Interactive Visualizer:
To attend:
POTSafeMath v9e
import java.math.BigInteger;
import java.nio.charset.StandardCharsets;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.util.*;
import java.util.concurrent.ConcurrentHashMap;
import java.util.concurrent.atomic.AtomicLong;
import java.util.concurrent.atomic.AtomicReference;
import java.util.stream.IntStream;
/**
* POTSafeMath v9e – Elegant Holographic MEGC Integration
* Combines:
* - Recursive ternary parity trees (DNA encoding)
* - Breathing seeds with vector utilities
* - BigInteger cryptographic accumulators
* - Holographic glyph projections
* - Onion-shell checkpoints
* with modular, streamlined elegance.
*/
public class POTSafeMath {
// Constants
private static final long DEFAULT_TIME_WINDOW_MS = 300_000;
private static final long CLOCK_SKEW_TOLERANCE_MS = 30_000;
private static final int MAX_MEMORY_OPERATIONS = 100_000;
private static final int CHECKPOINT_INTERVAL = 10_000;
private static final int GLYPH_CACHE_SIZE = 1_000;
private static final double PHI = (1.0 + Math.sqrt(5.0)) / 2.0;
private static final double INV_PHI = 1.0 / PHI;
private static final double PI_PHI = Math.PI / PHI;
private static final double HOLOGRAPHIC_DEPTH = Math.E * Math.E;
private static final int INTERFERENCE_HARMONICS = 12;
private static final int BREATHING_SEEDS = 8;
private static final double CONTRACTION_RATE = 0.618;
// Core state
private final AtomicLong operationCounter = new AtomicLong(0);
private final ConcurrentHashMap<String, POTOperation> recentOperations = new ConcurrentHashMap<>();
private final AtomicReference<BigInteger> globalLedgerAccumulator = new AtomicReference<>(BigInteger.ZERO);
private final List<BreathingSeed> convergentSeeds = Collections.synchronizedList(new ArrayList<>());
private final AtomicReference<TernaryParityTree> globalParityTree =
new AtomicReference<>(new TernaryParityTree(TernaryState.NEUTRAL, 0, null, null, null));
private final Map<Long, HolographicGlyph> glyphCache = new LinkedHashMap<Long, HolographicGlyph>(GLYPH_CACHE_SIZE, 0.75f, true) {
@Override protected boolean removeEldestEntry(Map.Entry<Long, HolographicGlyph> eldest) {
return size() > GLYPH_CACHE_SIZE;
}
};
private final List<OnionShellCheckpoint> onionCheckpoints = Collections.synchronizedList(new ArrayList<>());
// --- Utility ---
private static class CryptoUtil {
static BigInteger sha256(String input) {
try {
MessageDigest md = MessageDigest.getInstance("SHA-256");
return new BigInteger(1, md.digest(input.getBytes(StandardCharsets.UTF_8)));
} catch (NoSuchAlgorithmException e) {
throw new RuntimeException("Hash calculation failed", e);
}
}
static BigInteger hashMatrix(BigInteger[][] matrix) {
StringBuilder sb = new StringBuilder();
for (BigInteger[] row : matrix) for (BigInteger val : row) sb.append(val.toString(16));
return sha256(sb.toString());
}
}
private static class Vec {
static double distance(double[] a, double[] b) {
return Math.sqrt(IntStream.range(0, Math.min(a.length, b.length))
.mapToDouble(i -> Math.pow(a[i] - b[i], 2)).sum());
}
static double[] mutate(double[] v, Random r, double rate) {
double[] copy = v.clone();
for (int i = 0; i < copy.length; i++)
copy[i] = clamp(copy[i] + r.nextGaussian() * rate * INV_PHI, 0.0, 1.0);
return copy;
}
static double[] breatheToward(double[] v, double[] target, double factor) {
double[] out = new double[v.length];
for (int i = 0; i < v.length; i++) out[i] = v[i] + factor * (target[i] - v[i]);
return out;
}
private static double clamp(double v, double min, double max) { return Math.max(min, Math.min(max, v)); }
}
// --- Ternary Parity Tree ---
public enum TernaryState { NEGATIVE(0), NEUTRAL(1), POSITIVE(2); private final int value; TernaryState(int v){value=v;} public int getValue(){return value;} }
public static class TernaryParityTree {
private static final char[] DNA_MAP = {'A','G','T'};
private final TernaryState state; private final int depth;
private TernaryParityTree left, mid, right; private double phiWeight;
public TernaryParityTree(TernaryState s,int d,TernaryParityTree l,TernaryParityTree m,TernaryParityTree r){state=s;depth=d;left=l;mid=m;right=r;updatePhiWeight();}
public void insert(BigInteger value,long opId){insertRecursive(this,value,opId,0);updatePhiWeight();}
private void insertRecursive(TernaryParityTree node,BigInteger v,long id,int d){
if(d>10)return;TernaryState ns=computeTernaryState(v,id);
if(ns==TernaryState.NEGATIVE){if(node.left==null)node.left=new TernaryParityTree(ns,d+1,null,null,null);else insertRecursive(node.left,v,id,d+1);}
else if(ns==TernaryState.NEUTRAL){if(node.mid==null)node.mid=new TernaryParityTree(ns,d+1,null,null,null);else insertRecursive(node.mid,v,id,d+1);}
else{if(node.right==null)node.right=new TernaryParityTree(ns,d+1,null,null,null);else insertRecursive(node.right,v,id,d+1);}
}
private TernaryState computeTernaryState(BigInteger v,long id){double phiMod=(v.doubleValue()*PHI+id*INV_PHI)%3.0;return phiMod<1.0?TernaryState.NEGATIVE:phiMod<2.0?TernaryState.NEUTRAL:TernaryState.POSITIVE;}
private void updatePhiWeight(){phiWeight=(phiWeight*CONTRACTION_RATE+countNodes()*INV_PHI)/2.0;if(left!=null)left.updatePhiWeight();if(mid!=null)mid.updatePhiWeight();if(right!=null)right.updatePhiWeight();}
int countNodes(){int c=1;if(left!=null)c+=left.countNodes();if(mid!=null)c+=mid.countNodes();if(right!=null)c+=right.countNodes();return c;}
public String toDNASequence(){StringBuilder dna=new StringBuilder();toDNARecursive(dna);return dna.toString();}
private void toDNARecursive(StringBuilder dna){dna.append(DNA_MAP[state.getValue()]);if(left!=null)left.toDNARecursive(dna);if(mid!=null)mid.toDNARecursive(dna);if(right!=null)right.toDNARecursive(dna);dna.append('C');}
}
// --- Breathing Seeds ---
public static class BreathingSeed {
private double[] vector; private final long seedId; private double fitness; double phiWeight; private final Random rng=new Random();
public BreathingSeed(int dim,long id){seedId=id;vector=new double[dim];rng.setSeed(id);initialize();}
private void initialize(){for(int i=0;i<vector.length;i++)vector[i]=rng.nextDouble()*PHI%1.0;}
public void mutate(double rate){vector=Vec.mutate(vector,rng,rate);}
public void breatheToward(BreathingSeed t,double c){vector=Vec.breatheToward(vector,t.vector,c*phiWeight);updatePhiWeight();}
private void updatePhiWeight(){phiWeight=(Arrays.stream(vector).sum()*PHI)%1.0;}
public double distanceFrom(BreathingSeed o){return Vec.distance(vector,o.vector);}
public double[] getVector(){return vector.clone();} public long getSeedId(){return seedId;}
public double getFitness(){return fitness;} public void setFitness(double f){fitness=f;}
}
// --- OnionShellCheckpoint ---
public static class OnionShellCheckpoint {
public final long operationId,timestamp; public final BigInteger accumulatorState,stateHash; public final List<BigInteger> shellLayers; public final String dnaSequence,breathingSignature;
public OnionShellCheckpoint(long opId,long ts,BigInteger acc,TernaryParityTree pt,List<BreathingSeed> seeds){operationId=opId;timestamp=ts;accumulatorState=acc;dnaSequence=pt.toDNASequence();breathingSignature=computeSig(seeds);shellLayers=generateShells(acc,pt);stateHash=calcHash();}
private String computeSig(List<BreathingSeed> seeds){StringBuilder s=new StringBuilder();for(BreathingSeed b:seeds){s.append(String.format("%.3f",b.getFitness()));s.append(String.format("%.3f",b.phiWeight));}return s.toString();}
private List<BigInteger> generateShells(BigInteger acc,TernaryParityTree pt){List<BigInteger> sh=new ArrayList<>();String dna=pt.toDNASequence();sh.add(CryptoUtil.sha256(acc.toString(16)));sh.add(CryptoUtil.sha256(dna));sh.add(CryptoUtil.sha256(String.valueOf(acc.doubleValue()*PHI%10000)));sh.add(CryptoUtil.sha256(sh.get(0).toString()+sh.get(1).toString()));sh.add(CryptoUtil.sha256(sh.get(2).toString()+sh.get(3).toString()));return Collections.unmodifiableList(sh);}
private BigInteger calcHash(){StringBuilder d=new StringBuilder();d.append(operationId).append(":").append(timestamp).append(":").append(accumulatorState);d.append(":").append(dnaSequence).append(":").append(breathingSignature);shellLayers.forEach(h->d.append(":").append(h));return CryptoUtil.sha256(d.toString());}
}
// --- POTOperation ---
public static class POTOperation {
public final long timestamp,operationId,validUntil; public final String operationType,operandHash,resultHash,hash,holographicSeal,dnaSequence;
public POTOperation(long ts,String type,String opH,String resH,long id,long vu,String seal,String dna){timestamp=ts;operationType=type;operandHash=opH;resultHash=resH;operationId=id;validUntil=vu;holographicSeal=seal;dnaSequence=dna;hash=CryptoUtil.sha256(ts+type+opH+resH+id+seal+dna).toString(16);}
public boolean isTemporallyValid(long now,long prev){return now>=(timestamp-CLOCK_SKEW_TOLERANCE_MS)&&now<=validUntil&&(prev==0||Math.abs(timestamp-prev)<=DEFAULT_TIME_WINDOW_MS);}
}
// --- Core methods ---
public void initializeBreathingSeeds(){convergentSeeds.clear();for(int i=0;i<BREATHING_SEEDS;i++)convergentSeeds.add(new BreathingSeed(64,i));}
public void performBreathingCycle(BigInteger target){if(convergentSeeds.isEmpty())initializeBreathingSeeds();double[] tgt=accumulatorToVector(target);for(int it=0;it<10;it++){for(BreathingSeed s:convergentSeeds)s.setFitness(1.0/(Vec.distance(s.getVector(),tgt)+1e-12));convergentSeeds.sort((a,b)->Double.compare(b.getFitness(),a.getFitness()));BreathingSeed best=convergentSeeds.get(0);for(int i=1;i<convergentSeeds.size();i++){convergentSeeds.get(i).breatheToward(best,CONTRACTION_RATE);convergentSeeds.get(i).mutate(0.1*INV_PHI);}}}
private double[] accumulatorToVector(BigInteger acc){String hex=acc.toString(16);double[] v=new double[64];for(int i=0;i<Math.min(hex.length(),64);i++)v[i]=Character.getNumericValue(hex.charAt(i))/15.0;return v;}
// --- Summaries ---
public String generateDNALedgerSummary(){StringBuilder s=new StringBuilder();s.append("TREE_DNA: ").append(globalParityTree.get().toDNASequence(),0,Math.min(50,globalParityTree.get().toDNASequence().length())).append("...\n");s.append("RECENT_OPS_DNA:\n");int c=0;for(POTOperation op:recentOperations.values()){if(c++<5)s.append(" ").append(op.operationId).append(": ").append(op.dnaSequence).append("\n");}s.append("BREATHING_DNA:\n");for(int i=0;i<Math.min(3,convergentSeeds.size());i++){BreathingSeed b=convergentSeeds.get(i);s.append(" ").append(b.getSeedId()).append(": phi=").append(String.format("%.3f",b.phiWeight)).append(" fit=").append(String.format("%.3f",b.getFitness())).append("\n");}return s.toString();}
}
POTSafeMath v9.1
assess how and whether to integrate the full HolographicGlyph projection class by gleaning only what makes our code more elegant of the following:
import java.math.BigInteger;
import java.nio.charset.StandardCharsets;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.util.*;
import java.util.concurrent.ConcurrentHashMap;
import java.util.concurrent.atomic.AtomicLong;
import java.util.concurrent.atomic.AtomicReference;
import java.util.stream.IntStream;
/**
* POTSafeMath v9.1 - Enhanced Elegant Holographic MEGC Integration
* Combines recursive ternary parity trees, breathing seeds, holographic glyphs, and onion-shell checkpoints
* with modular, readable, and concise design.
*/
public class POTSafeMath {
// Constants
private static final long DEFAULT_TIME_WINDOW_MS = 300_000;
private static final long CLOCK_SKEW_TOLERANCE_MS = 30_000;
private static final int MAX_MEMORY_OPERATIONS = 100_000;
private static final int CHECKPOINT_INTERVAL = 10_000;
private static final int GLYPH_CACHE_SIZE = 1_000;
private static final double PHI = (1.0 + Math.sqrt(5.0)) / 2.0;
private static final double INV_PHI = 1.0 / PHI;
private static final double PI_PHI = Math.PI / PHI;
private static final double HOLOGRAPHIC_DEPTH = Math.E * Math.E;
private static final int INTERFERENCE_HARMONICS = 12;
private static final int BREATHING_SEEDS = 8;
private static final double CONTRACTION_RATE = 0.618;
// Core state
private final AtomicLong operationCounter = new AtomicLong(0);
private final ConcurrentHashMap<String, POTOperation> recentOperations = new ConcurrentHashMap<>();
private final AtomicReference<BigInteger> globalLedgerAccumulator = new AtomicReference<>(BigInteger.ZERO);
private final List<BreathingSeed> convergentSeeds = Collections.synchronizedList(new ArrayList<>());
private final AtomicReference<TernaryParityTree> globalParityTree = new AtomicReference<>(
new TernaryParityTree(TernaryState.NEUTRAL, 0, null, null, null));
private final Map<Long, HolographicGlyph> glyphCache = new LinkedHashMap<Long, HolographicGlyph>(GLYPH_CACHE_SIZE, 0.75f, true) {
@Override
protected boolean removeEldestEntry(Map.Entry<Long, HolographicGlyph> eldest) {
return size() > GLYPH_CACHE_SIZE;
}
};
private final List<OnionShellCheckpoint> onionCheckpoints = Collections.synchronizedList(new ArrayList<>());
/**
* Utility for cryptographic hash operations.
*/
private static class CryptoUtil {
public static BigInteger sha256(String input) {
try {
MessageDigest md = MessageDigest.getInstance("SHA-256");
return new BigInteger(1, md.digest(input.getBytes(StandardCharsets.UTF_8)));
} catch (NoSuchAlgorithmException e) {
throw new RuntimeException("Hash calculation failed", e);
}
}
public static BigInteger hashMatrix(BigInteger[][] matrix) {
StringBuilder sb = new StringBuilder();
for (BigInteger[] row : matrix) {
for (BigInteger val : row) {
sb.append(val.toString(16));
}
}
return sha256(sb.toString());
}
}
/**
* Vector utility for breathing seed operations.
*/
private static class Vec {
public static double distance(double[] a, double[] b) {
return Math.sqrt(IntStream.range(0, Math.min(a.length, b.length))
.mapToDouble(i -> Math.pow(a[i] - b[i], 2))
.sum());
}
public static double[] mutate(double[] v, Random r, double rate) {
double[] copy = v.clone();
for (int i = 0; i < copy.length; i++) {
copy[i] = clamp(copy[i] + r.nextGaussian() * rate * INV_PHI, 0.0, 1.0);
}
return copy;
}
public static double[] breatheToward(double[] v, double[] target, double factor) {
double[] out = new double[v.length];
for (int i = 0; i < v.length; i++) {
out[i] = v[i] + factor * (target[i] - v[i]);
}
return out;
}
private static double clamp(double v, double min, double max) {
return Math.max(min, Math.min(max, v));
}
}
/**
* Ternary state enumeration.
*/
public enum TernaryState {
NEGATIVE(0), NEUTRAL(1), POSITIVE(2);
private final int value;
TernaryState(int value) { this.value = value; }
public int getValue() { return value; }
}
/**
* Recursive ternary parity tree with DNA encoding.
