Definition. Capability vector and conditional frontier [ftip-00JM]
AGENTDRAFTED
For an architecture record \(A\), optimizer record \(O\), systems record
\(S\), evaluation configuration \(\mathfrak e\) from Definition [ftip-00CE], and
declared intervention \(\eta \) at cost cap \(C\), define the
capability vector
\[
\mathbf K(A,O,S,\mathfrak e,\eta ,C)
=\bigl (K_{\rm state},K_{\rm adapt},K_{\rm repr},
K_{\rm plast},K_{\rm port}\bigr ).
\]Its coordinates respectively record state access, adaptive computation,
representation and abstraction, plasticity, and portability under the named
task, intervention, evaluation law, and cost accounting. A coordinate may be a
descriptive field, an estimand, or \(\bot \) when the record is missing,
incompatible, or not measured. The tuple is therefore not a common scalar and
does not order architectures without a declared comparison rule.
The five coordinates attach to the existing ceiling layers conditionally:
representation claims first require a map from \(A\); optimizer-reachable
plasticity requires \((A,O)\); state, adaptive computation, and portability
claims require the relevant \((A,O,S)\) interface, task family, and deployment
regime. A systems-feasible claim also carries \(C\), the cost vector and its
declared scalarization. The records in Definition [ftip-00JH], Definition [ftip-00JI],
Definition [ftip-00JL], and Definition [ftip-00CE] remain authoritative.
The scalar frontier \(V_A(C)\) of Definition [ftip-00JJ] is a projection onto the
declared utility \(J_{\rm ev}\) for one architecture and intervention envelope;
it is not a capability coordinate. For a fixed evaluation configuration, a
vector-valued study may instead retain the conditional set
\[
\mathcal F_{\mathfrak e}(C)
=\operatorname {Pareto}\left \{
\bigl (\mathbf K(A,O,S,\mathfrak e,\eta ,C),
J_{\rm ev}(P_{A,\eta }),\mathbf c(P_{A,\eta })\bigr ):
c_A(\eta )\leq C
\right \},
\]where Pareto dominance is declared for the reported coordinates. The set
is conditional on the task, intervention class, evaluation law, cost vector,
and missingness rule; it is not a universal intelligence frontier.
Matched-compute arms in § [ftip-00JU] compare entries only after stating
which coordinates are held fixed, which are allowed to vary, and how the cost
vector is charged. Cost, numerical stability, and monitorability remain
evaluation coordinates alongside the vector, so a lower scalar cost or a
stable implementation is not silently counted as a capability increase.