Entropy, Rendering Capacity, and the Origin of Axiom A3: Why Does c(t) Decline? A Candidate Mechanism, Tested and Reported Honestly

Axiom A3 ("c(t) decreases monotonically over cosmic time") has always been asserted, notderived, inherited from Paper 1's fitted power law and never independently motivated. This paperexplores whether entropy production, rather than an unexplained decline in c itself, is the morefundamental driver: c(t) as a symptom of a shrinking rendering budget, not a free-standingpostulate. The framework combines Paper 10's "Total First Rendering" as a low-gravitational-entropyorigin state (in Penrose's sense) with Paper 7's committed/uncommitted cell bookkeeping into afixed holographic capacity S_max and an entropy-throttled c(t). It resolves a standing internalcontradiction in Paper 10 (gravity classified as both a topological mode and a rendering-densityeffect) and offers a structural reason why α_G is the one force coupling that isn't constant whilethe other three are. Tested quantitatively, the specific production law does not yet outperformthe project's existing empirical curve fits, and a direct attempt to unify the entropy drivingc(t) with the entropy setting cosmic temperature fails cleanly, showing that gravitational/structural entropy and thermodynamic/radiation entropy are distinct quantities that cannot becollapsed into one variable. A separate three-observable BBN convergence (helium-4, deuterium,and neutrino decoupling all pointing to the same narrow temperature-law exponent) stands as agenuine, unexplained empirical target for what a correct production law should predict. Allfindings, including the negative ones, are reported plainly.