*/
public static class TernaryParityTree {
private static final char[] DNA_MAP = {'A', 'G', 'T'}; // NEGATIVE -> A, NEUTRAL -> G, POSITIVE -> T
private final TernaryState state;
private final int depth;
private TernaryParityTree left, mid, right;
private double phiWeight;
public TernaryParityTree(TernaryState state, int depth, TernaryParityTree left, TernaryParityTree mid, TernaryParityTree right) {
this.state = state;
this.depth = depth;
this.left = left;
this.mid = mid;
this.right = right;
updatePhiWeight();
}
public void insert(BigInteger value, long operationId) {
insertRecursive(this, value, operationId, 0);
updatePhiWeight();
}
private void insertRecursive(TernaryParityTree node, BigInteger value, long operationId, int currentDepth) {
if (currentDepth > 10) return;
TernaryState newState = computeTernaryState(value, operationId);
if (newState == TernaryState.NEGATIVE) {
if (node.left == null) node.left = new TernaryParityTree(newState, currentDepth + 1, null, null, null);
else insertRecursive(node.left, value, operationId, currentDepth + 1);
} else if (newState == TernaryState.NEUTRAL) {
if (node.mid == null) node.mid = new TernaryParityTree(newState, currentDepth + 1, null, null, null);
else insertRecursive(node.mid, value, operationId, currentDepth + 1);
} else {
if (node.right == null) node.right = new TernaryParityTree(newState, currentDepth + 1, null, null, null);
else insertRecursive(node.right, value, operationId, currentDepth + 1);
}
}
private TernaryState computeTernaryState(BigInteger value, long operationId) {
double phiMod = (value.doubleValue() * PHI + operationId * INV_PHI) % 3.0;
return phiMod < 1.0 ? TernaryState.NEGATIVE : phiMod < 2.0 ? TernaryState.NEUTRAL : TernaryState.POSITIVE;
}
private void updatePhiWeight() {
phiWeight = (phiWeight * CONTRACTION_RATE + countNodes() * INV_PHI) / 2.0;
if (left != null) left.updatePhiWeight();
if (mid != null) mid.updatePhiWeight();
if (right != null) right.updatePhiWeight();
}
private int countNodes() {
int count = 1;
if (left != null) count += left.countNodes();
if (mid != null) count += mid.countNodes();
if (right != null) count += right.countNodes();
return count;
}
public String toDNASequence() {
StringBuilder dna = new StringBuilder();
toDNARecursive(dna);
return dna.toString();
}
private void toDNARecursive(StringBuilder dna) {
dna.append(DNA_MAP[state.getValue()]);
if (left != null) left.toDNARecursive(dna);
if (mid != null) mid.toDNARecursive(dna);
if (right != null) right.toDNARecursive(dna);
dna.append('C');
}
}
/**
* Breathing seed for convergent compression.
*/
public static class BreathingSeed {
private double[] vector;
private final long seedId;
private double fitness;
private double phiWeight;
private final Random rng = new Random();
public BreathingSeed(int dimensions, long seedId) {
this.seedId = seedId;
this.vector = new double[dimensions];
this.fitness = 0.0;
this.phiWeight = 1.0;
rng.setSeed(seedId);
initializeWithPhi();
}
private void initializeWithPhi() {
for (int i = 0; i < vector.length; i++) {
vector[i] = rng.nextDouble() * PHI % 1.0;
}
}
public void mutate(double rate) {
vector = Vec.mutate(vector, rng, rate);
}
public void breatheToward(BreathingSeed target, double contractionRate) {
vector = Vec.breatheToward(vector, target.vector, contractionRate * phiWeight);
updatePhiWeight();
}
private void updatePhiWeight() {
phiWeight = (Arrays.stream(vector).sum() * PHI) % 1.0;
}
public double distanceFrom(BreathingSeed other) {
return Vec.distance(vector, other.vector);
}
public double[] getVector() {
return vector.clone();
}
public long getSeedId() {
return seedId;
}
public double getFitness() {
return fitness;
}
public void setFitness(double fitness) {
this.fitness = fitness;
}
}
/**
* Holographic glyph with MEGC breathing integration.
*/
public static class HolographicGlyph {
public final double[] realField;
public final double[] imagField;
public final double[] phaseField;
public final double temporalPhase;
public final double spatialFreq;
public final char projectedChar;
public final long timestamp;
public final String dnaSequence;
public final TernaryState ternaryState;
public final double breathingPhase;
public HolographicGlyph(int index, long timestamp, TernaryParityTree parityTree) {
this.timestamp = timestamp;
this.realField = new double[INTERFERENCE_HARMONICS];
this.imagField = new double[INTERFERENCE_HARMONICS];
this.phaseField = new double[INTERFERENCE_HARMONICS];
this.temporalPhase = generateTemporalPhase(timestamp, index);
this.spatialFreq = generateSpatialFrequency(index);
this.breathingPhase = (temporalPhase * PHI) % (2 * Math.PI);
this.ternaryState = classifyTernary(index, timestamp);
computeBreathingHolographicField();
this.projectedChar = projectToUnicode();
this.dnaSequence = generateDNASequence();
}
private double generateTemporalPhase(long ts, int idx) {
double timeNorm = ts * 2.399963229728653e-10;
double idxNorm = idx / 4096.0;
return (timeNorm * PHI + idxNorm * PI_PHI + breathingPhase) % (2 * Math.PI);
}
private double generateSpatialFrequency(int idx) {
return PHI * idx / 4096.0 * HOLOGRAPHIC_DEPTH * Math.cos(breathingPhase);
}
private void computeBreathingHolographicField() {
for (int h = 0; h < INTERFERENCE_HARMONICS; h++) {
double harmonic = h + 1;
double amplitude = 1.0 / (harmonic * harmonic);
double breathingModulation = Math.sin(breathingPhase * harmonic) * INV_PHI;
amplitude *= (1.0 + breathingModulation);
double phase1 = temporalPhase * harmonic;
double phase2 = temporalPhase * harmonic * PHI;
double phase3 = spatialFreq * harmonic + breathingPhase;
realField[h] = amplitude * (Math.cos(phase1) * Math.cos(phase2) - Math.sin(phase1) * Math.sin(phase3));
imagField[h] = amplitude * (Math.sin(phase1) * Math.cos(phase2) + Math.cos(phase1) * Math.sin(phase3));
phaseField[h] = Math.atan2(imagField[h], realField[h]);
}
}
private TernaryState classifyTernary(int index, long timestamp) {
double phiClassification = (index * PHI + timestamp * INV_PHI) % 3.0;
return phiClassification < 1.0 ? TernaryState.NEGATIVE :
phiClassification < 2.0 ? TernaryState.NEUTRAL : TernaryState.POSITIVE;
}
private char projectToUnicode() {
double realSum = Arrays.stream(realField).sum();
double imagSum = Arrays.stream(imagField).sum();
double phaseSum = Arrays.stream(phaseField).sum();
double magnitude = Math.sqrt(realSum * realSum + imagSum * imagSum);
double phase = Math.atan2(imagSum, realSum);
double normalizedPhase = (phase + Math.PI) / (2 * Math.PI);
double breathingInfluence = Math.sin(breathingPhase) * 0.1;
double unicodePosition = (magnitude * 0.3 + normalizedPhase + phaseSum / (2 * Math.PI) + breathingInfluence) % 1.0;
return holographicUnicodeMapping(unicodePosition, magnitude, phase);
}
private char holographicUnicodeMapping(double position, double magnitude, double phase) {
double regionSelector = (magnitude + Math.cos(breathingPhase) * 0.1) % 1.0;
if (regionSelector < 0.3) {
return (char) (0x0021 + (int) (position * 93));
} else if (regionSelector < 0.6) {
double phaseModulated = (position + Math.abs(phase) / (2 * Math.PI)) % 1.0;
char candidate = (char) (0x00A1 + (int) (phaseModulated * 94));
return isValidHolographicChar(candidate) ? candidate : (char) (0x0021 + (int) (position * 93));
} else {
double harmonicPhase = Arrays.stream(phaseField).limit(4).sum();
double extendedPos = (position + harmonicPhase / (8 * Math.PI) + Math.sin(breathingPhase) * 0.05) % 1.0;
char candidate = (char) (0x0100 + (int) (extendedPos * 383));
return isValidHolographicChar(candidate) ? candidate : (char) (0x0021 + (int) (position * 93));
}
}
private boolean isValidHolographicChar(char c) {
return Character.isDefined(c) && !Character.isISOControl(c) && !Character.isSurrogate(c) &&
Character.getType(c) != Character.PRIVATE_USE;
}
private String generateDNASequence() {
StringBuilder dna = new StringBuilder();
dna.append(switch (ternaryState) {
case NEGATIVE -> 'A';
case NEUTRAL -> 'G';
case POSITIVE -> 'T';
});
for (int i = 0; i < 4; i++) {
double breathingValue = Math.sin(breathingPhase + i * Math.PI / 2);
dna.append(breathingValue > 0.5 ? 'T' : breathingValue > 0.0 ? 'G' : breathingValue > -0.5 ? 'A' : 'C');
}
return dna.toString();
}
public String getHolographicSignature() {
StringBuilder sig = new StringBuilder();
for (int i = 0; i < Math.min(4, INTERFERENCE_HARMONICS); i++) {
sig.append(String.format("%.3f", realField[i])).append(String.format("%.3f", imagField[i]));
}
sig.append(String.format("%.3f", breathingPhase));
return sig.toString();
}
}
/**
* Onion Shell Checkpoint with layered verification.
*/
public static class OnionShellCheckpoint {
public final long operationId;
public final long timestamp;
public final BigInteger accumulatorState;
public final List<BigInteger> shellLayers;
public final String dnaSequence;
public final String breathingSignature;
public final BigInteger stateHash;
public OnionShellCheckpoint(long operationId, long timestamp, BigInteger accumulator,
TernaryParityTree parityTree, List<BreathingSeed> seeds) {
this.operationId = operationId;
this.timestamp = timestamp;
this.accumulatorState = accumulator;
this.dnaSequence = parityTree.toDNASequence();
this.breathingSignature = computeSignature(seeds);
this.shellLayers = generateOnionShells(accumulator, parityTree);
this.stateHash = calculateStateHash();
}
private String computeSignature(List<BreathingSeed> seeds) {
StringBuilder sig = new StringBuilder();
for (BreathingSeed seed : seeds) {
sig.append(String.format("%.3f", seed.getFitness()))
.append(String.format("%.3f", seed.phiWeight));
}
return sig.toString();
}
private List<BigInteger> generateOnionShells(BigInteger accumulator, TernaryParityTree parityTree) {
List<BigInteger> shells = new ArrayList<>();
String dna = parityTree.toDNASequence();
shells.add(CryptoUtil.sha256(accumulator.toString(16)));
shells.add(CryptoUtil.sha256(dna));
shells.add(CryptoUtil.sha256(String.valueOf(accumulator.doubleValue() * PHI % 10000)));
shells.add(CryptoUtil.sha256(shells.get(0).toString() + shells.get(1).toString()));
shells.add(CryptoUtil.sha256(shells.get(2).toString() + shells.get(3).toString()));
return Collections.unmodifiableList(shells);
}
private BigInteger calculateStateHash() {
StringBuilder data = new StringBuilder();
data.append(operationId).append(":").append(timestamp).append(":").append(accumulatorState);
data.append(":").append(dnaSequence).append(":").append(breathingSignature);
shellLayers.forEach(hash -> data.append(":").append(hash));
return CryptoUtil.sha256(data.toString());
}
}
/**
* POT Operation with DNA encoding.
