The Serial Decoding Basin τ: Five Experiments on Convergence, Thermodynamic Anchoring, and the Geometry of Receiver-Limited Throughput

This study presents five reproducible experiments investigating whether serial decoding systems converge to a finite information parameter. First, zero-free-parameter prediction: the M-ary rate-distortion formula predicts ribosome throughput to 0.0004 bits residual, outperforming a naive log2(M) null model in 2 of 4 testable systems. Second, basin significance: bio-plausible (M, ε) sampling places 90.5% of samples in the 3–6 bit band versus 28.3% for random sampling (p ~ 0). Third, evolutionary convergence: gradient ascent on cost-constrained utility independently discovers K* ~ 23 for the molecular substrate, within 2 of the genetic code's 21 amino acids. Fourth, asymptotic convergence: the running mean across 21 systems converges to 4.16 ± 0.19 bits (95% CI), with confidence interval width shrinking as 1/√n. Fifth, thermodynamic anchoring: using four independently measured physical parameters, the Hopfield–Piñeros–Tlusty model predicts Ieff = 4.387 bits against the observed 4.390, residual 0.003 bits. This anchors the ribosome's operating point to kT (a single, ribosome-specific anchor, not a claim about the basin as a whole) and generates a falsifiable prediction. Because resolved per-event information cannot exceed the alphabet ceiling log2(21) = 4.392 bits and the 1/T thermodynamic model reaches that ceiling at T = 309.6 K (essentially the 310 K physiological anchor), cooling below 310 K is predicted to manifest not as more bits per event but as a lower translation error rate (higher fidelity), while heating above 310 K lowers resolved information below the ceiling (Ieff = 4.00 bits at 340 K); both are testable by ribosomal misincorporation assays at controlled temperature. The serial decoding basin parameter is the centroid of a geometric constraint rather than a fundamental constant.