Preserved mathematical and computational biology work: proofs, code, and reproducibility evidence.
Research status — 2026-10-31: biological research and autonomous research runs have stopped at the owner's request. This repository preserves the existing work for inspection and reproduction. Project status · Complete project index · Consolidated PR history.
中文 · First result · Research roadmap · For reviewers · 媒体资料
Maintained by Shawn Zeng (Zijian Zeng) / ArtificialZeng. The retained work concerns biochemical oscillations, molecular switches, reaction networks, and scientific computing.
Each public claim retains its scope, evidence, and unresolved limitations. Merging a packet into this repository does not establish biological novelty, external peer review, or upstream acceptance.
| Project | Deliverable | Evidence status |
|---|---|---|
| Mixed-mechanism phosphorylation | Exact instability bound, validated attracting cycles and nonzero period correction | Linux interval certificates and independent exact audits; priority/human review pending |
| Paper-Code Auditor | Reproducible software defects and a history-grounded reconstruction patch | Offline CPU regression checks; no training-result or author confirmation |
| ORD Data Auditor | Identifier guard, frozen-sample audit, and a checksum warning patch | 42 datasets / 20,720 reactions reproduced; no chemical-identity or upstream-acceptance claim |
| Protein Metric Auditor | Full released-score NDCG order audit | 217 assays / 95 configurations; secondary-metric rank shifts only |
| MEMOTE direction audit | Equivalent-reaction counterexamples and a two-line direction fix | Real complete ATP detector integration; maintainer acceptance pending |
| Reversible Markov embedding audit | Exact rational four-state counterexample to one positive-spectrum embedding implication | Two exact checkers and fresh AI review; author review and priority pending |
| Directed-cycle identifiability | Exact endpoint counterexample to Conjecture 4.6 and interior-leak inclusion proof | Nonzero exact minor and rational inverse; original-author confirmation pending |
| Dual-futile-cycle partial results | Eight-parameter spectral classification; full-parameter determinant-conditioned positivity of Delta4 | Separate exact reconstructions; general sixteen-parameter stability conjecture unresolved |
| RNA short-helix placements | Exact three-helix coloring classification and a comparable-short corollary | 288 normalized cases; exact unique-fold checks; AI review completed, human review and priority pending |
| Example 8 stability audit | Source-specific Jacobian correction and full-domain local stability proof | Exact witness, two symbolic implementations, ordinary/optimized archive replay; no broad open-problem resolution |
| MEMOTE API cache audit | Sequential API cache-lifecycle repair | Real API red/green checks; same-suite mutation and concurrency outside scope |
| Native GLPK presolver audit | Exact-input false-optimal solver counterexamples and a limited branch guard | Two independent grids; scaled tolerance residual explicitly retained; upstream confirmation pending |
| Boundary-relay isola | Exact mass-action counterexample for a given one-parameter family | Fresh AI scope review and two exact implementations; human review and priority unconfirmed |
| Compartment allocation beta gap | Positive-probability explosion theorem for 7/8 < beta < 1 | Fresh substantive AI mathematical review and finite exact checks; human review/priority pending; no almost-sure claim |
| Coexistence with waning immunity | Full-parameter feasible-root classification and uniqueness under ordered invasion | Fresh AI mathematical review and four exact checkers; actual-model Question 2 answered, abstract Conjecture 1 unresolved |
| Adjacent-port catenary audit | Exact singular-locus and transfer-differential classification for all chain lengths | Fresh AI math review and two exact checkers; human review/priority pending |
| Proportional-scaling audit | Exact counterexamples including strictly increased postinfection mortality | Three exact certificate checks; known bistability credited, main constant-recruitment theorem untouched |
| Three- and four-particle ancestral circulation | Complete N3 sign law and exact N4 reversal with a fixed rate ordering | Full polynomial identities and two-colour verification; human review and priority pending |
| 3-sunlet dimension proofs | General group-based models and cyclic inversion-symmetric models | Uniform kernel proofs and independent exact certificates; author review and priority pending |
| Mantis conditioned stationary support | Reachable-class and outside-support correction for finite initial-conditioned laws | Exact component oracles and actual API replay; one disclosed pre-existing full-suite numerical failure |