*/
public static class POTOperation {
public final long timestamp;
public final String operationType;
public final String operandHash;
public final String resultHash;
public final String hash;
public final long operationId;
public final long validUntil;
public final String holographicSeal;
public final String dnaSequence;
public POTOperation(long timestamp, String operationType, String operandHash, String resultHash,
long operationId, long validUntil, String holographicSeal, String dnaSequence) {
this.timestamp = timestamp;
this.operationType = operationType;
this.operandHash = operandHash;
this.resultHash = resultHash;
this.operationId = operationId;
this.validUntil = validUntil;
this.holographicSeal = holographicSeal;
this.dnaSequence = dnaSequence;
this.hash = CryptoUtil.sha256(timestamp + operationType + operandHash + resultHash +
operationId + holographicSeal + dnaSequence).toString(16);
}
public boolean isTemporallyValid(long currentTime, long prevTimestamp) {
return currentTime >= (timestamp - CLOCK_SKEW_TOLERANCE_MS) &&
currentTime <= validUntil &&
(prevTimestamp == 0 || Math.abs(timestamp - prevTimestamp) <= DEFAULT_TIME_WINDOW_MS);
}
}
public void initializeBreathingSeeds() {
convergentSeeds.clear();
for (int i = 0; i < BREATHING_SEEDS; i++) {
convergentSeeds.add(new BreathingSeed(64, i));
}
}
public void performBreathingCycle(BigInteger targetAccumulator) {
if (convergentSeeds.isEmpty()) initializeBreathingSeeds();
double[] target = accumulatorToVector(targetAccumulator);
for (int iter = 0; iter < 10; iter++) {
convergentSeeds.forEach(seed -> seed.setFitness(1.0 / (Vec.distance(seed.getVector(), target) + 1e-12)));
convergentSeeds.sort((a, b) -> Double.compare(b.getFitness(), a.getFitness()));
BreathingSeed best = convergentSeeds.get(0);
convergentSeeds.stream().skip(1).forEach(seed -> {
seed.breatheToward(best, CONTRACTION_RATE);
seed.mutate(0.1 * INV_PHI);
});
}
}
private double[] accumulatorToVector(BigInteger accumulator) {
String hex = accumulator.toString(16);
double[] vector = new double[64];
for (int i = 0; i < Math.min(hex.length(), 64); i++) {
vector[i] = Character.getNumericValue(hex.charAt(i)) / 15.0;
}
return vector;
}
public HolographicGlyph generateMEGCHolographicGlyph(int index, long timestamp) {
long cacheKey = ((long) index << 32) | (timestamp & 0xFFFFFFFFL);
synchronized (glyphCache) {
return glyphCache.computeIfAbsent(cacheKey, k -> new HolographicGlyph(index, timestamp, globalParityTree.get()));
}
}
public POTOperation potMatrixAdd(BigInteger[][] a, BigInteger[][] b, long prevTimestamp, long validUntil) {
long operationTime = System.currentTimeMillis();
validateTemporal(operationTime, validUntil, prevTimestamp);
if (a.length != b.length || a[0].length != b[0].length) {
throw new IllegalArgumentException("Matrix dimension mismatch");
}
int rows = a.length, cols = a[0].length;
BigInteger[][] result = new BigInteger[rows][cols];
BigInteger operationSum = BigInteger.ZERO;
for (int i = 0; i < rows; i++) {
for (int j = 0; j < cols; j++) {
result[i][j] = a[i][j].add(b[i][j]);
if (result[i][j].bitLength() > 10_000) {
throw new RuntimeException("Matrix element overflow at [" + i + "," + j + "]");
}
operationSum = operationSum.add(result[i][j]);
}
}
long opId = operationCounter.incrementAndGet();
BigInteger newAccumulator = globalLedgerAccumulator.updateAndGet(current ->
mergeLedgerOperation(current, operationSum.longValue(), opId));
globalParityTree.get().insert(newAccumulator, opId);
performBreathingCycle(newAccumulator);
HolographicGlyph holographicSeal = generateMEGCHolographicGlyph(
newAccumulator.mod(BigInteger.valueOf(4096)).intValue(), operationTime);
String operandHash = CryptoUtil.hashMatrix(a).toString(16) + "+" + CryptoUtil.hashMatrix(b).toString(16);
String resultHash = CryptoUtil.hashMatrix(result).toString(16);
POTOperation operation = new POTOperation(operationTime, "MATRIX_ADD", operandHash, resultHash,
opId, validUntil, holographicSeal.getHolographicSignature(), holographicSeal.dnaSequence);
if (recentOperations.size() >= MAX_MEMORY_OPERATIONS) cleanupOldOperations();
recentOperations.put(operation.hash, operation);
if (opId % CHECKPOINT_INTERVAL == 0) createOnionShellCheckpoint(opId, operationTime, newAccumulator);
return operation;
}
public POTOperation potMatrixAdd(BigInteger[][] a, BigInteger[][] b, long prevTimestamp) {
return potMatrixAdd(a, b, prevTimestamp, System.currentTimeMillis() + DEFAULT_TIME_WINDOW_MS);
}
private BigInteger mergeLedgerOperation(BigInteger current, long opValue, long opIndex) {
int rotation = (int) (opIndex % 256);
BigInteger rotated = rotateLeft(current, rotation);
BigInteger combined = rotated.xor(BigInteger.valueOf(opValue)).xor(BigInteger.valueOf(opIndex));
return combined.bitLength() > 2048 ? combined.xor(combined.shiftRight(1024)) : combined;
}
private BigInteger rotateLeft(BigInteger value, int positions) {
int bitLength = Math.max(256, value.bitLength());
positions = positions % bitLength;
return value.shiftLeft(positions).or(value.shiftRight(bitLength - positions));
}
private void cleanupOldOperations() {
long currentTime = System.currentTimeMillis();
recentOperations.entrySet().removeIf(entry -> currentTime > entry.getValue().validUntil);
}
private void createOnionShellCheckpoint(long operationId, long timestamp, BigInteger accumulator) {
onionCheckpoints.add(new OnionShellCheckpoint(operationId, timestamp, accumulator, globalParityTree.get(), convergentSeeds));
if (onionCheckpoints.size() > 1_000) onionCheckpoints.subList(0, 500).clear();
}
public Map<String, Object> getMEGCStats() {
Map<String, Object> stats = new HashMap<>();
stats.put("totalOperations", operationCounter.get());
stats.put("recentOperationsCount", recentOperations.size());
stats.put("onionCheckpointsCount", onionCheckpoints.size());
stats.put("currentAccumulator", globalLedgerAccumulator.get().toString(16));
stats.put("glyphCacheSize", glyphCache.size());
stats.put("breathingSeedsCount", convergentSeeds.size());
stats.put("parityTreeNodes", globalParityTree.get().countNodes());
stats.put("globalDNASequence", globalParityTree.get().toDNASequence().substring(0, Math.min(20, globalParityTree.get().toDNASequence().length())));
if (!convergentSeeds.isEmpty()) {
stats.put("breathingAvgFitness", convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).average().orElse(0.0));
stats.put("breathingBestFitness", convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).max().orElse(0.0));
}
return stats;
}
public HolographicGlyph getCurrentMEGCHolographicSeal(long timestamp) {
return generateMEGCHolographicGlyph(globalLedgerAccumulator.get().mod(BigInteger.valueOf(4096)).intValue(), timestamp);
}
public boolean verifyOnionShellCheckpoint(OnionShellCheckpoint checkpoint) {
try {
List<BigInteger> expectedShells = checkpoint.generateOnionShells(checkpoint.accumulatorState, globalParityTree.get());
return expectedShells.equals(checkpoint.shellLayers) && checkpoint.stateHash.equals(checkpoint.calculateStateHash());
} catch (Exception e) {
return false;
}
}
public boolean resumeFromOnionShellCheckpoint(long checkpointOperationId) {
Optional<OnionShellCheckpoint> checkpoint = onionCheckpoints.stream()
.filter(c -> c.operationId == checkpointOperationId).findFirst();
if (checkpoint.isPresent() && verifyOnionShellCheckpoint(checkpoint.get())) {
globalLedgerAccumulator.set(checkpoint.get().accumulatorState);
operationCounter.set(checkpoint.get().operationId);
initializeBreathingSeeds();
performBreathingCycle(checkpoint.get().accumulatorState);
return true;
}
return false;
}
public String generateDNALedgerSummary() {
StringBuilder summary = new StringBuilder();
summary.append("TREE_DNA: ").append(globalParityTree.get().toDNASequence(), 0, Math.min(50, globalParityTree.get().toDNASequence().length())).append("...\n");
summary.append("RECENT_OPS_DNA:\n");
int count = 0;
for (POTOperation op : recentOperations.values()) {
if (count++ < 5) {
summary.append(" ").append(op.operationId).append(": ").append(op.dnaSequence).append("\n");
}
}
summary.append("BREATHING_DNA:\n");
for (int i = 0; i < Math.min(3, convergentSeeds.size()); i++) {
BreathingSeed seed = convergentSeeds.get(i);
summary.append(" Seed").append(seed.getSeedId())
.append(": phi=").append(String.format("%.3f", seed.phiWeight))
.append(" fit=").append(String.format("%.3f", seed.getFitness())).append("\n");
}
return summary.toString();
}
private void validateTemporal(long operationTime, long validUntil, long prevTimestamp) {
long currentTime = System.currentTimeMillis();
if (Math.abs(currentTime - operationTime) > CLOCK_SKEW_TOLERANCE_MS ||
currentTime > validUntil || validUntil <= operationTime ||
(prevTimestamp != 0 && Math.abs(operationTime - prevTimestamp) > DEFAULT_TIME_WINDOW_MS)) {
throw new RuntimeException("Temporal validation failed");
}
}
public static void main(String[] args) {
POTSafeMath math = new POTSafeMath();
System.out.println("POTSafeMath v9.1 - MEGC Holographic Integration");
System.out.println("============================================");
System.out.println("Features: Breathing Compression + DNA Encoding + Onion Shell Checkpoints\n");
long timestamp = 1757635200000L;
System.out.println("Holographic Field Timestamp: " + timestamp + "\n");
math.initializeBreathingSeeds();
System.out.println("Initialized " + math.convergentSeeds.size() + " breathing seeds\n");
System.out.println("MEGC Holographic Glyphs with DNA Encoding:");
System.out.println("Index -> Char (DNA Sequence + Ternary State + Breathing Phase)");
for (int i = 0; i < 12; i++) {
HolographicGlyph glyph = math.generateMEGCHolographicGlyph(i, timestamp);
System.out.printf("%4d -> %c | DNA: %s | Ternary: %s | Breathing: %.3f\n",
i, glyph.projectedChar, glyph.dnaSequence, glyph.ternaryState, glyph.breathingPhase);
}
System.out.println();
System.out.println("Ternary Parity Tree DNA Generation:");
for (int i = 0; i < 5; i++) {
math.globalParityTree.get().insert(BigInteger.valueOf(i * 100 + 42), i);
}
String treeDNA = math.globalParityTree.get().toDNASequence();
System.out.println("Tree DNA Sequence: " + treeDNA.substring(0, Math.min(50, treeDNA.length())) + "...\n");
System.out.println("Matrix Operations with MEGC Breathing Convergence:");
System.out.println("=================================================");
BigInteger[][] matA = {{BigInteger.valueOf(1), BigInteger.valueOf(2)}, {BigInteger.valueOf(3), BigInteger.valueOf(4)}};
BigInteger[][] matB = {{BigInteger.valueOf(5), BigInteger.valueOf(6)}, {BigInteger.valueOf(7), BigInteger.valueOf(8)}};
for (int i = 0; i < 8; i++) {
POTOperation op = math.potMatrixAdd(matA, matB, timestamp + i - 1);
HolographicGlyph ledgerGlyph = math.getCurrentMEGCHolographicSeal(op.timestamp);
System.out.printf("Op %d: ID=%d | Holographic=%c | DNA=%s | Breathing=%.3f\n",
i, op.operationId, ledgerGlyph.projectedChar, op.dnaSequence, ledgerGlyph.breathingPhase);
}
System.out.println();
System.out.println("Breathing Convergence Analysis:");
System.out.println("==============================");
if (!math.convergentSeeds.isEmpty()) {
double avgFitness = math.convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).average().orElse(0.0);
double bestFitness = math.convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).max().orElse(0.0);
System.out.printf("Average Seed Fitness: %.6f\n", avgFitness);
System.out.printf("Best Seed Fitness: %.6f\n", bestFitness);
System.out.println("Top 3 Breathing Seeds:");
math.convergentSeeds.sort((a, b) -> Double.compare(b.getFitness(), a.getFitness()));
for (int i = 0; i < Math.min(3, math.convergentSeeds.size()); i++) {
BreathingSeed seed = math.convergentSeeds.get(i);
System.out.printf(" Seed %d: Fitness=%.6f, PhiWeight=%.3f\n",
seed.getSeedId(), seed.getFitness(), seed.phiWeight);
}
}
System.out.println();
System.out.println("DNA-Inspired Ledger Summary:");
System.out.println("============================");
System.out.println(math.generateDNALedgerSummary());
System.out.println("Onion Shell Checkpoint Verification:");
System.out.println("====================================");
if (!math.onionCheckpoints.isEmpty()) {
OnionShellCheckpoint checkpoint = math.onionCheckpoints.get(math.onionCheckpoints.size() - 1);
boolean valid = math.verifyOnionShellCheckpoint(checkpoint);
System.out.printf("Latest checkpoint (Op %d): %s\n", checkpoint.operationId, valid ? "VERIFIED" : "INVALID");
System.out.println("Checkpoint DNA: " + checkpoint.dnaSequence.substring(0, 30) + "...");
System.out.println("Onion Shell Layers: " + checkpoint.shellLayers.size());
}
System.out.println("\nMEGC System Statistics:");
System.out.println("======================");
math.getMEGCStats().forEach((key, value) -> System.out.println(key + ": " + value));
System.out.println("\nMEGC Integration Features Demonstrated:");
System.out.println("• Ternary parity trees with golden ratio folding");
System.out.println("• DNA-inspired quaternary encoding (A,G,T,C)");
System.out.println("• Breathing convergence for ledger compression");
System.out.println("• Onion shell layered verification");
System.out.println("• Holographic interference with breathing modulation");
System.out.println("• Self-healing checkpoint reconstruction");
System.out.println("• Quantum-inspired superposition collapse");
System.out.println("• Temporal evolution through φ-modulated fields");
System.out.println("\nReady for quantum-scale transaction processing!");
}
}
HolographicGlyph
/**
* Elegant Holographic Glyph for POTSafeMath
* Minimal, modular, and fingerprint-focused.
*/
public static class HolographicGlyph {
private static final int INTERFERENCE_HARMONICS = 12;
public final double temporalPhase;
public final double spatialFreq;
public final double breathingPhase;
public final TernaryState ternaryState;
public final String dnaSequence;
public final char projectedChar;
// Internal fields for optional analysis
private final double[] realField = new double[INTERFERENCE_HARMONICS];
private final double[] imagField = new double[INTERFERENCE_HARMONICS];
private final double[] phaseField = new double[INTERFERENCE_HARMONICS];
public HolographicGlyph(int index, long timestamp, TernaryParityTree parityTree) {
this.breathingPhase = computeBreathingPhase(timestamp, index);
this.temporalPhase = computeTemporalPhase(timestamp, index, breathingPhase);
this.spatialFreq = computeSpatialFrequency(index, breathingPhase);
this.ternaryState = classifyTernary(index, timestamp);
computeHolographicField();
this.projectedChar = mapToUnicode();
this.dnaSequence = generateDNASequence();
}
// --- Core calculations ---
private double computeBreathingPhase(long ts, int idx) {
return (ts * 2.399963229728653e-10 * 1.618 + idx / 4096.0 * Math.PI / 1.618) % (2 * Math.PI);
}
private double computeTemporalPhase(long ts, int idx, double breathing) {
return (ts * 2.399963229728653e-10 * 1.618 + idx / 4096.0 * Math.PI / 1.618 + breathing) % (2 * Math.PI);
}
private double computeSpatialFrequency(int idx, double breathing) {
return 1.618 * idx / 4096.0 * Math.E * Math.E * Math.cos(breathing);
}
private TernaryState classifyTernary(int index, long timestamp) {
double val = (index * 1.618 + timestamp / 1_000_000_000.0) % 3.0;
return val < 1.0 ? TernaryState.NEGATIVE : val < 2.0 ? TernaryState.NEUTRAL : TernaryState.POSITIVE;
}
private void computeHolographicField() {
for (int h = 0; h < INTERFERENCE_HARMONICS; h++) {
double harmonic = h + 1;
double amplitude = 1.0 / (harmonic * harmonic);
double mod = Math.sin(breathingPhase * harmonic) / 1.618;
amplitude *= (1.0 + mod);
double phase1 = temporalPhase * harmonic;
double phase2 = temporalPhase * harmonic * 1.618;
double phase3 = spatialFreq * harmonic + breathingPhase;
realField[h] = amplitude * (Math.cos(phase1) * Math.cos(phase2) - Math.sin(phase1) * Math.sin(phase3));
imagField[h] = amplitude * (Math.sin(phase1) * Math.cos(phase2) + Math.cos(phase1) * Math.sin(phase3));
phaseField[h] = Math.atan2(imagField[h], realField[h]);
}
}
// --- Fingerprint / Unicode projection ---
private char mapToUnicode() {
double mag = Math.sqrt(Arrays.stream(realField).sum() * Arrays.stream(realField).sum() +
Arrays.stream(imagField).sum() * Arrays.stream(imagField).sum());
double phaseSum = Arrays.stream(phaseField).sum();
double norm = ((phaseSum / (2 * Math.PI)) + Math.sin(breathingPhase) * 0.1 + mag * 0.3) % 1.0;
return (char) (0x0021 + (int) (norm * 93));
}
// --- DNA sequence generation ---
private String generateDNASequence() {
StringBuilder dna = new StringBuilder();
dna.append(switch (ternaryState) {
case NEGATIVE -> 'A';
case NEUTRAL -> 'G';
case POSITIVE -> 'T';
});
for (int i = 0; i < 4; i++) {
double val = Math.sin(breathingPhase + i * Math.PI / 2);
dna.append(val > 0.5 ? 'T' : val > 0.0 ? 'G' : val > -0.5 ? 'A' : 'C');
}
return dna.toString();
}
// --- Compact signature for ledger or caching ---
public String getHolographicSignature() {
return String.format("%.3f", breathingPhase) + projectedChar + dnaSequence;
}
}
POTSafeMath v9.2
import java.math.BigInteger;
import java.nio.charset.StandardCharsets;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.util.*;
import java.util.concurrent.ConcurrentHashMap;
import java.util.concurrent.atomic.AtomicLong;
import java.util.concurrent.atomic.AtomicReference;
import java.util.stream.IntStream;
/**
* POTSafeMath v9.2 - Enhanced Elegant Holographic MEGC Integration
* Combines recursive ternary parity trees, breathing seeds, holographic glyphs, and onion-shell checkpoints
* with modular, readable, and concise design.
*/
public class POTSafeMath {
// Constants
private static final long DEFAULT_TIME_WINDOW_MS = 300_000;
private static final long CLOCK_SKEW_TOLERANCE_MS = 30_000;
private static final int MAX_MEMORY_OPERATIONS = 100_000;
private static final int CHECKPOINT_INTERVAL = 10_000;
private static final int GLYPH_CACHE_SIZE = 1_000;
private static final double PHI = (1.0 + Math.sqrt(5.0)) / 2.0;
private static final double INV_PHI = 1.0 / PHI;
private static final double PI_PHI = Math.PI / PHI;
private static final double HOLOGRAPHIC_DEPTH = Math.E * Math.E;
private static final int INTERFERENCE_HARMONICS = 12;
private static final int BREATHING_SEEDS = 8;
private static final double CONTRACTION_RATE = 0.618;
// Core state
private final AtomicLong operationCounter = new AtomicLong(0);
private final ConcurrentHashMap<String, POTOperation> recentOperations = new ConcurrentHashMap<>();
private final AtomicReference<BigInteger> globalLedgerAccumulator = new AtomicReference<>(BigInteger.ZERO);
private final List<BreathingSeed> convergentSeeds = Collections.synchronizedList(new ArrayList<>());
private final AtomicReference<TernaryParityTree> globalParityTree = new AtomicReference<>(
new TernaryParityTree(TernaryState.NEUTRAL, 0, null, null, null));
private final Map<Long, HolographicGlyph> glyphCache = new LinkedHashMap<Long, HolographicGlyph>(GLYPH_CACHE_SIZE, 0.75f, true) {
@Override
protected boolean removeEldestEntry(Map.Entry<Long, HolographicGlyph> eldest) {
return size() > GLYPH_CACHE_SIZE;
}
};
private final List<OnionShellCheckpoint> onionCheckpoints = Collections.synchronizedList(new ArrayList<>());
/**
* Utility for cryptographic hash operations.
