Standalone computational specification

for _ in range(samples): a = rng.uniform(0.05, 0.95) u = rng.uniform(0.05, 0.95) lo, hi = a * u, a * u + 1.0 - a # Fractional positioning avoids a fixed endpoint margin. m = lo + rng.uniform(0.1, 0.9) * (hi - lo) psi = witness(a, u, m) for S in ((0,), (1,)): worst_df = max( worst_df, diagonal_residual_defect(strategy, psi, S, (0,)) ) worst_cocycle = max( worst_cocycle, abs(phi(a) * phi(u) - phi(m) * phi(a * u / m)) ) x = rng.uniform(0.05, 0.95) y = rng.uniform(0.05, 0.95) worst_product = max( worst_product, abs(phi(x) * phi(y) - phi(sqrt(x * y)) ** 2) ) worst_identity = max(worst_identity, abs(phi(x) - x))

return "sampled_diagonal_defect": worst_df, "sampled_cocycle_defect": worst_cocycle, "sampled_product_defect": worst_product, "sampled_phi_identity_defect": worst_identity, "status": "sampled diagnostics only",

def one_shot_ledger_from_ranks(ranks, s, s_out): ranks = tuple(ranks) require(bool(ranks) and all(isinstance(r, int) and r > 0 for r in ranks), "supply positive Choi ranks after removing zero maps") R = sum(ranks) e = ceil_log2(R) e_split = ceil_log2(len(ranks)) + ceil_log2(max(ranks)) require(s_out + e >= s, "ranks/dimensions cannot support the required isometry") return "environment_dimension": R, "environment_qubits": e, "aligned_environment_qubits": e_split, "one_shot_peak": s_out + e, "additional_slots_beyond_input": s_out + e - s, "status": "arithmetic with supplied ranks",

def run_exact_regressions(): g = Geometry( cap=(("A", 2), ("B", 2), ("C", 1)), latent=( ("ab1", frozenset(("A", "B"))), ("ab2", frozenset(("A", "B"))), ("bc", frozenset(("B", "C"))), ("ca", frozenset(("C", "A"))), ), ) g1 = activate(g, "ab1", "A", ("link", "ab1")) g2 = activate(g1, "ab2", "A", ("link", "ab2")) require(len(g2.active) == 2, "parallel identifiers collapsed") require(g2.mu() == g.mu(), "activation did not conserve mu") expect_guard_failure( lambda: activate(g2, "ab1", "A", ("link", "ab1")) ) g3 = activate(g2, "bc", "B", ("link", "bc")) expect_guard_failure( lambda: activate(g3, "ca", "C", ("link", "ca")) ) expect_guard_failure( lambda: retire_capacity( g3, "A", ("cap", "A"), occupancy="A": 2 ) ) g4 = retire_capacity(g3, "A", ("cap", "A"), occupancy="A": 1) g5 = delete_active(g4, "ab2", ("link", "ab2")) g6 = delete_latent(g5, "ca", ("link", "ca")) require(g6.mu() == g3.mu() - 3, "retirement ledger wrong")