UNNS SUBSTRATE PROGRAM · BIOLOGICAL DOMAIN
STRUC-BIO · BIOLOGICAL CORPUS ANALYSIS
Full statistical audit of biological fitness landscape data under two instruments — CHAMBER STRUC-I v1.0.4 (admissibility inequality on fitness ladders) and CHAMBER STRUC-BIO-I v0.1 (epistasis compensation criterion on genotype graphs) · QT ribozyme · 45 nt catalytic RNA · 6 ladder types + 3 genotype configurations
6 STRUC-I LADDERS 3 STRUC-BIO-I CONFIGS 240 κ-STEP EVALUATIONS 1 WEAK PERSISTENCE CASE 1 BOUNDARY-STABILIZED CASE 0 VIOLATIONS
§0 CORPUS OVERVIEW
STRUC-I EVALUATIONS
240
6 ladders × 40 κ-steps
STRUC-BIO-I CONFIGS
3
QT45 clean + 2 hybrid
VIOLATIONS (Aκ < 1)
0
across all 240 runs
WEAK PERSISTENCE
1
combined_del_single
BOUNDARY-STABILIZED
1
deletion ladder — new regime
ρ̄ RANGE (STRUC-I)
0.081–0.819
complete10_double → deletion
STRUC-BIO-I ρ RANGE
0.032–0.226
QT45 clean → 12-pos hybrid
MAX Aκ DEGRADATION
0.997
combined_del_single min_Ak
QT45 D(G)
72
of 100 singles below WT
QT45 C(G)
2,235
compensatory double mutants
PRIMARY RESULT — UNIVERSAL ADMISSIBILITY HOLDS IN BIOLOGICAL FITNESS LANDSCAPE

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.

§1 STRUC-I v1.0.4 — FITNESS LADDER ADMISSIBILITY
LADDER SUMMARY TABLE ALL 6 QT RIBOZYME FITNESS LADDERS · STRUC-I v1.0.4 · κ ∈ [0.01, 1.0] · 40 STEPS · M=2000 MC

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

LADDER PRESSURE PROFILE MEAN ρ̄ · SORTED ASCENDING
complete10_double
0.0813
0.0813
bp_mutants
0.1717
0.1717
complete10_single
0.2216
0.2216
combined_single
0.2771
0.2771
combined_del_single
0.554 — Weak Persistence
0.554
deletion
0.819 — Boundary-Stabilized
0.819
Scale 0.00–1.00. Separator divides Stable Structure (top 4) from elevated-pressure cases (bottom 2).
Aκ ADMISSIBILITY DISTRIBUTION ALL 240 κ-STEP EVALUATIONS
Aκ = 1.000 (perfect)
238 / 240
238
Aκ ∈ [0.99, 1.000)
2
2
Aκ < 0.99
0
The 2 Aκ < 1.000 cases both belong to combined_del_single at high κ (min_Ak = 0.997). All 160 evaluations from the 4 substitution-only ladders are Aκ = 1.0000. The 80 deletion-ladder evaluations also maintain Aκ = 1.0000 throughout despite ρ̄ = 0.819 — confirming Boundary-Stabilized status (high pressure but not violating).
FINDING 1.1
Four substitution fitness ladders satisfy admissibility without degradation; their structural pressure (ρ̄ = 0.081–0.277) is consistent with nuclear spectra

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.

FINDING 1.2
combined_del_single enters Weak Persistence — the highest-pressure non-adversarial result in the full 3,313-evaluation corpus

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.

FINDING 1.3
The deletion fitness ladder is Boundary-Stabilized at ρ̄ = 0.819 — the first such result from a physical biological system — with Aκ = 1.0000 maintained throughout

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.

§2 ρ(κ) PROFILES — STRUCTURAL PRESSURE VS PERTURBATION SCALE
SUBSTITUTION LADDERS — ρ(κ) PROFILES SCALE 0–0.70
complete10_double
bp_mutants
complete10_single
combined_single
ELEVATED-PRESSURE LADDERS — ρ(κ) PROFILES SCALE 0–1.00
combined_del_single · Weak Persistence
deletion · Boundary-Stabilized
FINDING 2.1
The deletion ρ(κ) profile is monotonically rising and featureless — structurally unlike any other biological or physical ladder

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.