*/
private static class CryptoUtil {
public static BigInteger sha256(String input) {
try {
MessageDigest md = MessageDigest.getInstance("SHA-256");
return new BigInteger(1, md.digest(input.getBytes(StandardCharsets.UTF_8)));
} catch (NoSuchAlgorithmException e) {
throw new RuntimeException("Hash calculation failed", e);
}
}
public static BigInteger hashMatrix(BigInteger[][] matrix) {
StringBuilder sb = new StringBuilder();
for (BigInteger[] row : matrix) {
for (BigInteger val : row) {
sb.append(val.toString(16));
}
}
return sha256(sb.toString());
}
}
/**
* Vector utility for breathing seed operations.
*/
private static class Vec {
public static double distance(double[] a, double[] b) {
return Math.sqrt(IntStream.range(0, Math.min(a.length, b.length))
.mapToDouble(i -> Math.pow(a[i] - b[i], 2))
.sum());
}
public static double[] mutate(double[] v, Random r, double rate) {
double[] copy = v.clone();
for (int i = 0; i < copy.length; i++) {
copy[i] = clamp(copy[i] + r.nextGaussian() * rate * INV_PHI, 0.0, 1.0);
}
return copy;
}
public static double[] breatheToward(double[] v, double[] target, double factor) {
double[] out = new double[v.length];
for (int i = 0; i < v.length; i++) {
out[i] = v[i] + factor * (target[i] - v[i]);
}
return out;
}
private static double clamp(double v, double min, double max) {
return Math.max(min, Math.min(max, v));
}
}
/**
* Ternary state enumeration.
*/
public enum TernaryState {
NEGATIVE(0), NEUTRAL(1), POSITIVE(2);
private final int value;
TernaryState(int value) { this.value = value; }
public int getValue() { return value; }
}
/**
* Recursive ternary parity tree with DNA encoding.
*/
public static class TernaryParityTree {
private static final char[] DNA_MAP = {'A', 'G', 'T'};
private final TernaryState state;
private final int depth;
private TernaryParityTree left, mid, right;
private double phiWeight;
public TernaryParityTree(TernaryState state, int depth, TernaryParityTree left, TernaryParityTree mid, TernaryParityTree right) {
this.state = state;
this.depth = depth;
this.left = left;
this.mid = mid;
this.right = right;
updatePhiWeight();
}
public void insert(BigInteger value, long operationId) {
insertRecursive(this, value, operationId, 0);
updatePhiWeight();
}
private void insertRecursive(TernaryParityTree node, BigInteger value, long operationId, int currentDepth) {
if (currentDepth > 10) return;
TernaryState newState = computeTernaryState(value, operationId);
if (newState == TernaryState.NEGATIVE) {
if (node.left == null) node.left = new TernaryParityTree(newState, currentDepth + 1, null, null, null);
else insertRecursive(node.left, value, operationId, currentDepth + 1);
} else if (newState == TernaryState.NEUTRAL) {
if (node.mid == null) node.mid = new TernaryParityTree(newState, currentDepth + 1, null, null, null);
else insertRecursive(node.mid, value, operationId, currentDepth + 1);
} else {
if (node.right == null) node.right = new TernaryParityTree(newState, currentDepth + 1, null, null, null);
else insertRecursive(node.right, value, operationId, currentDepth + 1);
}
}
private TernaryState computeTernaryState(BigInteger value, long operationId) {
double phiMod = (value.doubleValue() * PHI + operationId * INV_PHI) % 3.0;
return phiMod < 1.0 ? TernaryState.NEGATIVE : phiMod < 2.0 ? TernaryState.NEUTRAL : TernaryState.POSITIVE;
}
private void updatePhiWeight() {
phiWeight = (phiWeight * CONTRACTION_RATE + countNodes() * INV_PHI) / 2.0;
if (left != null) left.updatePhiWeight();
if (mid != null) mid.updatePhiWeight();
if (right != null) right.updatePhiWeight();
}
private int countNodes() {
int count = 1;
if (left != null) count += left.countNodes();
if (mid != null) count += mid.countNodes();
if (right != null) count += right.countNodes();
return count;
}
public String toDNASequence() {
StringBuilder dna = new StringBuilder();
toDNARecursive(dna);
return dna.toString();
}
private void toDNARecursive(StringBuilder dna) {
dna.append(DNA_MAP[state.getValue()]);
if (left != null) left.toDNARecursive(dna);
if (mid != null) mid.toDNARecursive(dna);
if (right != null) right.toDNARecursive(dna);
dna.append('C');
}
}
/**
* Breathing seed for convergent compression.
*/
public static class BreathingSeed {
private double[] vector;
private final long seedId;
private double fitness;
private double phiWeight;
private final Random rng = new Random();
public BreathingSeed(int dimensions, long seedId) {
this.seedId = seedId;
this.vector = new double[dimensions];
this.fitness = 0.0;
this.phiWeight = 1.0;
rng.setSeed(seedId);
initializeWithPhi();
}
private void initializeWithPhi() {
for (int i = 0; i < vector.length; i++) {
vector[i] = rng.nextDouble() * PHI % 1.0;
}
}
public void mutate(double rate) {
vector = Vec.mutate(vector, rng, rate);
}
public void breatheToward(BreathingSeed target, double contractionRate) {
vector = Vec.breatheToward(vector, target.vector, contractionRate * phiWeight);
updatePhiWeight();
}
private void updatePhiWeight() {
phiWeight = (Arrays.stream(vector).sum() * PHI) % 1.0;
}
public double distanceFrom(BreathingSeed other) {
return Vec.distance(vector, other.vector);
}
public double[] getVector() {
return vector.clone();
}
public long getSeedId() {
return seedId;
}
public double getFitness() {
return fitness;
}
public void setFitness(double fitness) {
this.fitness = fitness;
}
}
/**
* Holographic glyph with streamlined MEGC breathing integration.
*/
public static class HolographicGlyph {
public final double temporalPhase;
public final double spatialFreq;
public final double breathingPhase;
public final TernaryState ternaryState;
public final String dnaSequence;
public final char projectedChar;
public final long timestamp;
private final double[] realField = new double[INTERFERENCE_HARMONICS];
private final double[] imagField = new double[INTERFERENCE_HARMONICS];
private final double[] phaseField = new double[INTERFERENCE_HARMONICS];
public HolographicGlyph(int index, long timestamp, TernaryParityTree parityTree) {
this.timestamp = timestamp;
this.breathingPhase = computeBreathingPhase(timestamp, index);
this.temporalPhase = computeTemporalPhase(timestamp, index);
this.spatialFreq = computeSpatialFrequency(index);
this.ternaryState = classifyTernary(index, timestamp);
computeHolographicField();
this.projectedChar = mapToUnicode();
this.dnaSequence = generateDNASequence();
}
private double computeBreathingPhase(long ts, int idx) {
return (ts * 2.399963229728653e-10 * PHI + idx / 4096.0 * PI_PHI) % (2 * Math.PI);
}
private double computeTemporalPhase(long ts, int idx) {
double timeNorm = ts * 2.399963229728653e-10;
double idxNorm = idx / 4096.0;
return (timeNorm * PHI + idxNorm * PI_PHI + breathingPhase) % (2 * Math.PI);
}
private double computeSpatialFrequency(int idx) {
return PHI * idx / 4096.0 * HOLOGRAPHIC_DEPTH * Math.cos(breathingPhase);
}
private TernaryState classifyTernary(int index, long timestamp) {
double val = (index * PHI + timestamp * INV_PHI) % 3.0;
return val < 1.0 ? TernaryState.NEGATIVE : val < 2.0 ? TernaryState.NEUTRAL : TernaryState.POSITIVE;
}
private void computeHolographicField() {
for (int h = 0; h < INTERFERENCE_HARMONICS; h++) {
double harmonic = h + 1;
double amplitude = 1.0 / (harmonic * harmonic);
double modulation = Math.sin(breathingPhase * harmonic) * INV_PHI;
amplitude *= (1.0 + modulation);
double phase1 = temporalPhase * harmonic;
double phase2 = temporalPhase * harmonic * PHI;
double phase3 = spatialFreq * harmonic + breathingPhase;
realField[h] = amplitude * (Math.cos(phase1) * Math.cos(phase2) - Math.sin(phase1) * Math.sin(phase3));
imagField[h] = amplitude * (Math.sin(phase1) * Math.cos(phase2) + Math.cos(phase1) * Math.sin(phase3));
phaseField[h] = Math.atan2(imagField[h], realField[h]);
}
}
private char mapToUnicode() {
double realSum = Arrays.stream(realField).sum();
double imagSum = Arrays.stream(imagField).sum();
double phaseSum = Arrays.stream(phaseField).sum();
double magnitude = Math.sqrt(realSum * realSum + imagSum * imagSum);
double norm = (magnitude * 0.3 + phaseSum / (2 * Math.PI) + Math.sin(breathingPhase) * 0.1) % 1.0;
double regionSelector = (magnitude + Math.cos(breathingPhase) * 0.1) % 1.0;
if (regionSelector < 0.3) {
return (char) (0x0021 + (int) (norm * 93));
} else if (regionSelector < 0.6) {
double phaseModulated = (norm + Math.abs(Math.atan2(imagSum, realSum)) / (2 * Math.PI)) % 1.0;
char candidate = (char) (0x00A1 + (int) (phaseModulated * 94));
return isValidHolographicChar(candidate) ? candidate : (char) (0x0021 + (int) (norm * 93));
} else {
double harmonicPhase = Arrays.stream(phaseField).limit(4).sum();
double extendedPos = (norm + harmonicPhase / (8 * Math.PI) + Math.sin(breathingPhase) * 0.05) % 1.0;
char candidate = (char) (0x0100 + (int) (extendedPos * 383));
return isValidHolographicChar(candidate) ? candidate : (char) (0x0021 + (int) (norm * 93));
}
}
private boolean isValidHolographicChar(char c) {
return Character.isDefined(c) && !Character.isISOControl(c) && !Character.isSurrogate(c) &&
Character.getType(c) != Character.PRIVATE_USE;
}
private String generateDNASequence() {
StringBuilder dna = new StringBuilder();
dna.append(switch (ternaryState) {
case NEGATIVE -> 'A';
case NEUTRAL -> 'G';
case POSITIVE -> 'T';
});
for (int i = 0; i < 4; i++) {
double val = Math.sin(breathingPhase + i * Math.PI / 2);
dna.append(val > 0.5 ? 'T' : val > 0.0 ? 'G' : val > -0.5 ? 'A' : 'C');
}
return dna.toString();
}
public String getHolographicSignature() {
StringBuilder sig = new StringBuilder();
for (int i = 0; i < Math.min(4, INTERFERENCE_HARMONICS); i++) {
sig.append(String.format("%.3f", realField[i])).append(String.format("%.3f", imagField[i]));
}
sig.append(String.format("%.3f", breathingPhase)).append(projectedChar).append(dnaSequence);
return sig.toString();
}
}
/**
* Onion Shell Checkpoint with layered verification.
*/
public static class OnionShellCheckpoint {
public final long operationId;
public final long timestamp;
public final BigInteger accumulatorState;
public final List<BigInteger> shellLayers;
public final String dnaSequence;
public final String breathingSignature;
public final BigInteger stateHash;
public OnionShellCheckpoint(long operationId, long timestamp, BigInteger accumulator,
TernaryParityTree parityTree, List<BreathingSeed> seeds) {
this.operationId = operationId;
this.timestamp = timestamp;
this.accumulatorState = accumulator;
this.dnaSequence = parityTree.toDNASequence();
this.breathingSignature = computeSignature(seeds);
this.shellLayers = generateOnionShells(accumulator, parityTree);
this.stateHash = calculateStateHash();
}
private String computeSignature(List<BreathingSeed> seeds) {
StringBuilder sig = new StringBuilder();
for (BreathingSeed seed : seeds) {
sig.append(String.format("%.3f", seed.getFitness()))
.append(String.format("%.3f", seed.phiWeight));
}
return sig.toString();
}
private List<BigInteger> generateOnionShells(BigInteger accumulator, TernaryParityTree parityTree) {
List<BigInteger> shells = new ArrayList<>();
String dna = parityTree.toDNASequence();
shells.add(CryptoUtil.sha256(accumulator.toString(16)));
shells.add(CryptoUtil.sha256(dna));
shells.add(CryptoUtil.sha256(String.valueOf(accumulator.doubleValue() * PHI % 10000)));
shells.add(CryptoUtil.sha256(shells.get(0).toString() + shells.get(1).toString()));
shells.add(CryptoUtil.sha256(shells.get(2).toString() + shells.get(3).toString()));
return Collections.unmodifiableList(shells);
}
private BigInteger calculateStateHash() {
StringBuilder data = new StringBuilder();
data.append(operationId).append(":").append(timestamp).append(":").append(accumulatorState);
data.append(":").append(dnaSequence).append(":").append(breathingSignature);
shellLayers.forEach(hash -> data.append(":").append(hash));
return CryptoUtil.sha256(data.toString());
}
}
/**
* POT Operation with DNA encoding.
