Language as Constraint Geometry: Tripartite Attractor Structure in Tokenized Biological Communication Systems without External

Language as Constraint Geometry presents a reductionist, systems‑theoretic account of why all pre‑literate biological communication systems collapse into exactly three stable structural regimes. Instead of treating linguistic diversity as an unbounded cultural artifact, the paper shows that when a tokenized channel is subject to three universal pressures—acoustic or medium degradation, strict working‑memory limits, and intergenerational fidelity without external storage—the feasible structural space contracts to a thin manifold containing only three dynamically stable redundancy geometries. Under human biological parameters, these take the form of: (A) rhythmic‑segmental lattices, (B) harmonic‑contour architectures, and (C) templatic‑positional frames. The theory is derived from five axioms modeling serial copying under noise, bounded feature budgets, memory depth ≈4 ± 1 chunks, and zero external substrate, yielding a constraint polytope whose minima correspond exactly to the observed attractors. The paper illustrates these geometries through three ecologically extreme communication environments—dense‑canopy drumming, open‑ocean navigational chant, and horizon‑based spatial signaling—and shows that these same structures appear in non‑human biological systems, including cetacean song, pheromone gradients, and the reading‑frame organization of the genetic code. The model predicts that any pre‑literate system must fall into one of the three basins, and that transitional corpora will preserve measurable signatures of their originating attractor. Four ancient undeciphered or minimally attested corpora are evaluated using only redundancy distribution, mutual‑information curvature, and boundary‑entropy profiles; all align with the predicted basins at statistical levels that exclude chance or local frequency artifacts. Language as Constraint Geometry provides a null hypothesis for the space of possible pre‑literate communication architectures and a general framework for understanding how biological, acoustic, and cognitive limits jointly determine the deep structure of human and non‑human signaling. It is offered as a minimal substrate for future empirical, computational, and decipherment work. Related Works (Series Map). This paper is part of a six‑paper series developing a geometric framework for cognition, language, and applied inference: The Origin of Emergence — foundational mechanics of emergence https://zenodo.org/records/18807724). A Geometric Theory of Cognition — keystone theory https://zenodo.org/records/18807724). Language as Cognitive Geometry — structural form → patterns of thought (https://zenodo.org/records/18805427). Language as Constraint Geometry — tripartite attractor structure (https://zenodo.org/records/18807009). A Universal Decoder for Lost Oral Cultures — applied decoding under sparse priors (https://zenodo.org/records/18807013). Toward a Structural Model of Relationship Compatibility — applied compatibility modeling (DOI: 10.5281/zenodo.18050285). Series hub: GTC is supplemented by the two language pillars (LCG, LCnG) and two applications (UDLOC, SMRC). OoE provides the foundational emergence model that informs GTC.