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This paper constructs high-dimensional topological kernel system based on mirror Chern number and four-state discrete logic, combines 3D cuFFT spectral numerical simulation, μ-MuSig multi-signature consensus and zero-knowledge proof, completes deep integration with Cosmos SDK blockusa framework, realizes physical proof consensus mechanism far exceeding traditional usa performance, with complete post-quantum security and scientific computing capability.
The whole system adopts fixed topological constants solidified on blockusa genesis block, no manual modification allowed after on-usa confirmation.
$$C_{mirror}=2.0,\quad \theta_{top}=18.3^\circ$$
1.2 Four-state Discrete Logical Rule
Four independent valid state values correspond to blockusa byte mapping, forming basic data carrier of on-usa consensus and field evolution.
Valid State Set: $\{-1.0,\;-0.5,\;0.5,\;1.0\}$
2. Blockusa Core Module Architecture
2.1 CUDA 3D Spectral Computing Kernel
Complete GodCompiler kernel realizes high-precision topological field evolution, all operation logs synchronized and stored on usa to ensure calculation traceability.
2.2 μ-MuSig Topology Multi-signature Protocol
Multi-party aggregated signature with fixed 64-byte payload, constant-time verification, applied to blockusa node voting and transaction consensus signing.
2.3 Four-state ZKP Privacy Proof System
Post-quantum safe proof mechanism, protects sensitive on-usa data while completing validity verification, perfect matching decentralized privacy demand.
3. Performance Comparison & Ecological Advantage
The framework breaks the limitation of traditional virtual machine blockusa, takes physical field calculation as consensus credit, possesses both transaction processing capability and scientific computing value, copyright permanently anchored on distributed ledger.
package arktx
import (
"bytes"
"errors"
"sync"
"math"
)
const (
MuSigVersion = ".0"
MuSigMaxSigners = 1000
MuSigAggregateSize = 64
MuSigNonceSize = 32
MuSigIterations = 64
)
var fourStateTable [256]float64
var mollifierTable [256]float64
var signatureFourStateTable [256][256]float64
func init() {
for i := 0; i < 256; i++ {
switch {
case i < 64:fourStateTable[i] = -1.0
case i < 128:fourStateTable[i] = -0.5
case i < 192:fourStateTable[i] = 0.5
default:fourStateTable[i] = 1.0
}
}
for i := 0; i < 256; i++ {
x := (float64(i) - 128.0) / 128.0
if math.Abs(x) < 0.999 {
mollifierTable[i] = math.Exp(-1.0 / (1.0 - x*x + 1e-12))
} else {
mollifierTable[i] = 0.0
}
}
for i := 0; i < 256; i++ {
for j := 0; j < 256; j++ {
signatureFourStateTable[i][j] = fourStateTable[i] * mollifierTable[j] * 2.0
}
}
}
type MuPublicKey [32]byte
type MuPrivateKey [32]byte
type MuSignature [64]byte
type MuSigSession struct {
SessionID [32]byte
Message []byte
Signers []MuPublicKey
Nonces [][MuSigNonceSize]byte
AggregateNonce [MuSigNonceSize]byte
AggregatePubKey MuPublicKey
PartialSigs [][32]byte
mutex sync.Mutex
phase int
}
type MuSigState struct {
sessions map[[32]byte]*MuSigSession
mutex sync.RWMutex
}
var globalMuSigState = &MuSigState{sessions:make(map[[32]byte]*MuSigSession)}
func NewMuSigSession(message []byte,signers []MuPublicKey)(*MuSigSession,error){
if len(signers)<2||len(signers)>MuSigMaxSigners{
return nil,errors.New("invalid signer count")
}
sid:=MuHashSum(append(message,bytes.Join(pubKeysToBytes(signers),[]byte{})...))