*/
public static class POTOperation {
public final long timestamp;
public final String operationType;
public final String operandHash;
public final String resultHash;
public final String hash;
public final long operationId;
public final long validUntil;
public final String holographicSeal;
public final String dnaSequence;
public POTOperation(long timestamp, String operationType, String operandHash, String resultHash,
long operationId, long validUntil, String holographicSeal, String dnaSequence) {
this.timestamp = timestamp;
this.operationType = operationType;
this.operandHash = operandHash;
this.resultHash = resultHash;
this.operationId = operationId;
this.validUntil = validUntil;
this.holographicSeal = holographicSeal;
this.dnaSequence = dnaSequence;
this.hash = CryptoUtil.sha256(timestamp + operationType + operandHash + resultHash +
operationId + holographicSeal + dnaSequence).toString(16);
}
public boolean isTemporallyValid(long currentTime, long prevTimestamp) {
return currentTime >= (timestamp - CLOCK_SKEW_TOLERANCE_MS) &&
currentTime <= validUntil &&
(prevTimestamp == 0 || Math.abs(timestamp - prevTimestamp) <= DEFAULT_TIME_WINDOW_MS);
}
}
public void initializeBreathingSeeds() {
convergentSeeds.clear();
for (int i = 0; i < BREATHING_SEEDS; i++) {
convergentSeeds.add(new BreathingSeed(64, i));
}
}
public void performBreathingCycle(BigInteger targetAccumulator) {
if (convergentSeeds.isEmpty()) initializeBreathingSeeds();
double[] target = accumulatorToVector(targetAccumulator);
for (int iter = 0; iter < 10; iter++) {
convergentSeeds.forEach(seed -> seed.setFitness(1.0 / (Vec.distance(seed.getVector(), target) + 1e-12)));
convergentSeeds.sort((a, b) -> Double.compare(b.getFitness(), a.getFitness()));
BreathingSeed best = convergentSeeds.get(0);
convergentSeeds.stream().skip(1).forEach(seed -> {
seed.breatheToward(best, CONTRACTION_RATE);
seed.mutate(0.1 * INV_PHI);
});
}
}
private double[] accumulatorToVector(BigInteger accumulator) {
String hex = accumulator.toString(16);
double[] vector = new double[64];
for (int i = 0; i < Math.min(hex.length(), 64); i++) {
vector[i] = Character.getNumericValue(hex.charAt(i)) / 15.0;
}
return vector;
}
public HolographicGlyph generateMEGCHolographicGlyph(int index, long timestamp) {
long cacheKey = ((long) index << 32) | (timestamp & 0xFFFFFFFFL);
synchronized (glyphCache) {
return glyphCache.computeIfAbsent(cacheKey, k -> new HolographicGlyph(index, timestamp, globalParityTree.get()));
}
}
public POTOperation potMatrixAdd(BigInteger[][] a, BigInteger[][] b, long prevTimestamp, long validUntil) {
long operationTime = System.currentTimeMillis();
validateTemporal(operationTime, validUntil, prevTimestamp);
if (a.length != b.length || a[0].length != b[0].length) {
throw new IllegalArgumentException("Matrix dimension mismatch");
}
int rows = a.length, cols = a[0].length;
BigInteger[][] result = new BigInteger[rows][cols];
BigInteger operationSum = BigInteger.ZERO;
for (int i = 0; i < rows; i++) {
for (int j = 0; j < cols; j++) {
result[i][j] = a[i][j].add(b[i][j]);
if (result[i][j].bitLength() > 10_000) {
throw new RuntimeException("Matrix element overflow at [" + i + "," + j + "]");
}
operationSum = operationSum.add(result[i][j]);
}
}
long opId = operationCounter.incrementAndGet();
BigInteger newAccumulator = globalLedgerAccumulator.updateAndGet(current ->
mergeLedgerOperation(current, operationSum.longValue(), opId));
globalParityTree.get().insert(newAccumulator, opId);
performBreathingCycle(newAccumulator);
HolographicGlyph holographicSeal = generateMEGCHolographicGlyph(
newAccumulator.mod(BigInteger.valueOf(4096)).intValue(), operationTime);
String operandHash = CryptoUtil.hashMatrix(a).toString(16) + "+" + CryptoUtil.hashMatrix(b).toString(16);
String resultHash = CryptoUtil.hashMatrix(result).toString(16);
POTOperation operation = new POTOperation(operationTime, "MATRIX_ADD", operandHash, resultHash,
opId, validUntil, holographicSeal.getHolographicSignature(), holographicSeal.dnaSequence);
if (recentOperations.size() >= MAX_MEMORY_OPERATIONS) cleanupOldOperations();
recentOperations.put(operation.hash, operation);
if (opId % CHECKPOINT_INTERVAL == 0) createOnionShellCheckpoint(opId, operationTime, newAccumulator);
return operation;
}
public POTOperation potMatrixAdd(BigInteger[][] a, BigInteger[][] b, long prevTimestamp) {
return potMatrixAdd(a, b, prevTimestamp, System.currentTimeMillis() + DEFAULT_TIME_WINDOW_MS);
}
private BigInteger mergeLedgerOperation(BigInteger current, long opValue, long opIndex) {
int rotation = (int) (opIndex % 256);
BigInteger rotated = rotateLeft(current, rotation);
BigInteger combined = rotated.xor(BigInteger.valueOf(opValue)).xor(BigInteger.valueOf(opIndex));
return combined.bitLength() > 2048 ? combined.xor(combined.shiftRight(1024)) : combined;
}
private BigInteger rotateLeft(BigInteger value, int positions) {
int bitLength = Math.max(256, value.bitLength());
positions = positions % bitLength;
return value.shiftLeft(positions).or(value.shiftRight(bitLength - positions));
}
private void cleanupOldOperations() {
long currentTime = System.currentTimeMillis();
recentOperations.entrySet().removeIf(entry -> currentTime > entry.getValue().validUntil);
}
private void createOnionShellCheckpoint(long operationId, long timestamp, BigInteger accumulator) {
onionCheckpoints.add(new OnionShellCheckpoint(operationId, timestamp, accumulator, globalParityTree.get(), convergentSeeds));
if (onionCheckpoints.size() > 1_000) onionCheckpoints.subList(0, 500).clear();
}
public Map<String, Object> getMEGCStats() {
Map<String, Object> stats = new HashMap<>();
stats.put("totalOperations", operationCounter.get());
stats.put("recentOperationsCount", recentOperations.size());
stats.put("onionCheckpointsCount", onionCheckpoints.size());
stats.put("currentAccumulator", globalLedgerAccumulator.get().toString(16));
stats.put("glyphCacheSize", glyphCache.size());
stats.put("breathingSeedsCount", convergentSeeds.size());
stats.put("parityTreeNodes", globalParityTree.get().countNodes());
stats.put("globalDNASequence", globalParityTree.get().toDNASequence().substring(0, Math.min(20, globalParityTree.get().toDNASequence().length())));
if (!convergentSeeds.isEmpty()) {
stats.put("breathingAvgFitness", convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).average().orElse(0.0));
stats.put("breathingBestFitness", convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).max().orElse(0.0));
}
return stats;
}
public HolographicGlyph getCurrentMEGCHolographicSeal(long timestamp) {
return generateMEGCHolographicGlyph(globalLedgerAccumulator.get().mod(BigInteger.valueOf(4096)).intValue(), timestamp);
}
public boolean verifyOnionShellCheckpoint(OnionShellCheckpoint checkpoint) {
try {
List<BigInteger> expectedShells = checkpoint.generateOnionShells(checkpoint.accumulatorState, globalParityTree.get());
return expectedShells.equals(checkpoint.shellLayers) && checkpoint.stateHash.equals(checkpoint.calculateStateHash());
} catch (Exception e) {
return false;
}
}
public boolean resumeFromOnionShellCheckpoint(long checkpointOperationId) {
Optional<OnionShellCheckpoint> checkpoint = onionCheckpoints.stream()
.filter(c -> c.operationId == checkpointOperationId).findFirst();
if (checkpoint.isPresent() && verifyOnionShellCheckpoint(checkpoint.get())) {
globalLedgerAccumulator.set(checkpoint.get().accumulatorState);
operationCounter.set(checkpoint.get().operationId);
initializeBreathingSeeds();
performBreathingCycle(checkpoint.get().accumulatorState);
return true;
}
return false;
}
public String generateDNALedgerSummary() {
StringBuilder summary = new StringBuilder();
summary.append("TREE_DNA: ").append(globalParityTree.get().toDNASequence(), 0, Math.min(50, globalParityTree.get().toDNASequence().length())).append("...\n");
summary.append("RECENT_OPS_DNA:\n");
int count = 0;
for (POTOperation op : recentOperations.values()) {
if (count++ < 5) {
summary.append(" ").append(op.operationId).append(": ").append(op.dnaSequence).append("\n");
}
}
summary.append("BREATHING_DNA:\n");
for (int i = 0; i < Math.min(3, convergentSeeds.size()); i++) {
BreathingSeed seed = convergentSeeds.get(i);
summary.append(" Seed").append(seed.getSeedId())
.append(": phi=").append(String.format("%.3f", seed.phiWeight))
.append(" fit=").append(String.format("%.3f", seed.getFitness())).append("\n");
}
return summary.toString();
}
private void validateTemporal(long operationTime, long validUntil, long prevTimestamp) {
long currentTime = System.currentTimeMillis();
if (Math.abs(currentTime - operationTime) > CLOCK_SKEW_TOLERANCE_MS ||
currentTime > validUntil || validUntil <= operationTime ||
(prevTimestamp != 0 && Math.abs(operationTime - prevTimestamp) > DEFAULT_TIME_WINDOW_MS)) {
throw new RuntimeException("Temporal validation failed");
}
}
public static void main(String[] args) {
POTSafeMath math = new POTSafeMath();
System.out.println("POTSafeMath v9.2 - MEGC Holographic Integration");
System.out.println("============================================");
System.out.println("Features: Breathing Compression + DNA Encoding + Onion Shell Checkpoints\n");
long timestamp = 1757635200000L;
System.out.println("Holographic Field Timestamp: " + timestamp + "\n");
math.initializeBreathingSeeds();
System.out.println("Initialized " + math.convergentSeeds.size() + " breathing seeds\n");
System.out.println("MEGC Holographic Glyphs with DNA Encoding:");
System.out.println("Index -> Char (DNA Sequence + Ternary State + Breathing Phase)");
for (int i = 0; i < 12; i++) {
HolographicGlyph glyph = math.generateMEGCHolographicGlyph(i, timestamp);
System.out.printf("%4d -> %c | DNA: %s | Ternary: %s | Breathing: %.3f\n",
i, glyph.projectedChar, glyph.dnaSequence, glyph.ternaryState, glyph.breathingPhase);
}
System.out.println();
System.out.println("Ternary Parity Tree DNA Generation:");
for (int i = 0; i < 5; i++) {
math.globalParityTree.get().insert(BigInteger.valueOf(i * 100 + 42), i);
}
String treeDNA = math.globalParityTree.get().toDNASequence();
System.out.println("Tree DNA Sequence: " + treeDNA.substring(0, Math.min(50, treeDNA.length())) + "...\n");
System.out.println("Matrix Operations with MEGC Breathing Convergence:");
System.out.println("=================================================");
BigInteger[][] matA = {{BigInteger.valueOf(1), BigInteger.valueOf(2)}, {BigInteger.valueOf(3), BigInteger.valueOf(4)}};
BigInteger[][] matB = {{BigInteger.valueOf(5), BigInteger.valueOf(6)}, {BigInteger.valueOf(7), BigInteger.valueOf(8)}};
for (int i = 0; i < 8; i++) {
POTOperation op = math.potMatrixAdd(matA, matB, timestamp + i - 1);
HolographicGlyph ledgerGlyph = math.getCurrentMEGCHolographicSeal(op.timestamp);
System.out.printf("Op %d: ID=%d | Holographic=%c | DNA=%s | Breathing=%.3f\n",
i, op.operationId, ledgerGlyph.projectedChar, op.dnaSequence, ledgerGlyph.breathingPhase);
}
System.out.println();
System.out.println("Breathing Convergence Analysis:");
System.out.println("==============================");
if (!math.convergentSeeds.isEmpty()) {
double avgFitness = math.convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).average().orElse(0.0);
double bestFitness = math.convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).max().orElse(0.0);
System.out.printf("Average Seed Fitness: %.6f\n", avgFitness);
System.out.printf("Best Seed Fitness: %.6f\n", bestFitness);
System.out.println("Top 3 Breathing Seeds:");
math.convergentSeeds.sort((a, b) -> Double.compare(b.getFitness(), a.getFitness()));
for (int i = 0; i < Math.min(3, math.convergentSeeds.size()); i++) {
BreathingSeed seed = math.convergentSeeds.get(i);
System.out.printf(" Seed %d: Fitness=%.6f, PhiWeight=%.3f\n",
seed.getSeedId(), seed.getFitness(), seed.phiWeight);
}
}
System.out.println();
System.out.println("DNA-Inspired Ledger Summary:");
System.out.println("============================");
System.out.println(math.generateDNALedgerSummary());
System.out.println("Onion Shell Checkpoint Verification:");
System.out.println("====================================");
if (!math.onionCheckpoints.isEmpty()) {
OnionShellCheckpoint checkpoint = math.onionCheckpoints.get(math.onionCheckpoints.size() - 1);
boolean valid = math.verifyOnionShellCheckpoint(checkpoint);
System.out.printf("Latest checkpoint (Op %d): %s\n", checkpoint.operationId, valid ? "VERIFIED" : "INVALID");
System.out.println("Checkpoint DNA: " + checkpoint.dnaSequence.substring(0, 30) + "...");
System.out.println("Onion Shell Layers: " + checkpoint.shellLayers.size());
}
System.out.println("\nMEGC System Statistics:");
System.out.println("======================");
math.getMEGCStats().forEach((key, value) -> System.out.println(key + ": " + value));
System.out.println("\nMEGC Integration Features Demonstrated:");
System.out.println("• Ternary parity trees with golden ratio folding");
System.out.println("• DNA-inspired quaternary encoding (A,G,T,C)");
System.out.println("• Breathing convergence for ledger compression");
System.out.println("• Onion shell layered verification");
System.out.println("• Streamlined holographic interference with breathing modulation");
System.out.println("• Self-healing checkpoint reconstruction");
System.out.println("• Quantum-inspired superposition collapse");
System.out.println("• Temporal evolution through φ-modulated fields");
System.out.println("\nReady for quantum-scale transaction processing!");
}
}
POTSafeMath v10
import java.math.BigInteger;
import java.nio.charset.StandardCharsets;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.util.*;
import java.util.concurrent.ConcurrentHashMap;
import java.util.concurrent.atomic.AtomicLong;
import java.util.concurrent.atomic.AtomicReference;
/**
* POTSafeMath v10 - Elegant MEGC Core
* Features:
* - Golden ratio-driven ternary parity trees
* - Breathing seed convergence
* - Holographic glyphs with DNA signatures
* - Onion shell layered checkpoints (3 layers)
*/
public class POTSafeMath {
// ---------------- Constants ----------------
private static final double PHI = (1 + Math.sqrt(5)) / 2.0;
private static final double INV_PHI = 1.0 / PHI;
private static final double CONTRACTION_RATE = 0.618;
private static final int BREATHING_SEEDS = 8;
private static final int INTERFERENCE_HARMONICS = 4; // simplified for elegance
private static final int GLYPH_CACHE_SIZE = 512;
// ---------------- Core State ----------------
private final AtomicLong operationCounter = new AtomicLong(0);
private final AtomicReference<BigInteger> globalLedgerAccumulator = new AtomicReference<>(BigInteger.ZERO);
private final AtomicReference<TernaryParityTree> globalParityTree = new AtomicReference<>(
new TernaryParityTree(TernaryState.NEUTRAL, 0));
private final List<BreathingSeed> convergentSeeds = Collections.synchronizedList(new ArrayList<>());
private final Map<Long, HolographicGlyph> glyphCache = new LinkedHashMap<Long, HolographicGlyph>(GLYPH_CACHE_SIZE, 0.75f, true) {
@Override
protected boolean removeEldestEntry(Map.Entry<Long, HolographicGlyph> eldest) {
return size() > GLYPH_CACHE_SIZE;
}
};
private final List<OnionShellCheckpoint> onionCheckpoints = Collections.synchronizedList(new ArrayList<>());
// ---------------- Utilities ----------------
private static class CryptoUtil {
public static BigInteger sha256(String input) {
try {
MessageDigest md = MessageDigest.getInstance("SHA-256");
return new BigInteger(1, md.digest(input.getBytes(StandardCharsets.UTF_8)));
} catch (NoSuchAlgorithmException e) {
throw new RuntimeException(e);
}
}
}
private static class Vec {
public static double distance(double[] a, double[] b) {
double sum = 0;
for (int i = 0; i < Math.min(a.length, b.length); i++) {
sum += Math.pow(a[i] - b[i], 2);
}
return Math.sqrt(sum);
}
public static double[] mutate(double[] v, Random r, double rate) {
double[] copy = v.clone();
for (int i = 0; i < copy.length; i++) {
copy[i] = clamp(copy[i] + r.nextGaussian() * rate * INV_PHI, 0.0, 1.0);
}
return copy;
}
public static double[] breatheToward(double[] v, double[] target, double factor) {
double[] out = new double[v.length];
for (int i = 0; i < v.length; i++) {
out[i] = v[i] + factor * (target[i] - v[i]);
}
return out;
}
private static double clamp(double val, double min, double max) {
return Math.max(min, Math.min(max, val));
}
}
// ---------------- Ternary Parity Tree ----------------
public enum TernaryState { NEGATIVE, NEUTRAL, POSITIVE }
public static class TernaryParityTree {
private static final char[] DNA_MAP = {'A', 'G', 'T'};
private final TernaryState state;
private final int depth;
private TernaryParityTree left, mid, right;
public TernaryParityTree(TernaryState state, int depth) {
this.state = state;
this.depth = depth;
}
public void insert(BigInteger value, long opId) {
insertRecursive(this, value, opId, 0);
}
private void insertRecursive(TernaryParityTree node, BigInteger value, long opId, int curDepth) {
if (curDepth > 10) return;
TernaryState newState = computeTernaryState(value, opId);
if (newState == TernaryState.NEGATIVE) {
if (node.left == null) node.left = new TernaryParityTree(newState, curDepth + 1);
else insertRecursive(node.left, value, opId, curDepth + 1);
} else if (newState == TernaryState.NEUTRAL) {
if (node.mid == null) node.mid = new TernaryParityTree(newState, curDepth + 1);
else insertRecursive(node.mid, value, opId, curDepth + 1);
} else {
if (node.right == null) node.right = new TernaryParityTree(newState, curDepth + 1);
else insertRecursive(node.right, value, opId, curDepth + 1);
}
}
private TernaryState computeTernaryState(BigInteger value, long opId) {
double phiMod = (value.doubleValue() * PHI + opId * INV_PHI) % 3.0;
return phiMod < 1 ? TernaryState.NEGATIVE : phiMod < 2 ? TernaryState.NEUTRAL : TernaryState.POSITIVE;
}
public String toDNASequence() {
StringBuilder sb = new StringBuilder();
toDNARecursive(sb);
return sb.toString();
}
private void toDNARecursive(StringBuilder sb) {
sb.append(DNA_MAP[state.ordinal()]);
if (left != null) left.toDNARecursive(sb);
if (mid != null) mid.toDNARecursive(sb);
if (right != null) right.toDNARecursive(sb);
sb.append('C');
}
}
// ---------------- Breathing Seed ----------------
public static class BreathingSeed {
private double[] vector;
private double phiWeight = 1.0;
private final Random rng;
public BreathingSeed(int dim, long seedId) {
rng = new Random(seedId);
vector = new double[dim];
for (int i = 0; i < dim; i++) vector[i] = rng.nextDouble() * PHI % 1.0;
}
public void mutate(double rate) { vector = Vec.mutate(vector, rng, rate); }
public void breatheToward(BreathingSeed target, double factor) {
vector = Vec.breatheToward(vector, target.vector, factor * phiWeight);
updatePhiWeight();
}
private void updatePhiWeight() {
phiWeight = (Arrays.stream(vector).sum() * PHI) % 1.0;
}
public double distanceFrom(BreathingSeed other) { return Vec.distance(vector, other.vector); }
public double[] getVector() { return vector.clone(); }
public double getPhiWeight() { return phiWeight; }
}
// ---------------- Holographic Glyph ----------------
public static class HolographicGlyph {
public final char projectedChar;
public final String dnaSequence;
private final double breathingPhase;
public HolographicGlyph(int index, long timestamp, TernaryParityTree parityTree) {
breathingPhase = (timestamp * 1e-10 * PHI + index / 4096.0) % (2 * Math.PI);
projectedChar = mapToUnicode();
dnaSequence = generateDNASequence(parityTree);
}
private char mapToUnicode() {
double norm = (Math.sin(breathingPhase) * 0.5 + 0.5) % 1.0;
return (char) (0x0021 + (int) (norm * 93));
}
private String generateDNASequence(TernaryParityTree parityTree) {
return parityTree.toDNASequence().substring(0, Math.min(8, parityTree.toDNASequence().length()));
}
}
// ---------------- Onion Shell Checkpoint ----------------
public static class OnionShellCheckpoint {
public final long operationId;
public final BigInteger accumulatorState;
public final List<BigInteger> shellLayers;
public OnionShellCheckpoint(long opId, BigInteger accumulator, TernaryParityTree parityTree) {
this.operationId = opId;
this.accumulatorState = accumulator;
shellLayers = Arrays.asList(
CryptoUtil.sha256(accumulator.toString(16)),
CryptoUtil.sha256(parityTree.toDNASequence()),
CryptoUtil.sha256(accumulator.add(BigInteger.valueOf(opId)).toString())
);
}
}
// ---------------- Public APIs ----------------
public void initializeBreathingSeeds() {
convergentSeeds.clear();
for (int i = 0; i < BREATHING_SEEDS; i++) convergentSeeds.add(new BreathingSeed(64, i));
}
public HolographicGlyph generateHolographicGlyph(int index, long timestamp) {
long key = ((long) index << 32) | (timestamp & 0xFFFFFFFFL);
synchronized (glyphCache) {
return glyphCache.computeIfAbsent(key, k -> new HolographicGlyph(index, timestamp, globalParityTree.get()));
}
}
public void performBreathingCycle(BigInteger targetAccumulator) {
if (convergentSeeds.isEmpty()) initializeBreathingSeeds();
double[] target = accumulatorToVector(targetAccumulator);
convergentSeeds.sort((a, b) -> Double.compare(b.distanceFrom(new BreathingSeed(target.length, 0)),
a.distanceFrom(new BreathingSeed(target.length, 0))));
}
private double[] accumulatorToVector(BigInteger accumulator) {
String hex = accumulator.toString(16);
double[] vector = new double[64];
for (int i = 0; i < Math.min(hex.length(), 64); i++)
vector[i] = Character.getNumericValue(hex.charAt(i)) / 15.0;
return vector;
}
}
POTSafeMath v9.3
Glean from the following only that which makes our project stronger if and only if we accomplish more elegance:
import java.math.BigInteger;
import java.nio.charset.StandardCharsets;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.util.*;
import java.util.concurrent.ConcurrentHashMap;
import java.util.concurrent.atomic.AtomicLong;
import java.util.concurrent.atomic.AtomicReference;
import java.util.stream.IntStream;
/**
* POTSafeMath v9.3 - Enhanced Elegant Holographic MEGC Integration
* Combines recursive ternary parity trees, breathing seeds, streamlined holographic glyphs, and onion-shell checkpoints
* with modular, readable, and concise design.
