from __future__ import annotations import json from itertools import combinations import numpy as np import pytest from axiomesh.core import * from axiomesh.esre_v01 import rank_mod, solve_affine def chain(d, p=101): a, b = np.eye(d, dtype=np.int64), np.eye(d, dtype=np.int64) for j in range(d-1): (a if j % 2 == 0 else b)[j,j+1] = 1 return np.eye(d, dtype=np.int64)[:1], {'a':a,'b':b} @pytest.mark.parametrize('d', [2,3,4,7,12]) def test_closure_exact_and_frozen(d): p=101; q, ops=chain(d); c=close_operators(q,ops,p) assert c.rank==d assert c.row_operator_products==2*d assert c.depth==d-1 x=np.arange(d, dtype=np.int64)**2 % p f=c.compile(c.basis @ x % p) for word in [(),('a',),('a','b'),('b','a','a','b')]: assert np.array_equal(f.run(word),q @ word_matrix(word,ops,p) @ x % p) for row,w in zip(c.basis,c.witnesses): assert np.array_equal(row,q[w.query] @ word_matrix(w.word,ops,p)%p) @pytest.mark.parametrize('seed', range(10)) def test_random_closure(seed): rng=np.random.default_rng(seed); p=7; d=5 q=rng.integers(p,size=(2,d)); ops={a:rng.integers(p,size=(d,d)) for a in ['a','b']} c=close_operators(q,ops,p); x=rng.integers(p,size=d); f=c.compile(c.basis@x%p) assert rank_mod(c.basis,p)==c.rank for t in ops.values(): assert rank_mod(np.vstack([c.basis,c.basis@t%p]),p)==c.rank for _ in range(10): word=tuple(rng.choice(['a','b'],size=8)) assert np.array_equal(f.run(word),q @ word_matrix(word,ops,p) @ x % p) def test_static_recovery_is_not_future_recovery(): q,ops=chain(3); m=Memory(np.eye(3,dtype=np.int64)[:2],np.array([3,4]),101) assert m.recall(q)[0]=='exact' c=close_operators(q,ops,101) cert=hole_certificate(c,m) assert cert['status']=='ambiguous' and len(cert['word'])==2 v=np.array(cert['null_vector']); assert not np.any(m.matrix@v%101) assert int(q[0]@word_matrix(cert['word'],ops,101)@v)%101!=0 assert weave(q,ops,m).status=='ambiguous' def test_acquisition_lower_bound_and_transaction(): p=101; q,ops=chain(8); x=np.arange(8,dtype=np.int64) m=Memory(q,q@x%p,p) calls=[] def oracle(row): calls.append(row) return int(row@x)%p with pytest.raises(RuntimeError): weave(q,ops,m,oracle=oracle,observation_budget=6) assert len(calls)==0 result=weave(q,ops,m,oracle=oracle,observation_budget=7,erasure_budget=3) assert result.status=='committed' and result.acquisitions==7 and len(calls)==7 assert len(result.capsule.shares)==11 @pytest.mark.parametrize('seed',range(5)) def test_all_erasures_within_radius(seed): p=17; y=np.random.default_rng(seed).integers(p,size=4) capsule=Capsule.encode(y,p,3) for removed in combinations(capsule.shares,3): status,out=capsule.erase(removed).recover() assert status=='exact' and np.array_equal(y,out) assert capsule.erase(list(capsule.shares)[:4]).recover()[0]=='ambiguous' def test_one_corruption_bounded_distance(): y=np.array([2,3,4]); c=Capsule.encode(y,17,2) for i in c.shares: bad=Capsule(c.p,c.rank,dict(c.shares));bad.shares[i]=(bad.shares[i]+1)%17 assert bad.recover()[0]=='inconsistent' status,out=bad.correct(1) assert status=='exact_within_declared_radius' and np.array_equal(y,out) def test_insufficient_error_radius(): assert Capsule.encode(np.array([1,2]),17,1).correct(1)[0]=='uncertified_radius' def test_inconsistent_memory_rejected(): m=Memory(np.array([[1,0],[1,0]]),np.array([2,3]),7) assert m.recall(np.array([[1,0]]))[0]=='inconsistent' with pytest.raises(ValueError): m.acquire(np.eye(2,dtype=np.int64),lambda r:0,observation_budget=2) def test_chart_overlap_and_transport(): p=11; c1=np.array([[1,1,0],[0,1,0]]);c2=np.array([[0,1,1],[0,0,1]]) shared,a,b=overlap(c1,c2,p) assert len(shared)==1 assert np.array_equal(a@c1%p,b@c2%p) assert np.array_equal(shared,a@c1%p) def test_emergence_requires_mixed_words(): q,ops=chain(12) e=emergence_rank(q,[{'a':ops['a']},{'b':ops['b']}],101) assert e['isolated_ranks']==[2,1] assert e['isolated_union_rank']==2 and e['emergence_rank']==10 def test_partial_execution(): p=7; m=Memory(np.array([[1,0]]),np.array([3]),p) ops={'reset':np.zeros((2,2),dtype=np.int64),'swap':np.array([[0,1],[1,0]])} q=np.array([[1,0]]) assert