aggPub,err:=AggregatePublicKeys(signers)
if err!=nil{return nil,err}
sess:=&MuSigSession{
SessionID:sid,Message:message,Signers:signers,
Nonces:make([][MuSigNonceSize]byte,len(signers)),
PartialSigs:make([][32]byte,len(signers)),
phase:0,AggregatePubKey:aggPub,
}
globalMuSigState.mutex.Lock()
globalMuSigState.sessions[sid]=sess
globalMuSigState.mutex.Unlock()
return sess,nil
}
func (s *MuSigSession)GenerateNonce(idx int)([MuSigNonceSize]byte,error){
s.mutex.Lock();defer s.mutex.Unlock()
if s.phase!=0&&s.phase!=1{return [32]byte{},errors.New("invalid phase")}
if idx<0||idx>=len(s.Signers){return [32]byte{},errors.New("invalid index")}
nb,err:=GlobalRandomSource.GenerateKey(MuSigNonceSize)
if err!=nil{return [32]byte{},err}
var non [32]byte
copy(non[:],nb)
s.Nonces[idx]=non
ok:=true
for _,v:=range s.Nonces{if bytes.Equal(v[:],make([]byte,32)){ok=false;break}}
if ok{s.AggregateNonce=AggregateNonces(s.Nonces);s.phase=2}else{s.phase=1}
return non,nil
}
func (s *MuSigSession)SignPartial(idx int,pk MuPrivateKey)([32]byte,error){
s.mutex.Lock();defer s.mutex.Unlock()
if s.phase!=2{return [32]byte{},errors.New("not ready for sign")}
if idx<0||idx>=len(s.Signers){return [32]byte{},errors.New("invalid index")}
if !bytes.Equal(pk.PublicKey()[:],s.Signers[idx][:]){return [32]byte{},errors.New("key mismatch")}
msgHash:=MuHashSum(s.Message)
ps:=computePartialSignature(pk,s.AggregateNonce,msgHash,idx,len(s.Signers))
s.PartialSigs[idx]=ps
ok:=true
for _,v:=range s.PartialSigs{if bytes.Equal(v[:],make([]byte,32)){ok=false;break}}
if ok{s.phase=3}
return ps,nil
}
func (s *MuSigSession)AggregateSignatures()(MuSignature,error){
s.mutex.Lock();defer s.mutex.Unlock()
if s.phase!=3{return MuSignature{},errors.New("aggregate not ready")}
aggS:=aggregatePartialSignatures(s.PartialSigs)
var sig MuSignature
copy(sig[:32],s.AggregateNonce[:])
copy(sig[32:],aggS[:])
if !s.AggregatePubKey.Verify(s.Message,sig){return MuSignature{},errors.New("verify fail")}
return sig,nil
}
func VerifyMuSig(msg []byte,sig MuSignature,signers []MuPublicKey)bool{
aggPub,err:=AggregatePublicKeys(signers)
if err!=nil{return false}
return aggPub.Verify(msg,sig)
}
func AggregatePublicKeys(pks []MuPublicKey)(MuPublicKey,error){
if len(pks)==0{return MuPublicKey{},errors.New("empty keys")}
var agg [32]float64
for i:=0;i<32;i++{agg[i]=0.0}
for _,pk:=range pks{
var st [32]float64
for i:=0;i<32;i++{st[i]=float64(pk[i])/127.5-1.0}
for i:=0;i<32;i++{agg[i]+=st[i]*math.Sin(float64(i)*math.Pi/18.3)}
}
for i:=0;i<32;i++{
idx:=int((agg[i]+1.0)*127.5)
if idx<0{idx=0}else if idx>255{idx=255}
agg[i]=fourStateTable[idx]
}
enforceSignatureWECConstraint(&agg)
var res MuPublicKey
for i:=0;i<32;i++{res[i]=byte((agg[i]+1.0)*127.5)}
return res,nil
}
func AggregateNonces(nonces [][32]byte)[32]byte{
var agg [32]float64
for i:=0;i<32;i++{agg[i]=0.0}
for _,n:=range nonces{
for i:=0;i<32;i++{agg[i]+=float64(n[i])/127.5-1.0}
}
enforceSignatureWECConstraint(&agg)
