# Knowledge base

Verified components grouped into eleven subject areas and one verification section.

| Section | Modules |
|---|---:|
| [Collatz and discrete dynamics](collatz/README.md) | 19 |
| [Explicit logarithmic bounds](riemann/README.md) | 4 |
| [Almost-complex algebra](hopf/README.md) | 4 |
| [Polynomial functionals and integrals](lamzouri/README.md) | 3 |
| [Coordinate and multilinear geometry](finsler/README.md) | 3 |
| [Proof certificates and DAGs](proof-graphs/README.md) | 2 |
| [Cryptographic algebra and ZK components](cryptography/README.md) | 84 |
| [Quantum algebra, photonics, and mechanics](quantum-physics/README.md) | 82 |
| [Finance, liquidity, and mechanisms](finance/README.md) | 27 |
| [Distributed consensus](distributed/README.md) | 63 |
| [Exact numeric certificates](12_numeric_certificates/README.md) | 6 |
| [Registry and axiom audit](verification/README.md) | 4 |

301 top-level module cards; three nested support sources give 304 Lean files under Verification/, or 305 including Verification.lean. MasterSuite directly imports 261 modules; these counts describe different sets.

[Project value](SUMMARY.en.md) · [Validation](VERIFICATION.en.md) · [Contributing](CONTRIBUTING.en.md) · [Catalog](catalog.json)

The cards summarize formal results and their scope. Lean statements remain authoritative. No scientific priority is claimed.

[Verification hierarchy](../docs/verification-hierarchy.en.md) · [Normative qutrit contract](../docs/qutrit-conformance.en.md)