Official Open-Science Verification Repository for the Genomic Information Theory & Double-Stranded Codon Torus Research Programme (Complete with 568 MB Pre-Cached NCBI RefSeq/GenBank Archives, Zero-RNG Proofs & Pre-Computed Audit Reports).

Unlike standard bioinformatics repositories that require hours of external FTP downloads before a single test can run, this repository includes the entire 568 MB local NCBI cache (cds_cache/, 103 SHA-256 verified genomic files) and all pre-computed verification outputs (results_verified/):

For decades, synthetic biology and industrial mRNA design have relied on a zero-order assumption: if you replace every sense codon with its single "most frequent" human synonym (the Max-CAI / Max-GC3 standard), the amino-acid sequence on paper remains 100% identical, so translation should only improve.

Our mathematical theorems on the discrete codon torus $\mathbb{T}_4^3 = (\mathbb{Z}/4\mathbb{Z})^3$ and independent experimental wet-lab findings in Nature have converged to prove why this assumption fails:

In a landmark experimental study published in Nature (Mulroney et al., Nature 625, 189–194, 2024; DOI: 10.1038/s41586-023-06800-3), researchers from the Universities of Cambridge and Oxford tested in vitro, in HeLa cells, in mice, and in human blood samples how ribosomes translate artificially modified, codon-optimized mRNA (BNT162b2):

In the main text of Mulroney et al. (2024), the authors state that no adverse clinical outcomes have been associated with these frameshifted polypeptides. Yet on page 194 of the exact same Nature paper, under Competing interests, the fine print reads:

"T.E.M. and A.E.W. are inventors on a pending patent application (2305297.0) related to mRNA technology."

If single-codon Max-CAI / Max-GC3 optimization had no structural defect, there would be no need to file commercial UK Patent Application No. 2305297.0 to algorithmically recode mRNA sequences against ribosomal frameshifting. Without resolving ribosomal stalling and out-of-frame run-on translation, next-generation mRNA therapeutics (especially high-dose, repeat-dosing oncology and enzyme-replacement therapies) hit a fundamental biological barrier.

Where wet-lab mass spectrometry observed the downstream symptom (localized stalling and $+1$ frameshifting), our exact algebraic and information-theoretic audit across 54 RefSeq species and 9,834,024 held-out codon transitions uncovers the two-part mathematical root cause:

Strict Separation of Static "Form" vs. Dynamic Sequential "Program": Zero-order nucleotide frequencies, GC3 isochores, marginal codon usage (CAI), and single-stranded Chargaff/Perez 32-mirror-pair balances describe the static compositional form of a sequence (the 32-dimensional mirror-even subspace $V_+ \subset \mathbb{R}^{64}$). This programme measures the dynamic sequential program—the first-order and medium-range ($L = 30$ codons) conditional transition structure $P(C_i \mid C_{i-1})$ living on the mirror-odd subspace $V_-$ and the synonymous fiber bundle after all compositional, amino-acid, and strand-parity marginals are absorbed.

Zero Monte Carlo Surrogates in the Torus Proofs (codon_torus_real_audit_v3_bnt162b2.py): Every theorem in Preprint II (codon_torus_logos_perez_v3.tex.pdf) is proved deductively in exact algebra and information theory and audited analytically via exact plug-in conditional mutual information, held-out Dirichlet-smoothed log-likelihoods, and asymptotic/exact contingency-table likelihood-ratio ($G^2$) statistics with closed-form degrees of freedom ($\text{df} = 2709, 2460, 1849, 1681, 860, 779, 400, 361$). Zero random number generators are used (zero_random_generators_used = True).

Every Integer Is Derived (Anti-Numerology Policy): Every integer appearing in the torus framework ($2, 3, 4, 6, 7, 8, 16, 19, 20, 21, 24, 32, 40, 41, 42, 43, 48, 54, 56, 60, 61, 62, 63, 64, 361, 400, 779, 860, 1681, 1849, 2460, 2709$) is derived explicitly from a group order, free orbit count, simplex dimension $\sum_a (k_a - 1)$, or contingency-table degree-of-freedom formula.

Part I: The Double-Stranded Codon Torus $\mathbb{T}_4^3 = (\mathbb{Z}/4\mathbb{Z})^3$ & Exact Decompositions (v3.2–v3.5)

1. Duplex Geometry, Mirror Involution $\rho$, and the Two-Strand Fibration $\alpha_{\text{dup}}: 64 \to 56$

Discrete Torus & Fixed-Point-Free Involution (Theorem 2.5 & Corollary 2.6): Under $e: {\text{A,C,G,T}} \to \mathbb{Z}/4\mathbb{Z}$, the 64 codons form the discrete torus $\mathbb{T}4^3 = (\mathbb{Z}/4\mathbb{Z})^3$. Watson–Crick reverse complementation $\rho(c) = -Rc + 3\mathbf{1} \pmod 4$ is a fixed-point-free affine isometry in both Hamming ($d_H$) and Lee ($d{\text{Lee}}$) metrics, partitioning $\mathbb{T}4^3$ into 32 mirror orbits and splitting $\mathbb{R}^{64} = V+ \oplus V_-$ ($\dim V_+ = \dim V_- = 32$).

