The Grammar of Stability: Recursive Unit Formation and the Thermodynamics of Causal Saturation

We propose a scale-free organizational framework (“Grammar of Stability”) in which physical regularities, biological complexity, and cognitive/social architectures can be treated as repeated solutions to a single constraint: finite local capacity to index and maintain consistency among causal dependencies. We model the universe as a self-updating causal ledger—a locally finite partial order of events whose durable updates constitute stable constraints, and whose coarse-grained synchronization topology yields effective spacetime structure. Within this ledger, high-variance processes (“Words”) are selectively stabilized into write-locked primitives (“Letters”) that become the substrate for the next layer of composition. Three mechanisms are introduced. First, write-lock is an irreversible stabilization that creates durable ledger entries and must incur thermodynamic cost. Second, the Twist is defined strictly as a selection functional biasing which candidate stabilizations persist into durable entries; its origin is left agnostic. Third, causal saturation drives layer transitions: when realized local dependency structure approaches a maximum indexable causal density, the system self-heals either by (i) discrete Word→Letter write-lock events that reduce representational burden at the current grain, or (ii) a global “carry-forward” reformatting of indexability (inflation-like expansion of effective address space at a new admissible grain), with a hot exit interpreted as the dissipation footprint of massive irreversible compression. To avoid universal-clock objections, we define Capacity as a graph-geometric bound: the maximum indexable causal density within a bounded causal region (an Alexandrov interval / causal diamond) consistent with legible coarse-grained description at resolution . We define Load as realized causal density (or its incremental pressure) and analyze behavior via the dimensionless saturation ratio . A minimal hybrid toy model is provided in which a stability potential accumulates over ledger update steps but triggers discrete write-lock events upon threshold crossing, yielding critical intermittency near . We further show how boundary-limited indexability implies horizon-like interface simplicity and area-scaling of maximal hidden complexity. Discriminators emphasize (i) quantitative intermittency near criticality and (ii) dissipation budgets consistent with a hot post-carry-forward state.