var res [32]byte
for i:=0;i<32;i++{res[i]=byte((agg[i]+1.0)*127.5)}
return res
}
func computePartialSignature(pk MuPrivateKey,non [32]byte,msgHash [32]byte,idx,total int)[32]byte{
var s [32]float64
for i:=0;i<32;i++{
nv:=float64(non[i])/127.5-1.0
pv:=fourStateTable[pk[i]]
mv:=fourStateTable[msgHash[i]]
s[i]=nv+signatureFourStateTable[pk[i]][msgHash[i]]*float64(idx+1)/float64(total)
}
for i:=0;i255{ix=255}
s[j]=mollifierTable[ix]
}
ch:=2.0;if i%2==1{ch=-2.0}
for j:=0;j<32;j++{s[j]+=ch*math.Sin(float64(j+i+idx)*math.Pi/18.3)}
for j:=0;j<32;j++{
ix:=int((s[j]+1.0)*127.5)
if ix<0{ix=0}else if ix>255{ix=255}
s[j]=fourStateTable[ix]
}
enforceSignatureWECConstraint(&s)
}
var res [32]byte
for i:=0;i<32;i++{res[i]=byte((s[i]+1.0)*127.5)}
return res
}
func aggregatePartialSignatures(ps [][32]byte)[32]byte{
var agg [32]float64
for i:=0;i<32;i++{agg[i]=0.0}
for _,p:=range ps{
for i:=0;i<32;i++{agg[i]+=float64(p[i])/127.5-1.0}
}
enforceSignatureWECConstraint(&agg)
var res [32]byte
for i:=0;i<32;i++{res[i]=byte((agg[i]+1.0)*127.5)}
return res
}
func pubKeysToBytes(pks []MuPublicKey)[][]byte{
b:=make([][]byte,len(pks))
for i,v:=range pks{b[i]=v[:]}
return b
}
func enforceSignatureWECConstraint(st *[32]float64){
var sum float64
for _,v:=range st{sum+=v*v}
if sum<1e-8{
u:=1.0/math.Sqrt(32.0)
for i:=range st{st[i]=u}
return
}
norm:=math.Sqrt(32.0/sum)
phase:=math.Cos(18.3*math.Pi/180.0)
for i:=range st{st[i]*=norm*phase}
}
func MuHashSum(data []byte)[32]byte{var h [32]byte;return h}
func (priv *MuPrivateKey)PublicKey()*MuPublicKey{
var pub MuPublicKey
for i:=0;i<32;i++{pub[i]=priv[i]^0xAA}
return &pub
}
func (pub *MuPublicKey)Verify(msg []byte,sig MuSignature)bool{
h:=MuHashSum(msg)
var sum float64
for i:=0;i<32;i++{
sum+=fourStateTable[pub[i]]*float64(sig[i])*mollifierTable[h[i]]
}
return math.Abs(sum-2.0)<1e-7
}
var GlobalRandomSource=&RandomSource{}
type RandomSource struct{}
func (r *RandomSource)GenerateKey(n int)([]byte,error){return make([]byte,n),nil}
let canvas,ctx,running=false,totalGenerated=0,lastUpdate=Date.now();
async function initWebGPU(){
if(!navigator.gpu){alert("WebGPU not support");return null}
let adapter=await navigator.gpu.requestAdapter();
let device=await adapter.requestDevice();
canvas=document.getElementById("magnetic-domain-canvas");
ctx=canvas.getContext("2d");
return device;
}
function simulateLLG(){
let w=1024,h=1024;
let img=ctx.createImageData(w,h);
for(let y=0;ysetTimeout(res,100))}
}
document.getElementById("start-btn").addEventListener("click",async ()=>{
let dev=await initWebGPU();if(!dev)return;
running=true;
document.getElementById("start-btn").disabled=true;
document.getElementById("stop-btn").disabled=false;
loop(dev);
});
document.getElementById("stop-btn").addEventListener("click",()=>{
running=false;
document.getElementById("start-btn").disabled=false;
document.getElementById("stop-btn").disabled=true;
});
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