| GillesPy2 ODE failure propagation | Reject failed backend steps before publishing future-labelled results | Analytic baseline/candidate replay and independent AI review; upstream maintainer confirmation pending |
| Two-graph Moran fixation bounds | Every connected noncomplete regular graph, both type orientations; all matching deletions retained | Exact sum-of-squares and polynomial proofs; arbitrary irregular graphs unresolved; human review pending |
| TreeSwift gamma audit | Correct branching intervals, label dependence and crown-stem handling | Exact sign-flip witness; 714 + 1,774 generated cases; upstream review requested; GPL-3.0 subproject |
| Cogent3 gap-distance audit | Correct row-order-dependent distances under pairwise deletion | Exact shared-column oracle and real public API reproduction; upstream review requested; BSD3 source notices retained |
| Multi-pathogen coexistence correction | Exact all-positive counterexamples to the simultaneous-endemic-equilibrium assertion in Djuikem–Arino2025 Conjecture5 | Full16D ODE/NGM replay and separate AI proof check; classical exclusion credited; author review pending |
| Catalytic response threshold | Complete six-positive-rate steady-response classification for source Fig. 14B | Exact proof, two checkers and fresh AI review; priority and author confirmation pending |
| Random-switching reaction networks: common-support counterexample · Example 44 proof | Literal Conjecture 43 fails; Conjecture 46 holds on an explicit slow-switching interval | Two distinct models, complete probability arguments and exact checks; fresh AI review, source-author confirmation pending |
| ETE RF polytomy correction | Correct shared-leaf topology correction and invalid negative distances | Genuine native baseline/candidate checks; known upstream issue credited; inherited full-suite failures disclosed |
| Periodic adaptation | Exact all-waveform mean deficit and attracting periodic response for a published reversible motif | Complete ODE argument and two exact checkers; fresh AI review, human/priority verification pending |
| Forward-response scope audit | Exact moment twins and a local finite-jet repair of subsidiary source claims | Independent exact recomputation and AI mathematical review; author verification pending |
| Fixed-target switching clarification | Exact finite switching-rate example for a specified target proportion | Two exact checks; equivalent dispersal theory credited; local AI review is not human peer review |
Upstream review requests (submitted in order; acceptance pending):Paper-Code PR #1 · ORD PR #1165.
Historical open-problem research: selection, results, and parked leads. The complete index also includes later packets absent from the introductory table above.
For the fixed published rates, P=8 and S=40, an attracting periodic branch exists in each fixed compatibility class for every sufficiently large finite kinase total K. In original model time,
The positive coefficient certifies a finite-concentration bias: this local branch approaches its limiting period from above. No numerical K0 or remainder constant is given. Proofs, Linux interval runs, exact independent audits, and figure. Qualitative robustness overlaps existing conference work; novelty of the strict model-specific period certificate remains pending expert confirmation. The full source conjecture is unresolved.
The mixed-mechanism phosphorylation model studied by Conradi, Mincheva, and Shiu has a unique positive equilibrium. Their 2019 paper asks whether it can remain unstable as total kinase grows arbitrarily large.
Our exact result: at the paper's Table 1 reaction rates, with total phosphatase 8 and total substrate 40, the equilibrium has exactly two unstable and four stable eigenvalues on its six-dimensional compatibility class for every finite
In particular, the result holds for every K ≥ 23. The bound is sufficient and is not claimed to be sharp. Rational equilibrium parametrization and 125 strictly positive rational Bernstein coefficients give a certificate for the entire unbounded range, rather than a finite parameter scan.
| Evidence level | Current status |
|---|---|
| Equilibrium instability over the stated range | Exact proof and executable certificate |
| Selected finite-K trajectories and extrema | Floating-point numerical evidence |
| Attracting periodic branch for every sufficiently large K | Interval limiting-cycle certificate plus local persistence; no explicit K0 |
| Original Conjecture 6.2 | First assertion addressed; full conjecture unresolved |
| Novelty and priority | Unconfirmed; directly related 2023/2025 conference work exists |
| External human peer review / biological experiments | None reported |
Unstable equilibrium does not by itself prove a periodic orbit. The current result concerns a published mathematical model; it does not establish new behavior in living cells.
