The admissibility inequality inv(Pε; L) ≤ ν(Vε(L)) holds across all 240 STRUC-I κ-step evaluations of the QT ribozyme fitness landscape. The compensation criterion D(G) ≤ C(G) is satisfied for all three STRUC-BIO-I configurations. Zero clean violations were recorded under either instrument. The biological fitness landscape is fully admissible under the Universal Structural Law.
| LADDER NAME | TYPE | N | SUB? | MEAN Aκ | MIN Aκ | MEAN ρ | MAX ρ | ρ(κ=1) | STATE |
|---|---|---|---|---|---|---|---|---|---|
| complete10_double_global_ladder | double substitution fitness | 2,000 | YES | 1.0000 | 1.0000 | 0.0813 | 0.3235 | 0.3235 | Stable Structure |
| bp_mutants_global_ladder | base-pair mutation fitness | 69 | NO | 1.0000 | 1.0000 | 0.1717 | 0.4486 | 0.4486 | Stable Structure |
| complete10_single_global_ladder | single substitution fitness (complete) | 133 | NO | 1.0000 | 1.0000 | 0.2216 | 0.4215 | 0.4215 | Stable Structure |
| combined_single_global_ladder | combined single substitution fitness | 133 | NO | 1.0000 | 1.0000 | 0.2771 | 0.4120 | 0.4120 | Stable Structure |
| combined_del_single_global_ladder | deletion + single substitution combined | 46 | NO | 0.9994 | 0.9970 | 0.5540 | 0.5929 | 0.5348 | Weak Persistence |
| deletion_global_ladder | length-altering deletion mutations | 2,000 | YES | 1.0000 | 1.0000 | 0.8190 | 0.9057 | 0.7360 | Boundary-Stabilized |
The substitution-only fitness ladders (complete10_double, bp_mutants, complete10_single, combined_single) all achieve Aκ = 1.0000 at every κ-step with mean ρ̄ ranging from 0.081 to 0.277. This places them between the GOE baseline (0.087) and nuclear spectra (0.197) — structurally in the same regime as physically measured energy level spectra. The complete10_double ladder (ρ̄ = 0.081) is the lowest-pressure molecular fitness ladder in the full corpus, comparable to H₂O rovibrational spectra.
The combined_del_single ladder (n=46), which ranks deletion and single-substitution fitness values together, achieves mean ρ̄ = 0.554 with min_Ak = 0.997 — Weak Persistence. This exceeds the previous corpus maximum of ρ = 0.424 (Si_density, condensed-matter). The degradation is modest (Aκ = 0.9994 on average) and confined to the highest κ values. The law is satisfied; the elevated pressure indicates that mixing deletion-type and substitution-type fitness ranks within a single ladder creates structurally distinct geometry that approaches the persistence boundary.
The pure deletion ladder (n=2,000 subsampled) achieves ρ̄ = 0.819, max ρ = 0.906, and ρ at κ=1: 0.736. Despite this extreme structural pressure — the highest recorded for any physical system in the corpus — Aκ remains 1.0000 at every κ-step. This is the defining signature of Boundary-Stabilized: high pressure but complete admissibility. Deletion mutations represent a fundamentally different mode of sequence perturbation compared to substitutions; their fitness landscape appears to carry a structural fingerprint closer to the adversarial boundary without crossing it.
All substitution ladders show ρ(κ) curves that rise, fluctuate, and partially stabilise — consistent with multi-scale gap structure interacting with the vulnerability envelope. The deletion ladder profile is a smooth, near-monotonic rise from ρ ≈ 0.08 at κ = 0.01 to ρ ≈ 0.91 at κ ≈ 0.8, then slightly descending to ρ = 0.74 at κ = 1.0. This featureless profile suggests that deletion-induced fitness ranks lack the hierarchical gap structure that creates the mid-κ inflection points seen in physically meaningful ladders. The combined_del_single curve is flat at ρ ≈ 0.55–0.59 across nearly all κ, indicating constant structural pressure without κ-dependent features.
The measured QT45 landscape (D=72, C=2,235, ρ = 0.0322, z = +4.22) places the catalytic RNA's fitness landscape in the same structural pressure tier as the complete10_double STRUC-I ladder and near H₂O rovibrational spectra — the most relaxed physical systems in the 3,313-evaluation corpus. The law is satisfied with a margin of C/D = 31.0×. The z = +4.22 indicates the observed ρ is significantly above the null model, confirming genuine compensatory structure rather than statistical noise.
The full-44-position hybrid run has ρ ≈ null and z = −0.68, because the uniform fidelity shift makes 99.9% of doubles appear compensatory — saturating C and erasing signal. The 12-position window, without this saturation, achieves z = +10.27 with predominantly negative mean epistasis (−0.694), indicating that the positional subset under study carries strongly antagonistic epistasis that structurally elevates ρ above null. This divergence suggests that catalytic-core positions have fundamentally different epistatic architecture from the peripheral positions.
STRUC-I finds mean ρ̄ = 0.081–0.277 for substitution ladders; STRUC-BIO-I finds ρ = 0.032–0.226 for three genotype graph configurations. Despite measuring different mathematical objects — admissibility of fitness rank sequences (STRUC-I) vs epistasis compensation in double-mutant graphs (STRUC-BIO-I) — both instruments return STABLE verdicts with ρ values in the same absolute range as GOE random matrices and nuclear/molecular spectra. This cross-instrument consistency is the strongest evidence that biological fitness landscapes obey the same structural constraint as physical systems.
Zero violations were recorded across 240 STRUC-I κ-step evaluations and 3 STRUC-BIO-I runs. All Aκ ≥ 0.997. All D ≤ C. The biological fitness landscape is empirically non-falsified under the admissibility inequality.
The four substitution ladders cluster tightly. The complete10_double ladder (ρ̄ = 0.081) is comparable to H₂O rovibrational spectra. The combined_single ladder (ρ̄ = 0.277) is the highest-pressure substitution ladder, approaching the nuclear maximum. STRUC-BIO-I confirms: QT45 clean ρ = 0.032.
Deletion ladders (ρ̄ = 0.554–0.819) exceed the prior physical maximum of ρ = 0.424 (Si_density). The deletion_global_ladder is Boundary-Stabilized with Aκ = 1.0000, establishing that this elevated pressure does not imply violation. The structural law holds, but deletion landscapes are geometrically unlike substitution landscapes and warrant separate admissibility tracking.
The null model shuffles single-mutant fitness labels while holding double-mutant values fixed. QT45 clean ρ = 0.032 sits 4.22σ above the null mean of 0.030 — the observed compensatory structure exceeds random expectation. The 12-position hybrid at z = +10.27 shows the strongest signal of any configuration, driven by the positional restriction isolating antagonistically epistatic core positions. The full hybrid z ≈ 0 is an artefact of near-uniform fidelity correction collapsing all epistasis to positive.
No prior physical domain produced a Boundary-Stabilized verdict. The deletion ladder (ρ̄ = 0.819, Aκ = 1.0000) is the first. Simultaneously, the complete10_double fitness ladder (ρ̄ = 0.081) matches the most relaxed rovibrational molecular spectra. The biological domain therefore spans the widest ρ range of any single subject in the corpus: 0.081–0.819 — a factor of 10× from lowest to highest. This range exceeds condensed-matter (0.015–0.424, factor 28×) and nuclear (0.103–0.257, factor 2.5×) in absolute spread.