
while bits:
low=bits & -bits
result ^= columns[low.bit_length()-1]
bits ^= low
return result
def matrix_for(taps):
return [sum(1<<((i+t)%N) for t in taps) for i in range(N)]
def compose(left,right):
return [apply(left,col) for col in right]
def advance_matrix(taps,steps):
unit=[1<<i for i in range(N)]
power=matrix_for(taps)
while steps:
if steps & 1:
unit=compose(power,unit)
power=compose(power,power)
steps >>= 1
return unit
def direct_once(taps,initial):
result=0
for t in taps:
result ^= ((initial<<t)|(initial>>(N-t))) & MASK if t else initial
return result & MASK
def self_test():
for taps in LAWS:
for n in (0,1,2,3,9,21):
matrix=advance_matrix(taps,n)
for seat in (0,1,40,80):
v=1<<seat
expected=v
for _ in range(n):
expected=direct_once(taps,expected)
assert apply(matrix,v)==expected,(taps,n,seat)
return True
def build(c):
master=sha(TAG+"|"+c["nonce"]+"|"+"|".join(c["seat_commitments"][s] for s in SEATS))
lines=[f"PORTAL|schema={TAG}|nonce={c['nonce']}|master={master}|steps={STEPS}|laws=5|waves=12|bodies=81|json=0"]
for index,taps in enumerate(LAWS):
matrix=advance_matrix(taps,STEPS)
assert len(matrix)==81
for wave in range(12):
for body in range(N):
state=int(sha(master+"|"+str(index)+"|"+str(wave)+"|"+str(body)),16)&MASK
state^=1<<body
out=apply(matrix,state)
out_hex=f"{out:021x}"
check=sha(f"ASOLARIA|STATE|{index}|{wave}|{body}|{out_hex}")
lines.append(f"WAVE|law={index}|wave={wave}|body={body}|state={out_hex}|sha={check}|json=0")
assert len(lines)==4861
lines.append("END|records=4860|class=EXACT_GF2_DIGITAL_CALCULATION|json=0")
return ("\n".join(lines)+"\n").encode("ascii")
def main():
parser=argparse.ArgumentParser()
parser.add_argument("challenge")
parser.add_argument("output")
parser.add_argument("--self-test",action="store_true")
a=parser.parse_args()
if a.self_test:self_test()
payload=build(get_challenge(a.challenge))
Path(a.output).write_bytes(payload)
print(json.dumps({"status":"PASS","records":4860,
"sha256":hashlib.sha256(payload).hexdigest(),
"algorithm":"GF2-column-matrix","steps":STEPS}))
if __name__=="__main__":main()
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