This repository defines the parent method behind the manifold-constrained research program.
It exists so the core architecture is public in its own right rather than being inferable only from the theorem-library applications.
The theorem repos show the method applied to specific problems. This repository defines the method before the applications.
It makes public, in one place:
- the core manifold-constrained method,
- the local-to-global gate grammar,
- the restart and remainder logic,
- the cross-domain claim that the architecture is general and not limited to theorem applications.
- FOUNDATIONS.md: philosophical and methodological foundations of the parent method.
- MANIFOLD_CONSTRAINED_METHOD.md: canonical method statement.
- GATE_GRAMMAR.md: the common gate language and how it carries closure.
- RESTART_AND_REMAINDER.md: restart logic, no-Zeno discipline, and explicit remainder handling.
- CROSS_DOMAIN_MAPPING.md: how the same architecture maps across mathematics, AI, control, physics, and systems.
- TERMINOLOGY_LOCK.md: public definitions of the key phrases.
- PRIORITY_TIMELINE.md: dated public chronology for the architecture.
- CITATION_AND_ATTRIBUTION.md: concise public attribution guidance.
- COMPARISON_WITH_GENERIC_ARCHITECTURES.md: what differs from generic optimization / MoE / geometry branding.
The manifold-constrained method is a reusable architecture with the following load-bearing shape:
- define an admissible class,
- isolate a projected or protected core,
- control transport or continuation,
- make restart and re-entry rules explicit,
- preserve and account for the remainder,
- identify the endpoint or target object through explicit bridge conditions,
- certify final closure by a strict margin or equivalent nondegeneracy condition.
Canonical Lane is one theorem-facing realization of the parent method. The theorem-library repos are applications and test cases of the method, not its only possible form.