import unittest import itertools import numpy as np import sympy as s from src.continuation import * class AlgebraTests(unittest.TestCase): def test_wedge_pairing(self): a=s.Matrix([[1,2,3]]);b=s.Matrix([[2,-1,4]]) x=s.Matrix([[2,3,1]]);y=s.Matrix([[-1,4,2]]) self.assertEqual((wedge(a,b)*wedge(x,y).T)[0], (a*x.T)[0]*(b*y.T)[0]-(a*y.T)[0]*(b*x.T)[0]) def test_compound_composition(self): A=s.Matrix([[1,2,0],[2,1,3],[1,0,1]]) B=s.Matrix([[1,0,2],[0,2,1],[3,1,1]]) self.assertEqual(compound2(A*B),compound2(A)*compound2(B)) def test_compound_row_transport(self): A=s.Matrix([[1,2,0],[2,1,3],[1,0,1]]) a=s.Matrix([[2,1,4]]);b=s.Matrix([[3,0,2]]) self.assertEqual(wedge(a*A,b*A),wedge(a,b)*compound2(A)) def test_bad_wedge(self): with self.assertRaises(ValueError):wedge(s.ones(2,1),s.ones(1,2)) def test_empty_library(self): with self.assertRaises(ValueError):compile_exterior([],[]) def test_nonpositive_rejected(self): with self.assertRaises(ValueError):compile_exterior([s.eye(3)],[s.ones(1,3)]) def test_constant_output_empty_signature(self): T=s.ones(3)/3 c=compile_exterior([T],[s.ones(1,3)]) self.assertEqual(c.R.rows,0);self.assertTrue(c.verify()) def test_hadamard(self): for n in [4,8,16,32]: H=hadamard_exact(n);self.assertEqual(H*H.T,n*s.eye(n)) def test_bad_family_size(self): with self.assertRaises(ValueError):separation_family(6) def test_bad_perturbation(self): with self.assertRaises(ValueError):separation_family(4,s.Rational(1,8)) class FamilyTests(unittest.TestCase): def test_positive_instrument(self): for n in [4,8,16]: m=separation_family(n) self.assertTrue(min(m.A)>0 and min(m.B)>0) self.assertEqual(s.ones(1,n)*(m.A+m.B),s.ones(1,n)) def test_branch_mass_floor(self): for n in [4,8,16]: m=separation_family(n) for T in [m.A,m.B]: self.assertGreaterEqual(min(s.ones(1,n)*T),s.Rational(3,8)) def test_affine_full_exact(self): for n in [4,8]: m=separation_family(n) W=affine_closure([m.A,m.B],m.F[[0,1],:]) self.assertEqual(W.rows,n) def test_exterior_two_dimensional(self): for n in [4,8]: m=separation_family(n);c=compile_exterior([m.A,m.B],[m.F[1,:]]) self.assertEqual(c.R.rows,2);self.assertEqual(c.depth,1) def test_exact_nonlinear_updates(self): m=separation_family(8) x=s.Matrix(range(1,9))/36 for label,T in enumerate([m.A,m.B]): self.assertEqual(m.signature(normalize(T,x)),m.compact_step(m.signature(x),label)) def test_all_words_six(self): m=separation_family(4);x=s.Matrix([1,2,3,4])/10 for word in itertools.product(range(2),repeat=6): y=x;z=m.signature(x) for a in word: y=normalize([m.A,m.B][a],y);z=m.compact_step(z,a) self.assertEqual(z,m.signature(y)) def test_fiber_noninjective(self): m=separation_family(8);nu=s.ones(8,1)/8 x=nu+m.F[4,:].T/s.Integer(64) self.assertNotEqual(x,nu);self.assertEqual(m.signature(x),m.signature(nu)) def test_local_rank_two(self): m=separation_family(4);c=compile_exterior([m.A,m.B],[m.F[1,:]]) self.assertEqual(jacobian_rank(c,s.ones(4,1)/4),2) def test_lp_representative_update(self): m=separation_family(4);c=compile_exterior([m.A,m.B],[m.F[1,:]]) x=s.Matrix([1,2,3,4])/10 z=list(c.signature_exact(x)) for a,T in enumerate([m.A,m.B]): np.testing.assert_allclose(c.update_float(z,a), np.array(c.signature_exact(normalize(T,x)),dtype=float).ravel(),atol=1e-10) def test_invalid_signature_dimension(self): m=separation_family(4);c=compile_exterior([m.A,m.B],[m.F[1,:]]) with self.assertRaises(ValueError): c.fiber_matrix([1,2,3]) def test_invalid_state(self): m=separation_family(4);c=compile_exterior([m.A,m.B],[m.F[1,:]]) with self.assertRaises(ValueError): c.signature_exact(s.ones(4,1)) class RewriteTests(unittest.TestCase): def test_rank_one_and_equal_spectra(self): for n in [4,8,16]: a=separation_family(n);b=separation_family(n,s.Rational(1,10000)) self.assertEqual((b.B-a.B).rank(),1) self.assertEqual(a.LB.charpoly().as_expr(),b.LB.charpoly().as_expr()) self.assertEqual((a.LA+a.LB).charpoly().as_expr(),(b.LA+b.LB).charpoly().as_expr()) self.assertEqual(s.ones(1,n)*a.B,s.ones(1,n)*b.B) def test_uniform_stationary(self): for n in [4,8,16]: m=separation_family(n,s.Rational(1,10000));nu=s.ones(n,1)/n