human_below_life
plain-language theorem explainer
The declaration establishes that the rung for human compositional language lies strictly below the life-ignition threshold on the Z-complexity ladder. Researchers assembling the full chain of animal-cognition rungs cite this inequality when proving the complete ordering from counterfactual floor through vertebrates and cetaceans. The proof is a direct unfolding of the two constant definitions followed by numeric normalization.
Claim. Let $r_H = 17$ denote the rung assigned to human compositional language and $r_L = 19$ the life-ignition rung. Then $r_H < r_L$.
background
The module introduces the Z-complexity ladder as a geometric sequence indexed by integer rungs $k$, with values proportional to powers of the self-similar fixed point phi. Named thresholds include the bond rung at $k=8$ for sustained molecular recognition, the counterfactual-floor rung at $k=5$, the vertebrate rung at $k=12$, the octopus rung at $k=14$, the cetacean rung at $k=15$, the human rung at $k=17$, and the life rung at $k=19$ marking self-sustaining biological recognition from Biology.IgnitionThreshold.
proof idea
The proof is a one-line wrapper that unfolds the definitions of z_rung_human and z_rung_life, then applies norm_num to confirm the numeric inequality 17 < 19.
why it matters
This inequality supplies the final link required by the downstream rung_ordering theorem, which assembles the full strict chain z_rung_cf < z_rung_bond < ... < z_rung_human < z_rung_life. It completes the structural ordering of named rungs in the animal-cognition arc of Recognition Science, consistent with the phi-ladder forced by the Recognition Composition Law and the eight-tick octave.
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