HK-OS
DETERMINISTIC-CONSTRAINT-BUILD
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
S_{t+1}
GENERATE_CANDIDATE: l_i = (S_t, e_i, S_{t+1}, tau_i)
VALIDATE_CONSTRAINTS:
I(S_t) == I(S_{t+1}) AND
dA + dE == dL + dR AND
V(l_i) == 1
HASH_OUTPUT: SHA3-256(l_i || L_t)
]]>
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