HK-OS DETERMINISTIC-CONSTRAINT-BUILD PROOF_BACKED_ARTIFACT STATIC_DECLARATION_ONLY NO_FAKE_RUNTIME_STATE NAND(x,x) NAND(NAND(a,b), NAND(a,b)) NAND(NAND(a,a), NAND(b,b)) OR(NOT(a), b) AND(IMPLIES(a,b), IMPLIES(b,a)) AND(OR(a,b), NOT(AND(a,b))) active(agent) => trusted(agent) entropy(agent) <= 0.20 candidates = transform(agent_state, n) accept(c) = entropy(c) <= 0.20 AND proof(c) = true SymmetricOperator Q = (Q + transpose(Q))/2 Shannon_Nats H = -sum(p ln p) H <= 0.20 Reject states violating entropy constraint. entries ordered by tau_i V(l_i) = 1 S_{t+1}.conserved = S_t.conserved + dA S_{t+1}.energy = S_t.energy + dE S_{t+1}.obligations = S_t.obligations + dL S_{t+1}.released = S_t.released + dR dA + dE = dL + dR I(S_t) = I(S_{t+1}) forall q in ConservedQuantities: q(S_t) == q(S_{t+1}) JournalEntry -> Boolean S_t --T_{e_i}--> S_{t+1} S_{t+1} --Record--> l_i = (S_t, e_i, S_{t+1}, tau_i) L_{t+1} = L_t union {l_i} V(l_i) ? Valid : Invalid Valid -> Reconcile(L_{t+1}) -> Commit RepositoryAudit SchemaHash RuleHash TransformHash ConstraintGraph ValidationResult ArtifactHash Verify all l_i in L_t satisfy V(l_i) = 1 Sum(dA) + Sum(dE) == Sum(dL) + Sum(dR) over L_t forall f in C_t: f(S_0) == f(S_t) Hash(L_t) -> WORM_Chain