\section{The First Derived Frontier}
\label{sec:frontier}

The recursive kernel creates new work and new evidence. That success exposes
pressures the triad names but does not by itself operationalize. KFD-4, KFD-5,
and the draft KFD-6 are the first derived responses
\cite{kfd2026alpha42}. They are introduced here only to demonstrate the
foundation's generative force; their full mechanism belongs to companion
work.

\subsection{KFD-4: facts are viewed from somewhere}

KFD-1 preserves a declared fact world, but no participant consumes every fact
from every position. Relevance, consequence, visible object boundaries, and
available action depend on perspective. If a view hides its observer and
transformation history, selection can masquerade as reality and undermine the
trust assessment built on it.

KFD-4 therefore requires views to remain bound to declared perspectives. A
perspective-bearing view identifies its observer position, accepted fact cut,
projection boundary, consequence position, and known gaps. Changing
perspective may change relevance or presentation without silently changing
the source identities and causal relations required for comparison.

This is a direct pressure on the triad:

\begin{equation}
\text{non-drifting facts} + \text{multiple participants}
\Longrightarrow \text{declared perspective}.
\end{equation}

The Observer Paper develops this problem independently. The foundation needs
only the dependency: a stable world does not imply a view from nowhere.

\subsection{KFD-5: the world may lack an object}

Repeated action may reveal that the current ontology cannot economically
describe a recurring part of reality. Participants reconstruct the same
boundary, responsibility, or causal unit because no load-bearing object names
it. KFD calls a candidate object with independent identity, boundary,
authority, lifecycle, and operations a \emph{Primitive}.

The triad constrains discovery. Candidate genesis may come from judgment,
perspective transformation, anomaly, causal analysis, compression, or another
declared method. Qualification must remain separate. It asks whether facts,
alternatives, falsifiers, and real work support allowing the candidate to
carry responsibility. A compelling name or coherent model cannot certify
itself.

This pressure can be written as:

\begin{equation}
\text{successor facts} + \text{repeated reconstruction}
\Longrightarrow \text{candidate genesis} \neq \text{qualification}.
\end{equation}

KFD-5 is therefore not an unrelated creativity principle. It applies KFD-1
and KFD-2 to revision of the world itself, while KFD-3 lets different
participants contribute counterexamples and value judgments without fusing
their authorities.

\subsection{KFD-6: experience may support repeated discovery}

Once causal work histories become inspectable, an agent may compare many
Episodes and propose missing objects. The draft KFD-6 asks whether that
process can scale while remaining grounded in causal experience and unable to
certify itself. Corpus cuts, instrumentation loss, held-out evidence,
intervention bounds, and independent promotion authority become load-bearing.

The companion paper \emph{From Episodes to Primitives} develops this path
\cite{episodesPaper2026} as:

\begin{align}
\text{perspective-bound replay}
&\rightarrow \text{candidate genesis}
\rightarrow \text{independent qualification} \nonumber \\
&\rightarrow \text{held-out evaluation}
\rightarrow \text{separate promotion authority}.
\end{align}

KFD-6 remains draft. The relevant foundation result is not that autonomous
discovery already works. It is that scaling the recursive loop creates an
explicit new proof obligation: generated narrative must not replace the
causal world from which it claims to learn.

\subsection{Evaluation program}

The foundation should be evaluated by capabilities, not agreement with its
language:

\begin{description}[leftmargin=*,style=nextline]
  \item[Fact continuity.]
    Give independent participants the same declared coordinate at different
    times. Detect whether its meaning, gaps, and authority boundary remain
    recoverable or change silently.
  \item[Reliance test.]
    Give a fresh participant a claim and its declared evidence. Test whether
    the participant can recover the purpose, checked facts, residual risk, and
    responsibility without private oral context.
  \item[Cooperation-independence test.]
    Remove privileged interfaces and hidden prompts. Test whether participants
    can still inspect value and constraints, refuse or choose a bounded path,
    and leave a reviewable commitment.
  \item[Loop-integrity test.]
    Inject failure, reversal, missing evidence, or a contradictory consequence.
    The successor world should expose qualification or disagreement rather
    than rewrite the prior cut or synthesize success.
  \item[Alternative-kernel test.]
    Accept a narrower or differently named model if it preserves the same
    world, judgment, and action continuity at lower cost.
\end{description}

These tests can falsify an implementation and may narrow the theoretical
claim. Independent adoption and comparative measurement remain necessary
before asserting cross-domain sufficiency.