The 8-Doublet Theorem (Theorem 4.3): While the single-strand genetic code $\alpha: \mathbb{T}4^3 \to \mathcal{A}$ ($64 \to 21$) leaves a 43-dimensional synonymous simplex bundle ($41$ on sense codons), evaluating the code on both strands via $\alpha{\text{dup}}(c) = (\alpha(c), \alpha(\rho(c)))$ maps the sense wobble base onto the antisense leading base, partitioning $\mathbb{T}_4^3$ into 48 singletons and 8 binary doublets ({TAA,TAG}, {CAA,CAG}, {TCG,TCT}, {CCG,CCT} and their $\rho$-duals {TTA,CTA}, {TTG,CTG}, {CGA,AGA}, {CGG,AGG}) across 56 joint channels, collapsing the duplex synonymous dimension from $43$ to $64 - 56 = \mathbf{8}$.

2. Exact Tripartite, Quadripartite, and Two-Strand Decompositions Across 9 RefSeq Genomes (9,834,024 Held-Out Transitions)

For any joint distribution of consecutive codons $(C_{i-1}, C_i)$ with $A_i = \alpha(C_i)$ and $A_i^\rho = \alpha(\rho(C_i))$, total bigram mutual information decomposes with zero stationarity assumptions (Theorems 5.3, 5.4, 5.5):

$$I(C_{i-1}; C_i) = \underbrace{I(A_{i-1}; A_i)}{\text{Protein dipeptide syntax}} + \underbrace{I(C{i-1}; A_i \mid A_{i-1})}{d{2b}\text{ (Codon}\to\text{AA context)}} + \underbrace{I(A_{i-1}; C_i \mid A_i) + I(C_{i-1}; C_i \mid A_{i-1}, A_i)}{S{\text{syn}} = I(C_{i-1}; C_i \mid A_i) = S_{\text{anti}} + S_{\text{dup}}}$$

By Corollary 4.4, under $\rho(c) = -Rc + 3\mathbf{1} \pmod 4$, the sense preimages of the termination codons $\text{Stop} = {\text{TAA, TAG, TGA}}$ in antiparallel antisense frame -0 are exclusively the three wobble-A codons $\rho^{-1}(\text{Stop}) = F_{\text{Leu,Stop}} \cup F_{\text{Ser,Stop}} = {\text{TTA, CTA, TCA}}$, while the sense preimage of the canonical antisense start codon ATG is the wobble-T Histidine singleton $\rho^{-1}({\text{ATG}}) = F_{\text{His,Met}} = {\text{CAT}}$.

1. Universal Biosphere Invariant Across 54 Cellular RefSeq Taxa ($0.1416 \le \text{GC3} \le 0.9177$)

Evaluated against the 10-level null hierarchy (H0–H7), all 52 guard-passing cellular assemblies pass all 7 strict bootstrap criteria (d2b, d3, d3b, ΔH4(30), Δ5, Δ6, Δ7 $> 0$ at 95% CI), and all 55 cached assemblies are verified in results_verified/05_biosphere_55taxa_smoke/report_smoke.md.

Full report in results_verified/02_intron_exon_p53_ras_v14_6/p53_intron_exon_audit.md. Across all 14 human genes (TP53, TP63, TP73, BRCA1, PTEN, RB1, GAPDH, ACTB, HBB, KRAS, NRAS, HRAS, MYC, APOE), concatenated coding exons have $d_{3b} > 0$ (mean $+0.1721\text{ nats/codon}$, $0.00$ internal stops/100 codons) while excised introns ($-0.3097$, contrast $+0.48181\text{ nats/codon}$) and whole unspliced pre-mRNAs across all 3 reading frames (contrast $+0.41616\text{ nats/codon}$) are strictly negative ($14/14$, $p = 2^{-14} = 6.1 \times 10^{-5}$). In TP53, the mutable DNA-binding core (exons 5–8, codons 125–300, where 86% of somatic cancer mutations cluster) carries $2.34\times$ higher $d_{2b}$ ($+0.0989$ vs. $+0.0423$) and $1.78\times$ higher $d_{3b}$ ($+0.1454$ vs. $+0.0816$) than flanking exons.

