Open research in mathematics, machine intelligence, scientific computing, and autonomous research systems.
Questions become programmes. Programmes produce evidence. What survives scrutiny becomes knowledge.
Grand Challenge Labs builds executable research systems for turning difficult questions into evidence that can survive independent scrutiny.
Research · Mathematics Programme · Programme Atlas · Discussions
This table tracks material work currently in motion. It is a current-work surface, not a permanent taxonomy or a ranking of evidentiary strength.
| Frontier | Programme |
|---|---|
| Can mathematical discovery become an auditable computational process? | Mathematics Programme — BSD literal-p=2 theorem work; VGSE adjudication; odd-zeta certificate construction |
| Can agentic operations coordinate through authoritative, replayable semantics at pilot scale? | AETHER — semantic kernel; QA hardening; capacity planning |
| Can exact tensor-contraction decoding be validated and compared at larger quantum-code scale? | QUANTUM-TECHNOLOGIES — C90 exact decoder; 347-case matched comparison |
Rows appear here only while they represent material active work. Evidence and claim status remain with the governed programme records that support them.
MATHCERT has independently rebuilt and Lean-kernel-checked the exact supplied
formalizations for all ten results advertised by
openai/ten-proofs at pinned commit
94bc0feb6a9ff12c7d31d6de640a725c9d43d2b6.
| Checked surface | Result |
|---|---|
| Exact Lean source modules | 10 / 10 passed |
| Advertised headline declarations | 12 / 12 kernel accepted |
| Unexpected axioms | 0 |
| Independent review and protected replay | Complete |
Read the public verification note → · Inspect the protected MATHCERT record → · Replay evidence →
The result is exact: it verifies the supplied Lean proofs and their formal dependency graphs under the retained statement qualifications. It does not claim line-by-line identity with the PDF exposition, novelty, or priority.
| Stage | Discipline |
|---|---|
| 1. Frame the question | State the conjecture, engineering objective, or scientific uncertainty precisely. |
| 2. Make it executable | Build theory, experiments, datasets, software, proofs, and diagnostics. |
| 3. Attack the result | Reproduce, review, falsify, verify, and establish the claim boundary. |
| 4. Publish what survives | Promote only the evidence-supported result, with provenance attached. |
GitHub supplies the operational and evidentiary substrate; it does not itself confer mathematical or scientific authority.
View the GCL operational architecture
Organization-surface illustration, September 2026. This is a navigational summary; protected, content-addressed records in governed repositories remain authoritative.
The repositories are parts of one research system. They do not all occupy the same layer.
GRAND CHALLENGE LABS
│
├── Institutional stack
│ ├── INTELLECT ........ institutional reasoning, authority, and review
│ ├── AETHER ........... semantic coordination, provenance, and replay
│ └── gcl-standards .... shared technical and operating standards
│
├── Mathematics Programme
│ ├── MATH-PROGRAMME ... programme governance and map
│ ├── MATHFORGE ........ discover and reconstruct
│ ├── MATHSOLVE ........ organize and solve
│ └── MATHCERT ......... independently certify
│
├── Research programmes
│ ├── MODULUS .......... geometry-aware optimization and operator control
│ ├── RUNT ............. reversible normalized neural architectures
│ ├── CPS .............. collective neural computation and phase dynamics
│ └── other active scientific and engineering programmes
│
└── Research infrastructure
├── GLOSS ............ formal-to-natural semantics and loss accounting
├── TROVE-CURATA ..... governed data-curation programme; pre-activation
└── tooling, CI, publication, and supporting automation
The conceptual stack is:
| Layer | Question | Representative systems |
|---|---|---|
| Institution | Why and under what epistemic rules does research happen? | Grand Challenge Labs |
| Constitution | Who may judge, authorize, review, and preserve decisions? | INTELLECT |
| Semantic substrate | What does the system know, from what evidence, and at what point in history? | AETHER |
| Research machinery | How is inquiry turned into a repeatable discovery, solving, and certification process? | MATH-PROGRAMME, MATHFORGE, MATHSOLVE, MATHCERT |
| Research programmes | Which scientific and engineering questions are being attacked? | MODULUS, RUNT, CPS, and other active programmes |
| Research infrastructure | Which specialist systems make the research process more reliable or legible? | GLOSS, TROVE-CURATA, gcl-standards, CI and publication tooling |
In the mathematics programme, the epistemic pipeline is deliberately explicit:
MATHFORGE → MATHSOLVE → MATHCERT
discover organize certify
A source can motivate a claim. A computation can suggest a claim. A solving campaign can develop a claim. Certification is a separate act.
GCL research is designed to be inspectable rather than merely persuasive. Depending on the programme and claim class, evidence can include exact-head review, reproducible experiments, protected records, independent review, formal verification, explicit claim boundaries, immutable attestations, and post-merge readback.
Three-pillar architecture · Certification ladder · Claim-boundary doctrine · Standards
Current governed status
GI-AMEND-0001is effective under the protected INTELLECT authority schedule.GCL-GHOS-000.2.0is the admitted bounded-execution-continuity successor selected for the MATH-PROGRAMME pilot by protected admission87307a0c1fe5ff19b34bb08451e7d6281a7d5dea.- MATH-PROGRAMME actively adopts that exact admission through protected adoption
1a5e9cb24257be578b091ecd2c99d4119ff73b2c, while retaining the0.1.1and0.1.0lineage as history.
Machine-readable activation, admission, and adoption records take precedence over descriptive documents. These statuses do not grant GitHub independent constitutional, mathematical, certification, production, deployment, novelty, or commercial authority.
Read the research. Reproduce an experiment. Challenge a result. Improve a proof. Build on what survives.
Programme Atlas · Repositories · Discussions · Mathematics Programme
Grand Challenge Labs
Reproducible · Traceable · Governed · Open by default