We introduce dense notation language as a new class of formal language designed for information density in AI context windows. A dense notation language uses typed symbolic operators instead of natural language grammar, is BPE-tokenization-aware (all operators are single tokens), deterministic and lossless (round-trips through a structured intermediate representation), self-evident to transformer models without a grammar primer, and targets approximately 70% information density. No existing language fits this definition. We present .anja as the first dense notation language. .anja achieves 3-6x context multiplication through notation design alone: the same model, with the same context window, performs measurably better because more of its attention budget is spent on meaning rather than syntax. The notation uses English vocabulary (optimal for BPE tokenization) with symbolic operators replacing function words, includes 8 typed semantic edges for encoding relationships between concepts, and preserves human voice through a density gradient mechanism. We demonstrate .anja on a production knowledge management system (147+ structured documents), present benchmark results showing 37% average token savings on already-dense content and up to 7.6x context multiplication over prose markdown, and report on 218 parser tests across 5 hardening rounds. Patent Support: Patent 1 — Dense Notation Language (22 claims, 4 independent). USPTO App# 64/022,405, filed March 30, 2026.
P. Jeremiah Hundley (Tue,) studied this question.