Full report in results_verified/03_frontier_and_jcvi_syn_v14_7/frontier_audit.md. All 4 giant DNA viruses (Mimivirus, Megavirus, Pandoravirus, Pithovirus), all 4 deep-biosphere extremophiles (Desulforudis audaxviator at 2.8 km depth, Methanopyrus kandleri at $122^\circ\text{C}$, Aquifex aeolicus, Pyrococcus furiosus), and the Asgard archaeon Prometheoarchaeum syntrophicum MK-D1 pass STRICT_7/7_PASS. Blind cross-scoring under wild-type Mycoplasma mycoides isolates the foreign engineered vector genes (MMSYN1_0915 lacZ $d_{3b} = -0.4564$, MMSYN1_0918 HIS3 $-0.4286$, MMSYN1_0914 bla $-0.2353$) in JCVI-syn1.0 and confirms $0/412$ disrupted essential genes in JCVI-syn3.0 (while all 10 intergenic watermark cassettes $\ge 600\text{ nt}$ collapse to $d_{3b} \in [-0.4559, -0.1964]$).

Full report in results_verified/04_viral_trojan_and_maxcai_crash_v14_8/chimera_hgt_trojan_audit.md:

Clone the repository and run the master verification script run_all_audits.sh:

git clone https://github.com/Dr-Logvinovich/codon-torus-syntax.git cd codon-torus-syntax bash run_all_audits.sh

Or run individual modules directly:

1. Built-in unit tests (8 NCBI genetic code tables, 32 mirror orbits, 56 duplex channels, chain-rule < 1e-15):

python3 super_codon_proof_v14_8.py --self-test python3 -c "import codon_torus_real_audit_v3_bnt162b2 as ct; print(ct.self_test_torus_theorems())"

2. Double-Stranded Codon Torus Audit (9 RefSeq genomes + 17q22 locus + BNT162b2 & mRNA-1273 forensics):

python3 codon_torus_real_audit_v3_bnt162b2.py --cds-dir cds_cache --out-dir results_verified/01_codon_torus_and_bnt162b2_v3_5 --bnt162b2-audit

3. 14-Gene Human RefSeqGene Intron-Exon, Splicing & TP53/RAS Oncogenic Hotspot Audit (v14.6):

python3 super_codon_proof_v14_8.py --intron-exon-audit --intron-exon-genes TP53,TP63,TP73,BRCA1,PTEN,RB1,GAPDH,ACTB,HBB,KRAS,NRAS,HRAS,MYC,APOE --cds-dir cds_cache --out-dir results_verified/02_intron_exon_p53_ras_v14_6

4. 13-Genome Frontier Biosphere & Venter JCVI-syn1.0/3.0 Forensics Audit (v14.7):

python3 super_codon_proof_v14_8.py --frontier-audit --cds-dir cds_cache --out-dir results_verified/03_frontier_and_jcvi_syn_v14_7

5. Viral "Genetic Trojan" Scanner, Organelle OS Rewriting & Biotech Max-CAI Crash Test (v14.8):

python3 super_codon_proof_v14_8.py --chimera-audit --cds-dir cds_cache --out-dir results_verified/04_viral_trojan_and_maxcai_crash_v14_8

Citation (BibTeX)

@misc{LogvinovichPerez2026FormToProgram, author = {Logvinovich, Victor and Perez, Jean-Claude}, title = {{From Form to Program: Medium-Range Conditional Codon Syntax Inside Real Genes}}, year = {2026}, month = oct, version = {v14.8}, doi = {10.5281/zenodo.23479667}, url = {https://zenodo.org/records/23479667}, note = {GitHub Repository: https://github.com/Dr-Logvinovich/codon-torus-syntax, ORCID: 0009-0007-2040-6955, 0000-0001-6446-2042} }

@misc{LogvinovichPerez2026CodonTorus, author = {Logvinovich, Victor and Perez, Jean-Claude}, title = {{The Double-Stranded Codon Torus: Duplex Mirror Fibration of DNA Coding Space, Markovian Lumpability, and Information-Theoretic Consequences}}, year = {2026}, month = oct, version = {v3.5}, doi = {10.5281/zenodo.23508080}, url = {https://doi.org/10.5281/zenodo.23508080}, note = {GitHub Repository: https://github.com/Dr-Logvinovich/codon-torus-syntax, ORCID: 0009-0007-2040-6955, 0000-0001-6446-2042} }

Key External References on Ribosomal Stalling & mRNA Codon Optimization

Mulroney, T. E., Pöyry, T., Yam-Puc, J. C., et al., & Willis, A. E. (2024). $N^1$-methylpseudouridylation of mRNA causes $+1$ ribosomal frameshifting. Nature, 625(7993), 189–194. DOI: 10.1038/s41586-023-06800-3 (See also Competing Interests, p. 194: UK Patent Application No. 2305297.0).

Fang, E., Liu, X., Li, M., et al., & Li, J. (2022). Advances in COVID-19 mRNA vaccine development. Signal Transduction and Targeted Therapy (Nature portfolio), 7(1), 94. DOI: 10.1038/s41392-022-00950-y.

License

This project is licensed under the MIT License (code & scripts) and CC BY 4.0 (manuscripts & figures) — see the LICENSE file for details.