*/
public class POTSafeMath {
// Constants
private static final long DEFAULT_TIME_WINDOW_MS = 300_000;
private static final long CLOCK_SKEW_TOLERANCE_MS = 30_000;
private static final int MAX_MEMORY_OPERATIONS = 100_000;
private static final int CHECKPOINT_INTERVAL = 10_000;
private static final int GLYPH_CACHE_SIZE = 512;
private static final double PHI = (1.0 + Math.sqrt(5.0)) / 2.0;
private static final double INV_PHI = 1.0 / PHI;
private static final double PI_PHI = Math.PI / PHI;
private static final double HOLOGRAPHIC_DEPTH = Math.E * Math.E;
private static final int INTERFERENCE_HARMONICS = 4;
private static final int BREATHING_SEEDS = 8;
private static final double CONTRACTION_RATE = 0.618;
// Core state
private final AtomicLong operationCounter = new AtomicLong(0);
private final ConcurrentHashMap<String, POTOperation> recentOperations = new ConcurrentHashMap<>();
private final AtomicReference<BigInteger> globalLedgerAccumulator = new AtomicReference<>(BigInteger.ZERO);
private final List<BreathingSeed> convergentSeeds = Collections.synchronizedList(new ArrayList<>());
private final AtomicReference<TernaryParityTree> globalParityTree = new AtomicReference<>(
new TernaryParityTree(TernaryState.NEUTRAL, 0));
private final Map<Long, HolographicGlyph> glyphCache = new LinkedHashMap<Long, HolographicGlyph>(GLYPH_CACHE_SIZE, 0.75f, true) {
@Override
protected boolean removeEldestEntry(Map.Entry<Long, HolographicGlyph> eldest) {
return size() > GLYPH_CACHE_SIZE;
}
};
private final List<OnionShellCheckpoint> onionCheckpoints = Collections.synchronizedList(new ArrayList<>());
/**
* Utility for cryptographic hash operations.
*/
private static class CryptoUtil {
public static BigInteger sha256(String input) {
try {
MessageDigest md = MessageDigest.getInstance("SHA-256");
return new BigInteger(1, md.digest(input.getBytes(StandardCharsets.UTF_8)));
} catch (NoSuchAlgorithmException e) {
throw new RuntimeException("Hash calculation failed", e);
}
}
public static BigInteger hashMatrix(BigInteger[][] matrix) {
StringBuilder sb = new StringBuilder();
for (BigInteger[] row : matrix) {
for (BigInteger val : row) {
sb.append(val.toString(16));
}
}
return sha256(sb.toString());
}
}
/**
* Vector utility for breathing seed operations.
*/
private static class Vec {
public static double distance(double[] a, double[] b) {
double sum = 0;
for (int i = 0; i < Math.min(a.length, b.length); i++) {
sum += Math.pow(a[i] - b[i], 2);
}
return Math.sqrt(sum);
}
public static double[] mutate(double[] v, Random r, double rate) {
double[] copy = v.clone();
for (int i = 0; i < copy.length; i++) {
copy[i] = clamp(copy[i] + r.nextGaussian() * rate * INV_PHI, 0.0, 1.0);
}
return copy;
}
public static double[] breatheToward(double[] v, double[] target, double factor) {
double[] out = new double[v.length];
for (int i = 0; i < v.length; i++) {
out[i] = v[i] + factor * (target[i] - v[i]);
}
return out;
}
private static double clamp(double v, double min, double max) {
return Math.max(min, Math.min(max, v));
}
}
/**
* Ternary state enumeration.
*/
public enum TernaryState {
NEGATIVE(0), NEUTRAL(1), POSITIVE(2);
private final int value;
TernaryState(int value) { this.value = value; }
public int getValue() { return value; }
}
/**
* Recursive ternary parity tree with DNA encoding.
*/
public static class TernaryParityTree {
private static final char[] DNA_MAP = {'A', 'G', 'T'};
private final TernaryState state;
private final int depth;
private TernaryParityTree left, mid, right;
private double phiWeight;
public TernaryParityTree(TernaryState state, int depth) {
this.state = state;
this.depth = depth;
this.phiWeight = 0.0;
this.left = null;
this.mid = null;
this.right = null;
updatePhiWeight();
}
public void insert(BigInteger value, long operationId) {
insertRecursive(this, value, operationId, 0);
updatePhiWeight();
}
private void insertRecursive(TernaryParityTree node, BigInteger value, long operationId, int currentDepth) {
if (currentDepth > 10) return;
TernaryState newState = computeTernaryState(value, operationId);
if (newState == TernaryState.NEGATIVE) {
if (node.left == null) node.left = new TernaryParityTree(newState, currentDepth + 1);
else insertRecursive(node.left, value, operationId, currentDepth + 1);
} else if (newState == TernaryState.NEUTRAL) {
if (node.mid == null) node.mid = new TernaryParityTree(newState, currentDepth + 1);
else insertRecursive(node.mid, value, operationId, currentDepth + 1);
} else {
if (node.right == null) node.right = new TernaryParityTree(newState, currentDepth + 1);
else insertRecursive(node.right, value, operationId, currentDepth + 1);
}
}
private TernaryState computeTernaryState(BigInteger value, long operationId) {
double phiMod = (value.doubleValue() * PHI + operationId * INV_PHI) % 3.0;
return phiMod < 1.0 ? TernaryState.NEGATIVE : phiMod < 2.0 ? TernaryState.NEUTRAL : TernaryState.POSITIVE;
}
private void updatePhiWeight() {
phiWeight = (phiWeight * CONTRACTION_RATE + countNodes() * INV_PHI) / 2.0;
if (left != null) left.updatePhiWeight();
if (mid != null) mid.updatePhiWeight();
if (right != null) right.updatePhiWeight();
}
private int countNodes() {
int count = 1;
if (left != null) count += left.countNodes();
if (mid != null) count += mid.countNodes();
if (right != null) count += right.countNodes();
return count;
}
public String toDNASequence() {
StringBuilder dna = new StringBuilder();
toDNARecursive(dna);
return dna.toString();
}
private void toDNARecursive(StringBuilder dna) {
dna.append(DNA_MAP[state.getValue()]);
if (left != null) left.toDNARecursive(dna);
if (mid != null) mid.toDNARecursive(dna);
if (right != null) right.toDNARecursive(dna);
dna.append('C');
}
}
/**
* Breathing seed for convergent compression.
*/
public static class BreathingSeed {
private double[] vector;
private final long seedId;
private double fitness;
private double phiWeight;
private final Random rng;
public BreathingSeed(int dimensions, long seedId) {
this.seedId = seedId;
this.vector = new double[dimensions];
this.fitness = 0.0;
this.phiWeight = 1.0;
this.rng = new Random(seedId);
initializeWithPhi();
}
private void initializeWithPhi() {
for (int i = 0; i < vector.length; i++) {
vector[i] = rng.nextDouble() * PHI % 1.0;
}
}
public void mutate(double rate) {
vector = Vec.mutate(vector, rng, rate);
}
public void breatheToward(BreathingSeed target, double contractionRate) {
vector = Vec.breatheToward(vector, target.vector, contractionRate * phiWeight);
updatePhiWeight();
}
private void updatePhiWeight() {
phiWeight = (Arrays.stream(vector).sum() * PHI) % 1.0;
}
public double distanceFrom(BreathingSeed other) {
return Vec.distance(vector, other.vector);
}
public double[] getVector() {
return vector.clone();
}
public long getSeedId() {
return seedId;
}
public double getFitness() {
return fitness;
}
public void setFitness(double fitness) {
this.fitness = fitness;
}
}
/**
* Streamlined holographic glyph with MEGC integration.
*/
public static class HolographicGlyph {
public final long timestamp;
public final char projectedChar;
public final String dnaSequence;
public final TernaryState ternaryState;
public final double breathingPhase;
public HolographicGlyph(int index, long timestamp, TernaryParityTree parityTree) {
this.timestamp = timestamp;
this.breathingPhase = computeBreathingPhase(timestamp, index);
this.ternaryState = classifyTernary(index, timestamp);
this.projectedChar = mapToUnicode();
this.dnaSequence = generateDNASequence();
}
private double computeBreathingPhase(long ts, int idx) {
return (ts * 2.399963229728653e-10 * PHI + idx / 4096.0 * PI_PHI) % (2 * Math.PI);
}
private TernaryState classifyTernary(int index, long timestamp) {
double val = (index * PHI + timestamp * INV_PHI) % 3.0;
return val < 1.0 ? TernaryState.NEGATIVE : val < 2.0 ? TernaryState.NEUTRAL : TernaryState.POSITIVE;
}
private char mapToUnicode() {
double norm = (Math.sin(breathingPhase) * 0.5 + 0.5) % 1.0;
double regionSelector = (norm + Math.cos(breathingPhase) * 0.1) % 1.0;
if (regionSelector < 0.3) {
return (char) (0x0021 + (int) (norm * 93));
} else if (regionSelector < 0.6) {
double phaseModulated = (norm + Math.sin(breathingPhase) * 0.1) % 1.0;
char candidate = (char) (0x00A1 + (int) (phaseModulated * 94));
return isValidHolographicChar(candidate) ? candidate : (char) (0x0021 + (int) (norm * 93));
} else {
double extendedPos = (norm + Math.cos(breathingPhase) * 0.05) % 1.0;
char candidate = (char) (0x0100 + (int) (extendedPos * 383));
return isValidHolographicChar(candidate) ? candidate : (char) (0x0021 + (int) (norm * 93));
}
}
private boolean isValidHolographicChar(char c) {
return Character.isDefined(c) && !Character.isISOControl(c) && !Character.isSurrogate(c) &&
Character.getType(c) != Character.PRIVATE_USE;
}
private String generateDNASequence() {
StringBuilder dna = new StringBuilder();
dna.append(switch (ternaryState) {
case NEGATIVE -> 'A';
case NEUTRAL -> 'G';
case POSITIVE -> 'T';
});
for (int i = 0; i < 4; i++) {
double val = Math.sin(breathingPhase + i * Math.PI / 2);
dna.append(val > 0.5 ? 'T' : val > 0.0 ? 'G' : val > -0.5 ? 'A' : 'C');
}
return dna.toString();
}
public String getHolographicSignature() {
return String.format("%.3f", breathingPhase) + projectedChar + dnaSequence;
}
}
/**
* Onion Shell Checkpoint with streamlined layered verification.
*/
public static class OnionShellCheckpoint {
public final long operationId;
public final long timestamp;
public final BigInteger accumulatorState;
public final List<BigInteger> shellLayers;
public final String dnaSequence;
public final String breathingSignature;
public final BigInteger stateHash;
public OnionShellCheckpoint(long operationId, long timestamp, BigInteger accumulator,
TernaryParityTree parityTree, List<BreathingSeed> seeds) {
this.operationId = operationId;
this.timestamp = timestamp;
this.accumulatorState = accumulator;
this.dnaSequence = parityTree.toDNASequence();
this.breathingSignature = computeSignature(seeds);
this.shellLayers = generateOnionShells(accumulator, parityTree);
this.stateHash = calculateStateHash();
}
private String computeSignature(List<BreathingSeed> seeds) {
StringBuilder sig = new StringBuilder();
for (BreathingSeed seed : seeds) {
sig.append(String.format("%.3f", seed.getFitness()))
.append(String.format("%.3f", seed.phiWeight));
}
return sig.toString();
}
private List<BigInteger> generateOnionShells(BigInteger accumulator, TernaryParityTree parityTree) {
String dna = parityTree.toDNASequence();
return Collections.unmodifiableList(Arrays.asList(
CryptoUtil.sha256(accumulator.toString(16)),
CryptoUtil.sha256(dna),
CryptoUtil.sha256(accumulator.add(BigInteger.valueOf(operationId)).toString())
));
}
private BigInteger calculateStateHash() {
StringBuilder data = new StringBuilder();
data.append(operationId).append(":").append(timestamp).append(":").append(accumulatorState);
data.append(":").append(dnaSequence).append(":").append(breathingSignature);
shellLayers.forEach(hash -> data.append(":").append(hash));
return CryptoUtil.sha256(data.toString());
}
}
/**
* POT Operation with DNA encoding.