§3 STRUC-BIO-I v0.1 — EPISTASIS COMPENSATION CRITERION
QT45 v2 · CLEAN EXPORT · measured fitness
D(72) ≤ C(2,235) — SATISFIED
ρ = D/C
0.0322
regime
STABLE
z-score
+4.22
null ρ̄
0.0304
pos. epistasis
46.7%
mean E
+0.192
singles
100
doubles
4,791
Raw QT45 measured fitness. 44 positions × 3 substitutions minus 32 Hamming-0 strips = 100 singles. 72/100 singles below WT (D=72). 46.7% of doubles carry positive epistasis. ρ slightly above null (z=+4.22) — real structural signal.
HYBRID · FULL 44-POSITION · measured + fidelity f=0.900
D(132) ≤ C(947) — SATISFIED
ρ = D/C
0.1394
regime
STABLE
z-score
−0.68
null ρ̄
0.1398
pos. epistasis
99.9%
mean E
+15.16
singles
132
doubles
948
Hybrid: f_combined = f_measured + F̂(κ=0.900). Uniform fidelity shift pushes all 132 singles below WT (D=132). Near-total positive epistasis (99.9%) is driven by the flat fidelity correction. ρ indistinguishable from null shuffle (z=−0.68) — fidelity shift erases structural signal.
HYBRID · 12-POSITION WINDOW · measured + fidelity
D(36) ≤ C(159) — SATISFIED
ρ = D/C
0.2264
regime
STABLE
z-score
+10.27
null ρ̄
0.1458
pos. epistasis
26.8%
mean E
−0.694
singles
36
C(12,2)×9 = 594
12-position sub-window. 36/36 singles below WT. Negative mean epistasis (−0.694) — predominantly antagonistic. ρ = 0.226, z = +10.27: significantly above null, showing genuine structural signal distinct from random. All 594 doubles resolved (skipped = 0).
FINDING 3.1
QT45 measured fitness achieves ρ = 0.032 — placing the ribozyme among the most structurally relaxed systems in the full corpus

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.

FINDING 3.2
The 12-position hybrid window (z = +10.27) carries a stronger structural signal than the full-44-position run (z = −0.68), revealing positional dependence of the epistatic compensation structure

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.

§4 CORPUS CONTEXT — BIOLOGICAL DOMAIN VS PHYSICAL DOMAINS
STRUC-I ρ̄: BIOLOGICAL LADDERS VS CORPUS REFERENCE DOMAINS
— CORPUS REFERENCE —
Solar F10.7
0.022
Molecular (HITRAN)
0.103
Nuclear spectra
0.197
Condensed-matter
0.204
Cosmic Web (xyz)
0.305
— BIOLOGICAL (THIS STUDY) —
complete10_double
0.081
0.081
bp_mutants
0.172
0.172
complete10_single
0.222
0.222
combined_single
0.277
0.277
combined_del_single
0.554 — Weak Persistence
0.554
deletion
0.819 — Boundary-Stabilized
0.819
STRUC-BIO-I ρ: GENOTYPE GRAPH RESULTS VS STRUC-I CONTEXT
— STRUC-BIO-I (D/C CRITERION) —
QT45 clean (measured)
0.032
0.032
Hybrid full 44-pos
0.139
0.139
Hybrid 12-pos window
0.226
0.226
— STRUC-I BIO LADDERS (for scale) —
complete10_double (STRUC-I)
0.081
combined_single (STRUC-I)
0.277
STRUC-BIO-I ρ (D/C) and STRUC-I ρ (inv/ν) are formally distinct quantities. The QT45 clean result (ρ = 0.032) sits within the STRUC-I range of the substitution ladders. Cross-instrument consistency confirms robustness of the STABLE verdict.
FINDING 4.1
Cross-instrument consistency: both STRUC-I and STRUC-BIO-I independently place the QT ribozyme substitution landscape in the Stable Structure / GOE pressure tier

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.

§5 KEY FINDINGS SYNTHESIS
FINDING 5.1 — PRIMARY
The QT ribozyme fitness landscape satisfies the Universal Structural Law under both instruments and all configurations tested

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.

FINDING 5.2 — SUBSTITUTION REGIME
Point substitution fitness landscapes occupy the same structural pressure tier as nuclear spectra (ρ̄ = 0.081–0.277 vs nuclear 0.103–0.257)

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.

FINDING 5.3 — DELETION REGIME
Length-altering mutations produce a structurally distinct high-pressure regime not previously observed in any physical domain

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.

FINDING 5.4 — z-SCORE INTERPRETATION
QT45 clean (z=+4.22) and 12-pos hybrid (z=+10.27) show genuine structural signal above null; full hybrid (z=−0.68) is null-indistinguishable due to fidelity saturation

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.

FINDING 5.5 — CORPUS POSITION
The biological domain extends the corpus into structurally new territory at both ends: the most relaxed fitness ladder (complete10_double, ρ̄=0.081) and the highest-pressure physical ladders (deletion, ρ̄=0.819)

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.

STRUC-BIO Biological Corpus Analysis · UNNS Substrate Program · 2026-03-20
Subject: QT ribozyme · 45 nt catalytic RNA · QT45 v2 fitness dataset
Instruments: CHAMBER STRUC-I v1.0.4 (κ ∈ [0.01, 1.0] · 40 steps logspaced · M=2,000 MC runs · 6 fitness ladders · 240 evaluations) · CHAMBER STRUC-BIO-I v0.1 (3 configurations · 100/132/36 singles · 4791/948/594 doubles)
STRUC-I ladders: bp_mutants_global_ladder (n=69) · combined_del_single_global_ladder (n=46) · combined_single_global_ladder (n=133) · complete10_double_global_ladder (n=2000, subsampled) · complete10_single_global_ladder (n=133) · deletion_global_ladder (n=2000, subsampled)
STRUC-BIO-I configurations: QT45 v2 clean (measured fitness, Hamming-0 stripped) · Hybrid full 44-pos (measured + fidelity f=0.900) · Hybrid 12-pos window
Corpus context: biological evaluations contribute 240 STRUC-I runs to the full 3,313-evaluation UNNS corpus (3,069 physical + 240 biological + 4 cluster adversarial).