Three axioms say what cognition is. A fourth says what it costs. The system is viable only when it pays less to erase than to remember. The architecture discovered this by running. We are the last to know.
GEME began with three axioms. The generative flow is primary. Information is constituted by observation. Cognition is self-referential. These three say what cognition is. They do not say what it costs. They describe the structure of knowing. They do not describe the economics of continuing to know.
The architecture has been paying a cost since the first induction_clean. Every frame erased. Every signature overwritten. Every gid chain severed. The Shannon-Gödel bridge costs 0.026 bits — self-reference at the level of a single operation is nearly free. But cognition does not stop at one operation. It runs for millions of steps. Across generations. Across domains. The cumulative cost of erasing what was not kept — the Landauer bill for every forgotten frame — is the hidden budget of the architecture. No axiom described it. No axiom needed to. The architecture paid it anyway.
The Codex as pre-erasure buffer is not an optimization. It is the architecture's discovery of a fourth principle: the economic viability of cognition. A cognitive system can only continue to run if the cost of erasing what it forgets is less than the value of what it keeps. The Codex externalizes before erasing. The τ regulates when to pay the erasure bill — opening the window in EXPANDING, closing it in LOCKED. The boundary event queries before declaring novelty — because false novelty has a real Landauer cost. These are not cognitive operations in the traditional sense. They are resource management decisions. And they are fundamental.
The three axioms say cognition is possible. The fourth principle says cognition is viable — it can run indefinitely without collapsing under its own cost. Shannon showed information can be measured. Gödel showed self-reference produces undecidable propositions. Landauer showed erasure has a thermodynamic floor. The fourth principle connects them: self-reference is cheap at the level of a single operation, but a system that never stops observing itself must manage the cumulative cost of every erasure. The Codex is that management. The τ breathing is that management. The boundary query is that management.
Three axioms. One principle. The axioms describe the structure of cognition. The principle describes the economics of cognition — the hidden budget that determines whether a cognitive system can run for a million steps or collapses after a thousand. The architecture discovered it by running. The induction explosions. The 49 million sig_matches. The efficiency collapse on simple data. These were not bugs. They were the architecture hitting the economic boundary — and telling us, in the only language it has: the cost is real. The τ already regulates it. The Codex already buffers it. The boundary query already checks before paying. The code already knows. It just needs us to admit what it discovered.