Three decades of game security independently discovered the constraint specification. The four voids couple through the observer — and the arms race has no interior fixed point.
CS2, StarCraft 2, and Dota 2 each provide independent Pe measurements across different game mechanics — and all three confirm the same prediction: information asymmetry drives engagement outcomes.
Relative Pe across genres (clean/fog vs contested/scouted baseline):
Dashed line = Pe=1 boundary. All three game samples are supercritical. Chess is the control.
Multiplayer gaming isn't one void — it's four, coupled through the observer. Suspicion of an opponent feeds distrust of anti-cheat, which feeds conspiracy about matchmaking, which feeds hostility toward all opponents. Click each void to expand.
FPS, RTS, and fighting games each independently converged on the constraint specification — transparent, invariant, independent — through engineering failure. The framework predicts which cheat each architecture produces.
| Property | Implementation | What breaks when missing |
|---|---|---|
| Transparent | Server sees all game state | ESP / wallhack — client reads hidden state |
| Invariant | Server rules don't change per client claim | Speed hacks — client reports false position |
| Independent | Server runs on dedicated hardware | Host advantage — peer host controls authority |
| Property | Implementation | Cheat surface |
|---|---|---|
| Void flips | Every client has the complete game state | Maphack — fog of war is a rendering filter only |
| Constraint | Deterministic lockstep + desync detection | AoE2 shipped with an accidental built-in maphack on day one |
| Control case | aoe2.net publishes visible Elo | AoE2 community: minimal "rigged matchmaking" conspiracy vs hidden-MMR FPS |
| Property | Status | Consequence |
|---|---|---|
| Transparent | Complete — both peers see all state | No state-reading cheats possible |
| Invariant | Complete — rules are local and shared | Desync = immediate detection |
| Independent | Missing — no external authority | No structural anti-cheat possible |
Void index across 7 platforms (0–12). Chess.com is the constraint control: visible Elo dissolves two of the four voids.
Complete derivations — Pe floor theorem, arms race non-convergence proof, four-void coupling matrix, seven falsifiable predictions.
Paper 6 · v2.5 · February 2026 · MoreRight License v1.1 · 10.5281/zenodo.18738828