The Attention Budget: A Dynamics of Meaning-Systems Why a meaning-field has a master equation, in what currency it is paid, and how a system can starve with no one starving it

Abstract The dynamics of a meaning-system requires a budget. Energy will not serve — not because meaning is unconserved, but because in a society with surplus calories and insufficient waking hours, energy is no longer the quantity that runs out first. We argue that the budget is attention flux, and show that it satisfies the four conditions a budget must satisfy: bounded, rate-limited, carrying a minimum maintenance cost, and exactly the quantity contemporary information systems actually compete for. We state four theorems. Theorem 1 (conservation): within a window of constant total pool in which the multiplier is uncorrelated with the current share, share conservation pins the tail index of the attention-share distribution at one, so no allocation rule can move it; the only thing it can move is share concentration, read on the full-spectrum concentration coordinate. That independence premise is new in this version, and it may fail precisely in the setting this paper cares about, so it is written as a pre-test that must be run first. Theorem 2 (devaluation): what buys meaning is never the flux but the product of active fraction and flux; a platform's objective is to maximise the first and minimise the second, so this is not a price war but a currency devaluation. Theorem 3a (share axis): for a regime change in the share distribution the identification delay can lengthen only while the total pool grows — and this inherits Theorem 1's independence premise in full. Theorem 3b (stock axis): the distinguishability of the drainage of the meaning stock falls as the volatility-to-drift ratio of the stock distribution rises; this is where the subtitle's answer lives, and it carries one modelling assumption, marked C-tier. We further give six falsifiable predictions, two independent falsification routes, an equivalent test that bypasses tail estimation, an evidence-independence table, and an execution ledger. The ledger reads: as of this version, the number of executions on external data is zero. That fact matters as much as the claims above and must be cited with them.