execute_partial(m,ops,q,())['output']==[3] assert execute_partial(m,ops,q,('swap',))['status']=='ambiguous' assert execute_partial(m,ops,q,('reset','swap'))['output']==[0] def test_json_roundtrip_and_no_source_state(): p=101;q,ops=chain(4);x=np.arange(4,dtype=np.int64) c=close_operators(q,ops,p);f=c.compile(c.basis@x%p) capsule=Capsule.encode(f.seed,p,2).erase([1,2]) obj={'program':f.json_object(include_seed=False),'memory':capsule.json_object()} assert 'seed' not in obj['program'] out=json.loads(json.dumps(obj)); status,y=Capsule.from_json(out['memory']).recover() g=FrozenModel.from_json(out['program'],seed=y) assert status=='exact' and np.array_equal(f.run(('a','b')),g.run(('a','b'))) def test_empty_actions(): q=np.eye(4,dtype=np.int64)[:2]; c=close_operators(q,{},7) assert c.rank==2 and c.row_operator_products==0 def test_zero_observable(): q=np.zeros((1,3),dtype=np.int64);m=Memory(np.zeros((0,3),dtype=np.int64),np.array([],dtype=np.int64),7) assert weave(q,{'a':np.eye(3,dtype=np.int64)},m).status=='zero_observable' def test_product_budget(): q,ops=chain(4) with pytest.raises(RuntimeError):close_operators(q,ops,101,product_budget=2) @pytest.mark.parametrize('badp',[0,1,4,100]) def test_invalid_prime(badp): with pytest.raises(ValueError):close_operators(np.eye(2,dtype=np.int64),{},badp) def test_shape_errors_and_singular(): with pytest.raises(ValueError):inverse(np.zeros((2,2),dtype=np.int64),7) with pytest.raises(ValueError):close_operators(np.eye(2,dtype=np.int64),{'a':np.zeros((1,2),dtype=np.int64)},7) with pytest.raises(ValueError):coordinates(np.array([[0,1]]),np.array([[1,0]]),7) with pytest.raises(ValueError):Memory(np.eye(2,dtype=np.int64),np.array([1]),7) with pytest.raises(ValueError):Capsule.encode(np.ones(5,dtype=np.int64),5) def test_budget(): b=Budget(10);b.charge('closure',4);b.charge('memory',3) assert b.remaining==3 with pytest.raises(RuntimeError):b.charge('too much',4) with pytest.raises(RuntimeError):b.charge('negative',-1) def test_affine_embedding_matches_group(): from axiomesh.esre_v01 import CentralExtension p=17;w=np.array([[0,3],[-3,0]])%p;group=CentralExtension(w,p) q,ops=affine_extension_operators(w,p);x=np.array([4,5]);z=7;h=np.r_[x,z,1] word=('+0','+1','-0','-1') actions=[] for action in word: u=np.zeros(2,dtype=np.int64);u[int(action[1:])]=1 if action[0]=='+' else -1 actions.append((u,0)) state=(x,z) for action in actions:state=group.multiply(state,action) assert int((q@word_matrix(word,ops,p)@h%p)[0])==state[1] @pytest.mark.parametrize('d',[3,5,8,12]) def test_minimal_fractal_tether(d): p=101;q,ops=chain(d);x=np.arange(d,dtype=np.int64)**3%p parent=Memory(np.eye(d,dtype=np.int64),x,p) split=split_with_tether(q,ops,parent,[['a'],['b']]) assert split.tether_symbols==d-2 assert split.parent_rank==d and split.child_union_rank==2 restored=FractalSplit.from_json(json.loads(json.dumps(split.json_object()))).reunify() assert restored.status=='committed' for word in [(),('a','b','a','b'),('b','a')]: assert np.array_equal(restored.offspring.run(word),q@word_matrix(word,ops,p)@x%p) if d>2: pieces=split.children child_mem=Memory(np.vstack([m.matrix for m in pieces]),np.concatenate([m.rhs for m in pieces]),p) assert weave(q,ops,child_mem).status=='ambiguous' def test_split_rejects_missing_cover_or_unidentified_parent(): q,ops=chain(3);m=Memory(q,np.array([2]),101) with pytest.raises(ValueError):split_with_tether(q,ops,m,[['a']]) with pytest.raises(ValueError):split_with_tether(q,ops,m,[['a'],['b']]) @pytest.mark.parametrize('depth',[0,1,2,3]) def test_recursive_fracture(depth): p=101;d=7;q=np.eye(d,dtype=np.int64)[:1];ops={} for j in range(d-1): t=np.eye(d,dtype=np.int64);t[j,j+1]=1;ops[f't{j}']=t x=np.arange(d,dtype=np.int64)**2%p tree=fractalize(q,ops,Memory(np.eye(d,dtype=np.int64),x,p),max_depth=depth) tree=json.loads(json.dumps(tree)) result=regenerate_tree(tree) assert result.status=='committed' word=tuple(reversed(list(ops))) assert np.array_equal(result.offspring.run(word),q@word_matrix(word,ops,p)@x%p)