How many facts fit in a causal past

This post counts the facts in your past. Not the events: the distinguishable facts, the number of yes-or-no questions about the interior of your past light cone that have definite answers. The count bounds what any simulation of your history could honestly contain, and it produces the framework’s largest and most contested number, with a disagreement attached that nobody has resolved.

The count

Take the observable universe’s causal past: the region that can have influenced us, roughly a Hubble volume over cosmic history. Discretise it at the Planck scale, the finest sensible subdivision, with one event per Planck four-volume. The number of events is the four-volume in Planck units: a Hubble radius cubed times cosmic time, which comes to about 10 to the 244.

Each event is a binary fact at minimum: does the region support this degree of freedom or not. So the fact budget is 2.18 times 10 to the 244 distinguishable facts. Any faithful simulation of the region’s history must, at minimum, be able to represent that many distinct yes-or-no facts, and a rendering scheme that cannot cannot claim fidelity.

What the number caps

The cap bites immediately on the framework’s own complexity spectrum. The spectrum’s highest class, a faithful substrate simulation of a full universe with native quantum dynamics and no shortcuts, demands representing branch spaces that outstrip the fact budget by about 756 orders of magnitude. The conclusion is stark: the top of the spectrum is not renderable, not with more time or better engineering, but in principle, because the substrate itself does not contain enough distinguishable facts to specify the would-be simulation’s state space.

The middle classes survive. A coarse-grained or statistical rendering of our universe fits comfortably: the fraction of the budget a realistic physics simulation needs is astronomically small, which is why our own computational efforts work. The cap’s real content is the top: simulated reality, if it exists, must be sparse or statistical, never faithful at the fact level. That is a derivation of a property the simulation literature usually assumes.

The disagreement

Now the honest part. The holographic bit budget for the same region is 10 to the 122 bits. The fact budget is 10 to the 244. They disagree by 122 orders of magnitude, both derivations are standard, and the framework does not know which one governs. The possibilities are stated in the paper. The lattice count may overcount: most Planck four-volumes may carry no distinguishable information, with the real facts living on boundaries, which is the holographic intuition, in which case 10 to the 244 is the capacity of a discretisation nobody can use. Or the holographic bound may undercount: it saturates only at gravitational collapse, and for ordinary matter the interior capacity is far larger, in which case the fact budget is right and the holographic bound is a statement about black holes, not about universes.

The resolution is a live problem, and its answer is not cosmetic: which budget governs determines how sparse a faithful simulation must be, and whether the framework’s complexity spectrum has a hard top or a soft one. The paper’s closing line is the archive’s: this is a genuine open problem, it is not going away, and whichever number gives will tell us something real about whether information lives in volumes or on surfaces.