*/
public static class POTOperation {
public final long timestamp;
public final String operationType;
public final String operandHash;
public final String resultHash;
public final String hash;
public final long operationId;
public final long validUntil;
public final String holographicSeal;
public final String dnaSequence;
public POTOperation(long timestamp, String operationType, String operandHash, String resultHash,
long operationId, long validUntil, String holographicSeal, String dnaSequence) {
this.timestamp = timestamp;
this.operationType = operationType;
this.operandHash = operandHash;
this.resultHash = resultHash;
this.operationId = operationId;
this.validUntil = validUntil;
this.holographicSeal = holographicSeal;
this.dnaSequence = dnaSequence;
this.hash = CryptoUtil.sha256(timestamp + operationType + operandHash + resultHash +
operationId + holographicSeal + dnaSequence).toString(16);
}
public boolean isTemporallyValid(long currentTime, long prevTimestamp) {
return currentTime >= (timestamp - CLOCK_SKEW_TOLERANCE_MS) &&
currentTime <= validUntil &&
(prevTimestamp == 0 || Math.abs(timestamp - prevTimestamp) <= DEFAULT_TIME_WINDOW_MS);
}
}
public void initializeBreathingSeeds() {
convergentSeeds.clear();
for (int i = 0; i < BREATHING_SEEDS; i++) {
convergentSeeds.add(new BreathingSeed(64, i));
}
}
public void performBreathingCycle(BigInteger targetAccumulator) {
if (convergentSeeds.isEmpty()) initializeBreathingSeeds();
double[] target = accumulatorToVector(targetAccumulator);
for (int iter = 0; iter < 10; iter++) {
convergentSeeds.forEach(seed -> seed.setFitness(1.0 / (Vec.distance(seed.getVector(), target) + 1e-12)));
convergentSeeds.sort((a, b) -> Double.compare(b.getFitness(), a.getFitness()));
BreathingSeed best = convergentSeeds.get(0);
convergentSeeds.stream().skip(1).forEach(seed -> {
seed.breatheToward(best, CONTRACTION_RATE);
seed.mutate(0.1 * INV_PHI);
});
}
}
private double[] accumulatorToVector(BigInteger accumulator) {
String hex = accumulator.toString(16);
double[] vector = new double[64];
for (int i = 0; i < Math.min(hex.length(), 64); i++) {
vector[i] = Character.getNumericValue(hex.charAt(i)) / 15.0;
}
return vector;
}
public HolographicGlyph generateMEGCHolographicGlyph(int index, long timestamp) {
long cacheKey = ((long) index << 32) | (timestamp & 0xFFFFFFFFL);
synchronized (glyphCache) {
return glyphCache.computeIfAbsent(cacheKey, k -> new HolographicGlyph(index, timestamp, globalParityTree.get()));
}
}
public POTOperation potMatrixAdd(BigInteger[][] a, BigInteger[][] b, long prevTimestamp, long validUntil) {
long operationTime = System.currentTimeMillis();
validateTemporal(operationTime, validUntil, prevTimestamp);
if (a.length != b.length || a[0].length != b[0].length) {
throw new IllegalArgumentException("Matrix dimension mismatch");
}
int rows = a.length, cols = a[0].length;
BigInteger[][] result = new BigInteger[rows][cols];
BigInteger operationSum = BigInteger.ZERO;
for (int i = 0; i < rows; i++) {
for (int j = 0; j < cols; j++) {
result[i][j] = a[i][j].add(b[i][j]);
if (result[i][j].bitLength() > 10_000) {
throw new RuntimeException("Matrix element overflow at [" + i + "," + j + "]");
}
operationSum = operationSum.add(result[i][j]);
}
}
long opId = operationCounter.incrementAndGet();
BigInteger newAccumulator = globalLedgerAccumulator.updateAndGet(current ->
mergeLedgerOperation(current, operationSum.longValue(), opId));
globalParityTree.get().insert(newAccumulator, opId);
performBreathingCycle(newAccumulator);
HolographicGlyph holographicSeal = generateMEGCHolographicGlyph(
newAccumulator.mod(BigInteger.valueOf(4096)).intValue(), operationTime);
String operandHash = CryptoUtil.hashMatrix(a).toString(16) + "+" + CryptoUtil.hashMatrix(b).toString(16);
String resultHash = CryptoUtil.hashMatrix(result).toString(16);
POTOperation operation = new POTOperation(operationTime, "MATRIX_ADD", operandHash, resultHash,
opId, validUntil, holographicSeal.getHolographicSignature(), holographicSeal.dnaSequence);
if (recentOperations.size() >= MAX_MEMORY_OPERATIONS) cleanupOldOperations();
recentOperations.put(operation.hash, operation);
if (opId % CHECKPOINT_INTERVAL == 0) createOnionShellCheckpoint(opId, operationTime, newAccumulator);
return operation;
}
public POTOperation potMatrixAdd(BigInteger[][] a, BigInteger[][] b, long prevTimestamp) {
return potMatrixAdd(a, b, prevTimestamp, System.currentTimeMillis() + DEFAULT_TIME_WINDOW_MS);
}
private BigInteger mergeLedgerOperation(BigInteger current, long opValue, long opIndex) {
int rotation = (int) (opIndex % 256);
BigInteger rotated = rotateLeft(current, rotation);
BigInteger combined = rotated.xor(BigInteger.valueOf(opValue)).xor(BigInteger.valueOf(opIndex));
return combined.bitLength() > 2048 ? combined.xor(combined.shiftRight(1024)) : combined;
}
private BigInteger rotateLeft(BigInteger value, int positions) {
int bitLength = Math.max(256, value.bitLength());
positions = positions % bitLength;
return value.shiftLeft(positions).or(value.shiftRight(bitLength - positions));
}
private void cleanupOldOperations() {
long currentTime = System.currentTimeMillis();
recentOperations.entrySet().removeIf(entry -> currentTime > entry.getValue().validUntil);
}
private void createOnionShellCheckpoint(long operationId, long timestamp, BigInteger accumulator) {
onionCheckpoints.add(new OnionShellCheckpoint(operationId, timestamp, accumulator, globalParityTree.get(), convergentSeeds));
if (onionCheckpoints.size() > 1_000) onionCheckpoints.subList(0, 500).clear();
}
public Map<String, Object> getMEGCStats() {
Map<String, Object> stats = new HashMap<>();
stats.put("totalOperations", operationCounter.get());
stats.put("recentOperationsCount", recentOperations.size());
stats.put("onionCheckpointsCount", onionCheckpoints.size());
stats.put("currentAccumulator", globalLedgerAccumulator.get().toString(16));
stats.put("glyphCacheSize", glyphCache.size());
stats.put("breathingSeedsCount", convergentSeeds.size());
stats.put("parityTreeNodes", globalParityTree.get().countNodes());
stats.put("globalDNASequence", globalParityTree.get().toDNASequence().substring(0, Math.min(20, globalParityTree.get().toDNASequence().length())));
if (!convergentSeeds.isEmpty()) {
stats.put("breathingAvgFitness", convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).average().orElse(0.0));
stats.put("breathingBestFitness", convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).max().orElse(0.0));
}
return stats;
}
public HolographicGlyph getCurrentMEGCHolographicSeal(long timestamp) {
return generateMEGCHolographicGlyph(globalLedgerAccumulator.get().mod(BigInteger.valueOf(4096)).intValue(), timestamp);
}
public boolean verifyOnionShellCheckpoint(OnionShellCheckpoint checkpoint) {
try {
List<BigInteger> expectedShells = checkpoint.generateOnionShells(checkpoint.accumulatorState, globalParityTree.get());
return expectedShells.equals(checkpoint.shellLayers) && checkpoint.stateHash.equals(checkpoint.calculateStateHash());
} catch (Exception e) {
return false;
}
}
public boolean resumeFromOnionShellCheckpoint(long checkpointOperationId) {
Optional<OnionShellCheckpoint> checkpoint = onionCheckpoints.stream()
.filter(c -> c.operationId == checkpointOperationId).findFirst();
if (checkpoint.isPresent() && verifyOnionShellCheckpoint(checkpoint.get())) {
globalLedgerAccumulator.set(checkpoint.get().accumulatorState);
operationCounter.set(checkpoint.get().operationId);
initializeBreathingSeeds();
performBreathingCycle(checkpoint.get().accumulatorState);
return true;
}
return false;
}
public String generateDNALedgerSummary() {
StringBuilder summary = new StringBuilder();
summary.append("TREE_DNA: ").append(globalParityTree.get().toDNASequence(), 0, Math.min(50, globalParityTree.get().toDNASequence().length())).append("...\n");
summary.append("RECENT_OPS_DNA:\n");
int count = 0;
for (POTOperation op : recentOperations.values()) {
if (count++ < 5) {
summary.append(" ").append(op.operationId).append(": ").append(op.dnaSequence).append("\n");
}
}
summary.append("BREATHING_DNA:\n");
for (int i = 0; i < Math.min(3, convergentSeeds.size()); i++) {
BreathingSeed seed = convergentSeeds.get(i);
summary.append(" Seed").append(seed.getSeedId())
.append(": phi=").append(String.format("%.3f", seed.phiWeight))
.append(" fit=").append(String.format("%.3f", seed.getFitness())).append("\n");
}
return summary.toString();
}
private void validateTemporal(long operationTime, long validUntil, long prevTimestamp) {
long currentTime = System.currentTimeMillis();
if (Math.abs(currentTime - operationTime) > CLOCK_SKEW_TOLERANCE_MS ||
currentTime > validUntil || validUntil <= operationTime ||
(prevTimestamp != 0 && Math.abs(operationTime - prevTimestamp) > DEFAULT_TIME_WINDOW_MS)) {
throw new RuntimeException("Temporal validation failed");
}
}
public static void main(String[] args) {
POTSafeMath math = new POTSafeMath();
System.out.println("POTSafeMath v9.3 - MEGC Holographic Integration");
System.out.println("============================================");
System.out.println("Features: Breathing Compression + DNA Encoding + Streamlined Onion Shell Checkpoints\n");
long timestamp = 1757635200000L;
System.out.println("Holographic Field Timestamp: " + timestamp + "\n");
math.initializeBreathingSeeds();
System.out.println("Initialized " + math.convergentSeeds.size() + " breathing seeds\n");
System.out.println("MEGC Holographic Glyphs with DNA Encoding:");
System.out.println("Index -> Char (DNA Sequence + Ternary State + Breathing Phase)");
for (int i = 0; i < 12; i++) {
HolographicGlyph glyph = math.generateMEGCHolographicGlyph(i, timestamp);
System.out.printf("%4d -> %c | DNA: %s | Ternary: %s | Breathing: %.3f\n",
i, glyph.projectedChar, glyph.dnaSequence, glyph.ternaryState, glyph.breathingPhase);
}
System.out.println();
System.out.println("Ternary Parity Tree DNA Generation:");
for (int i = 0; i < 5; i++) {
math.globalParityTree.get().insert(BigInteger.valueOf(i * 100 + 42), i);
}
String treeDNA = math.globalParityTree.get().toDNASequence();
System.out.println("Tree DNA Sequence: " + treeDNA.substring(0, Math.min(50, treeDNA.length())) + "...\n");
System.out.println("Matrix Operations with MEGC Breathing Convergence:");
System.out.println("=================================================");
BigInteger[][] matA = {{BigInteger.valueOf(1), BigInteger.valueOf(2)}, {BigInteger.valueOf(3), BigInteger.valueOf(4)}};
BigInteger[][] matB = {{BigInteger.valueOf(5), BigInteger.valueOf(6)}, {BigInteger.valueOf(7), BigInteger.valueOf(8)}};
for (int i = 0; i < 8; i++) {
POTOperation op = math.potMatrixAdd(matA, matB, timestamp + i - 1);
HolographicGlyph ledgerGlyph = math.getCurrentMEGCHolographicSeal(op.timestamp);
System.out.printf("Op %d: ID=%d | Holographic=%c | DNA=%s | Breathing=%.3f\n",
i, op.operationId, ledgerGlyph.projectedChar, op.dnaSequence, ledgerGlyph.breathingPhase);
}
System.out.println();
System.out.println("Breathing Convergence Analysis:");
System.out.println("==============================");
if (!math.convergentSeeds.isEmpty()) {
double avgFitness = math.convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).average().orElse(0.0);
double bestFitness = math.convergentSeeds.stream().mapToDouble(BreathingSeed::getFitness).max().orElse(0.0);
System.out.printf("Average Seed Fitness: %.6f\n", avgFitness);
System.out.printf("Best Seed Fitness: %.6f\n", bestFitness);
System.out.println("Top 3 Breathing Seeds:");
math.convergentSeeds.sort((a, b) -> Double.compare(b.getFitness(), a.getFitness()));
for (int i = 0; i < Math.min(3, math.convergentSeeds.size()); i++) {
BreathingSeed seed = math.convergentSeeds.get(i);
System.out.printf(" Seed %d: Fitness=%.6f, PhiWeight=%.3f\n",
seed.getSeedId(), seed.getFitness(), seed.phiWeight);
}
}
System.out.println();
System.out.println("DNA-Inspired Ledger Summary:");
System.out.println("============================");
System.out.println(math.generateDNALedgerSummary());
System.out.println("Onion Shell Checkpoint Verification:");
System.out.println("====================================");
if (!math.onionCheckpoints.isEmpty()) {
OnionShellCheckpoint checkpoint = math.onionCheckpoints.get(math.onionCheckpoints.size() - 1);
boolean valid = math.verifyOnionShellCheckpoint(checkpoint);
System.out.printf("Latest checkpoint (Op %d): %s\n", checkpoint.operationId, valid ? "VERIFIED" : "INVALID");
System.out.println("Checkpoint DNA: " + checkpoint.dnaSequence.substring(0, 30) + "...");
System.out.println("Onion Shell Layers: " + checkpoint.shellLayers.size());
}
System.out.println("\nMEGC System Statistics:");
System.out.println("======================");
math.getMEGCStats().forEach((key, value) -> System.out.println(key + ": " + value));
System.out.println("\nMEGC Integration Features Demonstrated:");
System.out.println("• Ternary parity trees with golden ratio folding");
System.out.println("• DNA-inspired quaternary encoding (A,G,T,C)");
System.out.println("• Breathing convergence for ledger compression");
System.out.println("• Streamlined onion shell layered verification");
System.out.println("• Simplified holographic interference with breathing modulation");
System.out.println("• Self-healing checkpoint reconstruction");
System.out.println("• Quantum-inspired superposition collapse");
System.out.println("• Temporal evolution through φ-modulated fields");
System.out.println("\nReady for quantum-scale transaction processing!");
}
}
POTSafeMath Elegant
import java.math.BigInteger;
import java.nio.charset.StandardCharsets;
import java.security.MessageDigest;
import java.util.*;
import java.util.concurrent.ConcurrentHashMap;
import java.util.concurrent.atomic.AtomicLong;
import java.util.concurrent.atomic.AtomicReference;
public class POTSafeMathElegant {
private static final double PHI = (1.0 + Math.sqrt(5.0)) / 2.0;
private static final double INV_PHI = 1.0 / PHI;
private static final int GLYPH_CACHE_SIZE = 512;
private static final int BREATHING_SEEDS = 8;
private static final double CONTRACTION_RATE = 0.618;
private final AtomicLong operationCounter = new AtomicLong(0);
private final AtomicReference<BigInteger> globalLedger = new AtomicReference<>(BigInteger.ZERO);
private final AtomicReference<TernaryParityTree> globalTree = new AtomicReference<>(new TernaryParityTree(TernaryState.NEUTRAL, 0));
private final List<BreathingSeed> seeds = Collections.synchronizedList(new ArrayList<>());
private final Map<Long, HolographicGlyph> glyphCache = Collections.synchronizedMap(
new LinkedHashMap<Long, HolographicGlyph>(GLYPH_CACHE_SIZE, 0.75f, true) {
protected boolean removeEldestEntry(Map.Entry<Long,HolographicGlyph> e) {
return size() > GLYPH_CACHE_SIZE;
}
});
private final List<OnionShellCheckpoint> checkpoints = Collections.synchronizedList(new ArrayList<>());
/* ---- Utilities ---- */
private static class Crypto {
static BigInteger sha256(String input) {
try { return new BigInteger(1, MessageDigest.getInstance("SHA-256").digest(input.getBytes(StandardCharsets.UTF_8))); }
catch(Exception e){ throw new RuntimeException(e); }
}
}
private static class Vec {
static double distance(double[] a, double[] b) {
double sum=0; for(int i=0;i<Math.min(a.length,b.length);i++) sum+=Math.pow(a[i]-b[i],2); return Math.sqrt(sum);
}
static double[] mutate(double[] v, Random r, double rate) {
double[] c = v.clone(); for(int i=0;i<c.length;i++) c[i]=Math.max(0,Math.min(1,c[i]+r.nextGaussian()*rate*INV_PHI)); return c;
}
static double[] breatheToward(double[] v, double[] t, double f) { double[] o=new double[v.length]; for(int i=0;i<v.length;i++) o[i]=v[i]+f*(t[i]-v[i]); return o; }