Read the five-page note · Read the proof · Inspect the certificate
Numerical illustration, not a rigorous periodic-orbit certificate. The curves show finite-concentration effects and convergence toward a limiting model.
Python 3.12 or 3.13. The exact verification requires only SymPy and the Python standard library; no GPU, API key, or model weights are needed.
git clone https://github.com/ArtificialZeng/AI-Biology-Lab.git
cd AI-Biology-Lab
python3 -m venv .venv
source .venv/bin/activate
python -m pip install -r requirements-exact.txt
python scripts/reproduce.py verifyThis runs three checks: reconstruction of the manuscript matrix, a direct nine-equation formulation, and a second reduction with an exact tangent-space identity and Routh root count. Each uses rational arithmetic. Runs take place in a temporary copy; results are saved under ignored artifacts/ and the archived evidence stays unchanged. See reproduction instructions.
For numerical reproduction and figures:
python -m pip install -r requirements.txt
python scripts/reproduce.py numerics
python scripts/reproduce.py figure- Obtain an explicit finite-K threshold and a usable remainder constant.
- Certify amplitude corrections and clarify scalar-projection invariance.
- Extend the validated parameter region.
- Clarify priority with directly overlapping research and obtain external human review.
These remain uncompleted historical targets; no autonomous work is scheduled to pursue them. The roadmap preserves their acceptance criteria. External validation is required before claims of priority or resolution of the full conjecture.
projects/mixed-phosphorylation/ First research project, proof, data, and note
scripts/reproduce.py Reproduction entry point
docs/ Research plan, validation, and media information
.github/workflows/ Continuous exact verification
The project uses AI for derivation, coding, search, and review. Separate AI review passes and independent implementations are useful checks; they are not external human peer review. See AI use and provenance.
- Conradi, Mincheva, and Shiu (2019), Emergence of oscillations in a mixed-mechanism phosphorylation system, arXiv version used.
- Suwanmajo and Krishnan (2015), Mixed mechanisms of multi-site phosphorylation.
- Related work requiring priority clarification: Grasse, SBHD 2023, poster 48; Grasse and Conradi, BIOMATH 2025 abstract.
Third-party papers are linked, not redistributed. Original repository code is available under the MIT license; third-party code and data retain their own licenses, recorded in each project's THIRD_PARTY.md. Citation metadata is in CITATION.cff.
Round 002 adds exact complex/positive fiber counts for two-leak directed cycles, a necessary-and-sufficient extra-sensor criterion for two-leak bidirected trees, and a narrowly scoped COBRApy loopless-selection repair. Each package includes executable evidence and review limitations; original-author confirmation and priority remain pending.
The retained-root tree classification replaces the two-leak restriction by any known set of L leak locations. If q is the maximum number of vertex-disjoint observation-to-leak paths, the generic transfer-data rank is 2n−2+q and the generic ambiguity dimension is L−q. Thus full generic local identifiability holds exactly when q=L. The earlier two-leak path rule is a corollary of this same contribution.
The proof passed a separate AI mathematical review, with independent rational forest, resolvent and positive-similarity checks. The public verifiers retain their checks under python -O and preserve archived evidence. Historical priority and external human review remain pending; the broad multiple-input/output problem remains unresolved.
FASTCC direction auditor reproduces a negative-only reaction constraint defect and a minimal existing-API repair (COBRApy PR1500): independent baseline 1 failed / 4 passed, candidate 5 passed, plus 24 exact finite cases. GLPK coverage; AI review is not maintainer acceptance or external human peer review. Related SPECTRA PR1495 is credited.
Proof and reproducible checks for the strict two-environment full-basin exclusion question in Schreiber (2025), with a finite-period classification. Exact analytic claims, finite computational checks, and limits of source/author verification are distinguished in the packet.
Proof and exact checks for an indecomposable all-positive-rate reaction family with a globally stable positive state and regular complex zeros, yet without species-coordinate lex shape. The packet credits prior obstructions and distinguishes the mixed-coordinate repair.