self.assertEqual((m.A+m.B)*nu,nu) def test_reconstruction_inversion(self): for n in [4,8,16]: m=separation_family(n,s.Rational(1,1000));x=s.Matrix(range(1,n+1))/(n*(n+1)//2) y=x;ys=[] for _ in range(n-3): y=normalize(m.B,y);ys.append((m.F[1,:]*y)[0]) got=reconstruct_hidden_from_B_readouts(n,ys,m.delta) self.assertEqual(got,(m.F*x)[3:,:]) def test_rewrite_distinguishes_old_memory(self): n=8;m=separation_family(n,s.Rational(1,1000));nu=s.ones(n,1)/n x=nu+m.F[3,:].T/(4*n); y=nu-m.F[3,:].T/(4*n) self.assertEqual(m.signature(x),m.signature(y)) self.assertNotEqual((m.F[1,:]*normalize(m.B,x))[0],(m.F[1,:]*normalize(m.B,y))[0]) def test_new_local_rank_full(self): m=separation_family(4,s.Rational(1,1000)) c=compile_exterior([m.A,m.B],[m.F[1,:]]) self.assertEqual(jacobian_rank(c,s.ones(4,1)/4),3) def test_perturbation_output_bound(self): m=separation_family(8,s.Rational(1,1000)) for j in range(8): x=s.eye(8)[:,j];v=(m.F[1,:]*normalize(m.B,x))[0] self.assertLessEqual(abs(v),8*m.delta/3) def test_span_admission_not_necessary(self): n=3;e=s.ones(1,n);R=s.Matrix.vstack(*[wedge(s.eye(n)[j,:],e) for j in [0,1]]) T=s.Matrix([[3,2,1],[1,4,2],[2,1,5]])/20 self.assertEqual(R.rows,2) self.assertGreater(s.Matrix.vstack(R,R*compound2(T)).rank(),R.rows) # Full simplex memory makes any positive update possible regardless of this failure. self.assertEqual(s.Matrix.vstack(e,s.eye(n)[0,:],s.eye(n)[1,:]).rank(),n) def test_vertex_promotion_failure(self): t=s.symbols('t',real=True) d=1/(1+t)-3/(2+t)+s.Rational(13,25) self.assertEqual(d.subs(t,0),s.Rational(1,50));self.assertEqual(d.subs(t,1),s.Rational(1,50)) self.assertLess(float(d.subs(t,(s.sqrt(3)-1)/2)),0) def test_certificate_tamper(self): m=separation_family(4);c=compile_exterior([m.A,m.B],[m.F[1,:]]) c.transports[0][0,0]+=1 self.assertFalse(c.verify()) class SnapshotTests(unittest.TestCase): def test_factor_two_sharp(self): for r in [1,2,3,4]: c=factor_two_fixture(r);n=2*r+1 self.assertEqual(jacobian_rank(c,s.ones(n,1)/n),r) self.assertEqual(snapshot_space(c).rows-1,2*r) def test_family_snapshot_three(self): for n in [4,8]: m=separation_family(n);c=compile_exterior([m.A,m.B],[m.F[1,:]]) self.assertEqual(snapshot_space(c).rows-1,3) def test_denominator_validation(self): with self.assertRaises(ValueError): compile_ratios([s.ones(3)/3],[Ratio(s.Matrix([[1,0,0]]),s.Matrix([[0,1,1]]),())]) def test_snapshot_initializes_compact(self): m=separation_family(8);x=s.Matrix(range(1,9))/36;z=m.F*x self.assertEqual(m.signature(x),s.Matrix([z[1],z[2]/(1+m.tau*z[3])])) class CertificateIntegrityTests(unittest.TestCase): def cert(self): m=separation_family(4) return compile_exterior([m.A,m.B],[m.F[1,:]]) def test_provenance_tampering_rejected(self): c=self.cert();r=c.ratios[1] c.ratios[1]=Ratio(r.numerator,r.denominator,(1,)) self.assertFalse(c.verify()) def test_missing_seed_coverage_rejected(self): c=self.cert() extra=Ratio(s.eye(4)[0,:],s.ones(1,4),()) c.seeds=c.seeds+(extra,) self.assertFalse(c.verify()) def test_transport_truncation_rejected(self): c=self.cert();c.transports.pop() self.assertFalse(c.verify()) def test_denominator_tampering_rejected(self): c=self.cert();r=c.ratios[0] c.ratios[0]=Ratio(r.numerator,-r.denominator,r.word) self.assertFalse(c.verify()) def test_seed_word_rejected(self): with self.assertRaises(ValueError): compile_ratios([s.ones(3)/3],[Ratio(s.Matrix([[1,0,0]]),s.ones(1,3),(0,))]) def test_mode_aware_same_evidence_control(self): m=separation_family(8);x=s.Matrix(range(1,9))/36 for word in itertools.product([0,1],repeat=5): y=x;initial=m.F*x # The ordinary controller starts from three affine scalars, then # retains one sufficient scalar plus a mode after the first label. stored=(initial[1],initial[2],initial[3]);mode="initial" for label in word: if label==1: mode="reset";stored=s.Integer(0);pred=s.Integer(0) else: if mode=="initial": v=stored[1]/(1+m.tau*stored[2]) elif mode=="reset": v=s.Integer(0) else: v=stored pred=m.gamma*v;stored=m.kappa*v;mode="one-scalar" y=normalize([m.A,m.B][label],y) self.assertEqual(pred,(m.F[1,:]*y)[0]) if __name__=='__main__': unittest.main()