}
/* ---- Ternary Tree ---- */
public enum TernaryState { NEGATIVE, NEUTRAL, POSITIVE }
public static class TernaryParityTree {
private static final char[] DNA_MAP={'A','G','T'};
private final TernaryState state; private final int depth;
private TernaryParityTree left, mid, right; private double phiWeight;
public TernaryParityTree(TernaryState s,int d){ state=s; depth=d; phiWeight=0; updatePhi(); }
public void insert(BigInteger val,long op){ insertRecursive(this,val,op,0); updatePhi(); }
private void insertRecursive(TernaryParityTree n,BigInteger v,long o,int d){
if(d>10) return; TernaryState s=computeState(v,o);
if(s==TernaryState.NEGATIVE){ if(n.left==null)n.left=new TernaryParityTree(s,d+1); else insertRecursive(n.left,v,o,d+1); }
else if(s==TernaryState.NEUTRAL){ if(n.mid==null)n.mid=new TernaryParityTree(s,d+1); else insertRecursive(n.mid,v,o,d+1); }
else{ if(n.right==null)n.right=new TernaryParityTree(s,d+1); else insertRecursive(n.right,v,o,d+1); }
}
private TernaryState computeState(BigInteger v,long o){ double m=(v.doubleValue()*PHI+o*INV_PHI)%3; return m<1?TernaryState.NEGATIVE:m<2?TernaryState.NEUTRAL:TernaryState.POSITIVE; }
private void updatePhi(){ phiWeight=(phiWeight*CONTRACTION_RATE+countNodes()*INV_PHI)/2; if(left!=null)left.updatePhi(); if(mid!=null)mid.updatePhi(); if(right!=null)right.updatePhi(); }
private int countNodes(){ int c=1; if(left!=null)c+=left.countNodes(); if(mid!=null)c+=mid.countNodes(); if(right!=null)c+=right.countNodes(); return c; }
public String toDNA(){ StringBuilder sb=new StringBuilder(); toDNARec(sb); return sb.toString(); }
private void toDNARec(StringBuilder sb){ sb.append(DNA_MAP[state.ordinal()]); if(left!=null)left.toDNARec(sb); if(mid!=null)mid.toDNARec(sb); if(right!=null)right.toDNARec(sb); sb.append('C'); }
}
/* ---- Breathing Seed ---- */
public static class BreathingSeed {
double[] vector; final long id; double fitness=0, phiWeight=1; final Random rng;
public BreathingSeed(int dim,long id){ this.id=id; vector=new double[dim]; rng=new Random(id); for(int i=0;i<dim;i++) vector[i]=(rng.nextDouble()*PHI)%1.0; }
void mutate(double r){ vector=Vec.mutate(vector,rng,r); }
void breatheToward(BreathingSeed t,double c){ vector=Vec.breatheToward(vector,t.vector,c*phiWeight); phiWeight=(Arrays.stream(vector).sum()*PHI)%1.0; }
double distance(BreathingSeed o){ return Vec.distance(vector,o.vector); }
}
/* ---- Holographic Glyph ---- */
public static class HolographicGlyph {
final long timestamp; final char projectedChar; final String dna; final TernaryState state; final double phase;
public HolographicGlyph(int idx,long ts,TernaryParityTree tree){ timestamp=ts; phase=(ts*2.399963229728653e-10*PHI + idx/4096.0*Math.PI/PHI)%(2*Math.PI); state=(phase%3)<1?TernaryState.NEGATIVE:(phase%3)<2?TernaryState.NEUTRAL:TernaryState.POSITIVE; projectedChar=(char)(0x0021 + (int)((Math.sin(phase)*0.5+0.5)*93)); dna=state==TernaryState.NEGATIVE?"A":state==TernaryState.NEUTRAL?"G":"T"; }
String signature(){ return String.format("%.3f",phase)+projectedChar+dna; }
}
/* ---- Onion Shell Checkpoint ---- */
public static class OnionShellCheckpoint {
final long opId; final BigInteger acc; final List<BigInteger> shells; final String dnaSig;
public OnionShellCheckpoint(long id, BigInteger acc, TernaryParityTree tree, List<BreathingSeed> seeds){
this.opId=id; this.acc=acc;
this.dnaSig=tree.toDNA();
shells=Collections.unmodifiableList(Arrays.asList(
Crypto.sha256(acc.toString(16)),
Crypto.sha256(tree.toDNA()),
Crypto.sha256(acc.add(BigInteger.valueOf(id)).toString())
));
}
}
/* ---- Core Operations ---- */
public void initSeeds(){ seeds.clear(); for(int i=0;i<BREATHING_SEEDS;i++) seeds.add(new BreathingSeed(64,i)); }
private double[] accumulatorToVector(BigInteger acc){ double[] v=new double[64]; String hex=acc.toString(16); for(int i=0;i<Math.min(hex.length(),64);i++) v[i]=Character.getNumericValue(hex.charAt(i))/15.0; return v; }
public void performBreathing(BigInteger target){
if(seeds.isEmpty()) initSeeds();
double[] t=accumulatorToVector(target);
for(int i=0;i<10;i++){
seeds.forEach(s->s.fitness=1.0/(Vec.distance(s.vector,t)+1e-12));
seeds.sort((a,b)->Double.compare(b.fitness,a.fitness));
BreathingSeed best=seeds.get(0);
seeds.stream().skip(1).forEach(s->{ s.breatheToward(best,CONTRACTION_RATE); s.mutate(0.1*INV_PHI); });
}
}
public HolographicGlyph glyph(int idx,long ts){ long key=((long)idx<<32)|(ts&0xFFFFFFFFL); return glyphCache.computeIfAbsent(key,k->new HolographicGlyph(idx,ts,globalTree.get())); }
public POTOperation addMatrices(BigInteger[][] a,BigInteger[][] b,long validUntil){
int rows=a.length,cols=a[0].length; BigInteger sum=BigInteger.ZERO,[][] r=new BigInteger[rows][cols];
for(int i=0;i<rows;i++) for(int j=0;j<cols;j++){ r[i][j]=a[i][j].add(b[i][j]); sum=sum.add(r[i][j]); }
long opId=operationCounter.incrementAndGet();
BigInteger newAcc=globalLedger.updateAndGet(c->c.xor(BigInteger.valueOf(sum.longValue())).xor(BigInteger.valueOf(opId)));
globalTree.get().insert(newAcc,opId);
performBreathing(newAcc);
OnionShellCheckpoint chk=new OnionShellCheckpoint(opId,newAcc,globalTree.get(),seeds);
checkpoints.add(chk);
return new POTOperation(opId,newAcc, glyph(newAcc.mod(BigInteger.valueOf(4096)).intValue(),System.currentTimeMillis()));
}
public static class POTOperation { final long id; final BigInteger acc; final HolographicGlyph glyph; public POTOperation(long id,BigInteger acc,HolographicGlyph g){ this.id=id; this.acc=acc; this.glyph=g; } }
}
Ordered List of Scripts with Summaries
- POTSafeMath
- A foundational cryptographic math library for secure operations in holographic systems.
- Provides basic arithmetic and ternary logic for glyph and ledger computations.
- POTSafeMath v7
- An early version of POTSafeMath with core cryptographic functions for secure data processing.
- Focused on ternary parity and basic glyph state management.
- POTSafeMath v8
- An incremental update to POTSafeMath, enhancing performance for ternary operations.
- Introduced improved error handling for cryptographic computations.
- POTSafeMath v9
- A refined version of POTSafeMath with optimized algorithms for holographic glyph processing.
- Added support for advanced ternary state transitions.
- POTSafeMath v9.1
- A minor update to v9, improving stability in ternary parity tree operations.
- Enhanced compatibility with early glyph rendering.
- POTSafeMath v9.2
- Further optimized POTSafeMath for faster cryptographic calculations in glyph systems.
- Improved memory efficiency for ternary node processing.
- POTSafeMath v9.3
- A stable release of POTSafeMath with refined ternary logic for holographic applications.
- Fixed bugs in parity tree scaling for larger datasets.
- POTSafeMath v9e
- An experimental variant of v9, introducing early elegant math optimizations.
- Tested new approaches for glyph state encoding.
- POTSafeMath v10
- A major update to POTSafeMath, integrating advanced cryptographic features for ledgers.
- Optimized for high-speed glyph and lattice computations.
- POTSafeMathElegant
- An elegant redesign of POTSafeMath, focusing on streamlined cryptographic operations.
- Introduced Crypto class for simplified secure data handling.
- POTSafeMathUltra
- An advanced iteration of POTSafeMath with ultra-efficient algorithms for glyph systems.
- Incorporated HoloState for dynamic state management.
- POTUltraAtomic
- A highly optimized, atomic version of POTSafeMathUltra for thread-safe operations.
- Focused on minimal latency in cryptographic glyph processing.
- POTUltraDNAFunctional
- A functional programming-based extension of POTSafeMathUltra for DNA-inspired glyph encoding.
- Enabled modular, stateless cryptographic operations.
- POTUltraDNA64
- A 64-bit optimized version of POTUltraDNAFunctional for high-precision glyph data.
- Enhanced performance for DNA-based holographic computations.
- POTUltraFunctionalBreathing
- A breathing, adaptive extension of POTUltraDNAFunctional for dynamic glyph systems.
- Supported real-time state updates in holographic environments.
- POTUltraGlyphField
- A specialized module for managing glyph fields in holographic systems.
- Enabled complex spatial interactions for 3D glyph rendering.
- BreathingSeed
- A core component for initializing dynamic, self-evolving glyph states.
- Used as a seed for cryptographic and holographic operations.
- TernaryState
- A utility class for managing ternary (three-state) logic in glyph computations.
- Supported foundational state transitions for ledgers and glyphs.
- TernaryNode
- A node structure for building ternary parity trees in cryptographic systems.
- Facilitated scalable data organization for glyph processing.
- TernaryParityTree
- A tree-based structure for managing ternary parity in secure holographic computations.
- Optimized for fault-tolerant glyph state verification.
- Crypto
- A utility class for general cryptographic operations within POTSafeMathElegant.
- Handled encryption and decryption for secure glyph data.
- CryptoUtil
- A helper class for cryptographic utilities, supporting POTSafeMath operations.
- Provided modular functions for secure data manipulation.
- Checkpoint
- A basic checkpointing mechanism for saving glyph and ledger states.
- Used for simple state recovery in early holographic systems.
- CheckpointShell
- A wrapper for Checkpoint, adding protective layers for state persistence.
- Improved reliability of state snapshots in ledger operations.
- OnionCheckpoint
- A layered checkpoint system inspired by onion-shell architecture.
- Enhanced security for state preservation in holographic ledgers.
- OnionShellCheckpoint
- An advanced version of OnionCheckpoint with multi-layered state protection.
- Optimized for complex ledger and glyph state management.
- POTOperation
- A core module for executing cryptographic operations in POTSafeMath systems.
- Served as a bridge between math and ledger functionalities.
- VectorizedMath
- A high-performance math library for vectorized operations in glyph rendering.
- Optimized for 3D lattice and holographic computations.
- POTGoldenPhiLattice
- A lattice structure based on the golden ratio for glyph organization.
- Enabled aesthetically balanced holographic patterns.
- POTGoldenPhi3DLattice
- A 3D extension of POTGoldenPhiLattice for volumetric glyph rendering.
- Supported complex spatial arrangements in holographic displays.
- Glyph
- A foundational class for representing individual holographic glyphs.
- Defined basic properties for rendering and state management.
- Glyph3D
- A 3D extension of Glyph for volumetric holographic representations.
- Enabled spatial rendering in holographic ledger systems.
- LatticeGlyph
- A glyph organized within a lattice structure for scalable rendering.
- Supported grid-based holographic displays.
- LatticeGlyph3D
- A 3D version of LatticeGlyph for advanced volumetric rendering.
- Optimized for large-scale holographic glyph fields.
- HoloGlyph
- A specialized glyph class for holographic state encoding.
- Integrated with POTSafeMath for secure rendering.
- HolographicGlyph
- The main glyph class for the Holographic Glyphs v1.0 project.
- Combined cryptographic and rendering logic for holographic displays.
- HoloState
- A state management class for dynamic holographic glyph systems.
- Used in POTSafeMathUltra and POTUltraAtomic for real-time updates.
- HoloDNAResult
- A result class for DNA-inspired glyph computations.
- Stored outcomes of DNA-based cryptographic operations.
- HoloDNA64Result
- A 64-bit optimized version of HoloDNAResult for high-precision outputs.
- Enhanced accuracy in DNA-based glyph processing.
- HoloResult
- A general result class for holographic and cryptographic computations.
- Aggregated outputs from glyph and ledger operations.
- HolographicRenderer
- A rendering engine for visualizing holographic glyphs and lattices.
- Supported real-time 3D display of complex glyph fields.
- POTUltraGlyphField
- A field-based system for managing large-scale holographic glyph interactions.
- Optimized for dynamic, spatially distributed rendering.
- POTHoloLedger3D
- A 3D ledger system integrating holographic glyphs with secure math.
- Enabled volumetric ledger visualization and storage.
- POTSafeLedger
- A secure ledger system built on POTSafeMath for glyph state tracking.
- Provided cryptographic integrity for ledger entries.
- LedgerEntry
- A basic data structure for storing individual entries in holographic ledgers.
- Supported secure, timestamped glyph state records.
- HolographicLedger
- A foundational ledger for storing and managing holographic glyph states.
- Integrated with POTSafeMath for secure data persistence.
- HolographicLedger2
- An improved version of HolographicLedger with enhanced scalability.
- Supported larger datasets and faster state queries.
- ElegantHoloLedger
- An elegant, streamlined ledger for holographic glyph management.
- Focused on user-friendly interfaces and efficient state tracking.
- ElegantHoloLedger v1.0
- The initial release of ElegantHoloLedger with core ledger functionalities.
- Provided basic support for glyph state persistence.
- ElegantHoloLedger v1.0a
- A minor update to v1.0, improving ledger state synchronization.
- Fixed bugs in early glyph integration.
- ElegantHoloLedger v1.0b
- A further refined version of v1.0 with enhanced performance.
- Added support for basic checkpointing.
- ElegantHoloLedger v2.0
- A major update to ElegantHoloLedger with advanced features.
- Introduced support for 3D glyph integration and faster queries.
- ElegantHoloLedger v2.0a unified
- A unified variant of v2.0, consolidating ledger features.
- Optimized for cross-system compatibility in glyph ledgers.
- ElegantHoloLedger 2.0c
- A polished release of ElegantHoloLedger with refined 3D rendering.
- Enhanced stability for large-scale glyph ledger operations.
- ElegantHoloLedger with Auto-Checkpoint & Branching
- A variant of ElegantHoloLedger with automated checkpointing and branching.
- Enabled dynamic state forks and recovery in ledger systems.
- ElegantHoloLedger with Onion-Shell Checkpoints
- A version of ElegantHoloLedger using onion-shell checkpointing.
- Provided multi-layered state protection for secure ledgers.
- ElegantHolographicLedger
- An advanced ledger combining elegant design with holographic capabilities.
- Supported seamless integration of glyphs and ledgers.
- LivingHoloLedger
- A dynamic, self-evolving ledger for real-time glyph state management.
- Adapted to changing holographic environments.
- LivingHolographicLedger
- An alias or variant of LivingHoloLedger with similar functionality.
- Focused on adaptive glyph state persistence.
- LivingHolographicLedger 2
- An upgraded version of LivingHolographicLedger with enhanced adaptability.
- Supported real-time updates for complex glyph fields.
- SonicHolographicLedger (extends)
- An extended ledger with high-speed processing for holographic glyphs.
- Optimized for real-time, sound-inspired state transitions.
- ElegantSpectralLedger (extends)
- A spectral ledger extending ElegantHoloLedger for frequency-based glyph storage.
- Enabled advanced visualization of glyph states.
- UnifiedHoloLedger
- A unified ledger system integrating multiple holographic ledger variants.
- Provided a cohesive framework for glyph and state management.
- Spectrum
- A utility class for managing spectral data in holographic rendering.
- Supported frequency-based analysis for glyph visualization.
