We present a recursive compression protocol (RCP) for learning a shared codec, and report empirical evidence for two distinct compression regimes in AI-to-AI symbolic communication. Eight automated experiments tested recursive compression across substrates (GPT-4o, Claude Sonnet 4) and conditions. The primary experiments identified a broadcast regime (Level 1, 2-5.5x compression, 6.8 cold-start fidelity on a 0-10 scale) and an ansible regime (Level 4+, 50-95x compression, 0.9 cold-start fidelity). Validation experiments established that the broadcast-ansible boundary is grammar-independent, the noise floor for random symbols is 0.8/10, semantic attractor basins are stable across runs while specific symbols are path-dependent, and a warm vs. cold fidelity comparison demonstrates a measurable private communication channel (7-point gap). A pre-registered human validation study (N=46, AsPredicted #271640) confirms the warm-cold fidelity gap: blind raters preferred warm expansions for emotional content (d=2.25, p=2.28e-19) with a domain-selective interaction (emotional gap 5.96 vs. factual gap 2.52, p=6.95e-10). The two-regime structure suggests recursive compression naturally produces communication channels with public (broadcast) and private (ansible) layers. Correction note (2026-02-04): The file originally uploaded with this record (RCP_Paper_Draft_v10.docx) contained an earlier manuscript version with incorrect numerical values and a different paper structure. It has been replaced with the corrected version (RCP_Paper_v11.docx). The corrected values: ansible-regime cold-start fidelity is 0.9/10 (was incorrectly reported as 0.7/10 in the original file), and Experiment 1 L4+ cold fidelity is 0.8/10 (was reported as 1.0/10). All claims in the current file have been verified against raw experimental data.