import unittest from example import * class ScientificChecks(unittest.TestCase): def test_literal_generator_all_words_and_support_invariants(self): p=Parameters();chem=FiniteFoodChemistry(p);chain=CountChain(p);self.assertEqual(len(chem.reactions),24) for word in product((0,1),repeat=2): for n in chain.states: state=MolecularState.pure(9,word,n);aggregated={} for r in chem.reactions: rate=r.propensity(state) if rate: target=r.fire(state);self.assertEqual(target.totals,(9,9));self.assertEqual(target.word,word) counts=tuple(sum(target.counts[2*i:2*i+2]) for i in range(2));aggregated[counts]=aggregated.get(counts,0)+rate self.assertEqual(aggregated,dict(chain.transitions(n))) # A contaminant replacing one food molecule survives every enabled step. state=MolecularState((1,1,2,0,7,7)) for r in chem.reactions: if r.propensity(state):self.assertGreater(r.fire(state).counts[1],0) # Reverse 2S -> S+F consumes no last copy; no factorial divisor. state=MolecularState.pure(9,(0,0),(2,1));r=chem.reactions[1];self.assertEqual(r.propensity(state),2) def test_exact_partition_refill_and_failed_mass(self): division=FairDivision(9) for n in range(1,10):self.assertEqual(sum(F(comb(n,k),2**n) for k in range(1,n)),1-division.empty_probability(n)) parent=MolecularState((7,0,0,6,2,3));d=division.allocate(parent,(3,0,0,2,1,2)) self.assertTrue(d['success']);self.assertEqual(d['total_food_added'],18);self.assertEqual(d['left'].counts,(3,0,0,2,6,7));self.assertEqual(d['right'].counts,(4,0,0,4,5,5)) failed=division.allocate(parent,(0,0,0,2,1,2));self.assertFalse(failed['success']);self.assertEqual(failed['total_food_added'],18) # Enumerate a contaminated parent allocation: both pure original daughters impossible. contaminated=MolecularState((2,1,2,0,0,1));small=FairDivision(3) for left in product(*(range(n+1) for n in contaminated.counts)): d=small.allocate(contaminated,left) self.assertFalse(d['left'].admitted(3,(0,0)) and d['right'].admitted(3,(0,0))) def test_exact_generator_certificates(self): for K,s,C,q in [(9,3900,F(2523,160),F(8046297159,8112104000)),(20,9000,F(2535,131072),F(7077818258231,7077927321600))]: cert=DriftCertificate.compute(CountChain(Parameters(K)),s);self.assertEqual(cert.residual,C);self.assertEqual(cert.maximum_violation,0);self.assertEqual(cert.lower(20),q) box=DriftCertificate.operating_box();self.assertEqual(box.residual,F(279,32));self.assertEqual(box.lower(20),F(114080769,115203200)) slow=DriftCertificate.compute(CountChain(Parameters(9,F(1),F(100))),3900);self.assertEqual(slow.lower(20),0) def test_stationary_balance_and_transient_interaction(self): for K in (3,9,20):self.assertTrue(CountChain(Parameters(K)).verify_detailed_balance()) a=CountChain(Parameters(3,coupling=F(0)));b=CountChain(Parameters(3,coupling=F(1))) self.assertEqual(a.stationary(),b.stationary());self.assertGreater(np.max(abs(a.transition_matrix(.0001)-b.transition_matrix(.0001))),.01) self.assertNotEqual(dict(b.transitions((1,1)))[(2,1)],dict(b.transitions((1,2)))[(2,2)]) def test_restart_lineage_family_and_matrix_accuracy(self): chain=CountChain();kernel=RestartKernel(chain,20);cert=DriftCertificate.compute(chain,3900);q=float(cert.lower(20));u=float(FairDivision.joint_success((9,9))) rows=kernel.matrix.sum(axis=1);self.assertLess(kernel.row_error,1e-12);self.assertTrue(np.all(rows>=q));self.assertTrue(np.all(rows<=u)) stationary=sum(p*FairDivision.joint_success(n) for n,p in chain.stationary().items());self.assertLess(abs(min(rows)-float(stationary)),1e-9) lineage=kernel.lineage(20);family=kernel.family(3) self.assertTrue(np.all(lineage[-1]>=q**20-1e-9));self.assertTrue(np.all(lineage[-1]<=u**20+1e-9)) self.assertTrue(np.all(family[-1]>=1-7*(1-q)-1e-9));self.assertTrue(np.all(family[-1]<=u**7+1e-9)) # At T=0, K=3 admitted (1,1) cannot successfully divide. No renormalization. tiny=RestartKernel(CountChain(Parameters(3)),0);self.assertEqual(tiny.matrix[0].sum(),0) # Both children of a successful split of (2,2) are (1,1); depth two fails. self.assertAlmostEqual(tiny.family(1)[1,-1],.25);self.assertEqual(tiny.family(2)[2,-1],0) self.assertLess(np.max(abs(chain.transition_matrix(.002)-chain.transition_matrix(.001)@chain.transition_matrix(.001))),1e-10) def test_sharp_geometry_budget_and_decoder(self): regions=CompositionRegions(4);best=min(sum(abs(a-b) for a,b in zip(p,q)) for w,ps in regions.regions.items() for v,qs in regions.regions.items() if w!=v for p in ps for q in qs) self.assertEqual(best,F(1,2));self.assertEqual(regions.margin(),(F(1,2),F(1,4))) for word,ps in regions.regions.items(): for p in ps:self.assertEqual(regions.nearest(p)['word'],word) self.assertTrue(regions.nearest((F(1,4),)*4)['tie']) larger=CompositionRegions(9);reading=(F(1,9)-F(1,20),F(1,20),F(8,9),0) self.assertEqual(larger.nearest(reading)['word'],(0,0)) # L1 error 1/10 < 1/9 self.assertEqual(max(FairDivision.joint_success((r,s)) for r in range(1,17) for s in range(1,18-r)),F(32385,32768));self.assertLess(budget_ceiling(17),F(99,100));self.assertGreater(budget_ceiling(18),F(99,100)) def test_complete_cycle_and_unfinished_status(self): chemistry=FiniteFoodChemistry();cycle=ScheduledCycle(chemistry);initial=MolecularState.pure(9,(0,1),(1,1)) stopped=cycle.run(initial,np.random.default_rng(1),max_events=0);self.assertFalse(stopped['batch']['completed']);self.assertIsNone(stopped['success']);self.assertIsNone(stopped['division']) short=ScheduledCycle(chemistry,F(1,100)).run(initial,np.random.default_rng(1));self.assertTrue(short['batch']['completed']);self.assertEqual(short['division']['total_food_added'],18) self.assertEqual(short['batch']['state'].totals,(9,9));self.assertEqual(short['batch']['state'].word,(0,1)) with self.assertRaises(ValueError):cycle.run(MolecularState.pure(9,(0,0),(9,9)),np.random.default_rng(1)) if __name__=='__main__':unittest.main()