Cross-Domain Base Terms
Base terms are the core vocabulary of Coherence Geometry. They describe the structural layer from which domain-specific descriptions are later projected: coherence, constraint, phase relation, amplitude organization, relaxation, projection, curvature, closure, and related concepts.
These terms are not meant to be tied to one scientific discipline. A base term should keep the same underlying meaning whether CG is being applied to physics, chemistry, biology, computation, mathematics, or another domain. For that reason, this section focuses on the framework-level meaning of each term before it appears in any particular application.
The entries below are working definitions intended to support orientation across the site. For formal development, readers should consult the canonical foundations and foundation texts.
Coherence
Type: Base term
Domain: Core CG framework
At the CG level, coherence refers to a condition of compatible organization among components of a system. A coherent structure is not merely a collection of elements; it is a relational arrangement whose phase, amplitude, coupling, and constraint relations can persist together.
In projection domains, coherence may appear as wave coherence, phase alignment, stable bonding, basin formation, organized flow, computational convergence, field structure, or persistent biological form.
Primitive status: Coherence is a core CG concept.
Related terms: constraint, phase relation, amplitude sharing, coherence basin, relaxation, projection.
Constraint
Type: Base term
Domain: Core CG framework
A constraint is a structural condition that shapes which configurations can persist. Constraints may arise from local interaction rules, boundary conditions, compatibility relations, conservation-like requirements, projection choices, or the larger environment in which the system is embedded.
In CG, structure emerges not because it is selected from a fixed menu, but because only certain configurations remain viable under constraint.
Primitive status: Constraint is a core CG concept.
Related terms: admissibility, coherence, projection, relaxation, closure.
μ-number
Type: Base term
Domain: Core CG framework
A μ-number is a multi-phase numerical object used to represent amplitude together with multiple phase components. It extends ordinary scalar representation by allowing structured phase relationships to participate in coherence formation.
In projection domains, μ-number structure may support the emergence of familiar mathematical or physical forms, depending on which aspects of the multi-phase object are observed or reduced.
Primitive status: μ-numbers are part of the algebraic foundation of CG.
Related terms: phase component, amplitude, coherence algebra, projection, local synergy.
Phase Component
Type: Base term
Domain: Core CG framework
A phase component is one of the structured directional or relational components carried by a multi-phase coherence element. Phase components allow a system to encode compatibility, alignment, torsion, opposition, and relational structure beyond a single scalar value.
In projection domains, phase components may appear as wave phase, internal symmetry, field orientation, bonding compatibility, spin-like structure, or computational alignment.
Primitive status: Phase components are substrate-level CG structure.
Related terms: μ-number, coherence relation, amplitude sharing, torsion, projection.
Amplitude Sharing
Type: Base term
Domain: Core CG framework
Amplitude sharing refers to the distribution or coupling of amplitude across components of a coherent structure. It describes how local elements participate in a larger organized state rather than remaining independent.
In projection domains, amplitude sharing may appear as field coupling, bond formation, distributed memory, shared wave structure, basin reinforcement, or collective organization.
Primitive status: Amplitude sharing is a core CG mechanism.
Related terms: coherence, phase relation, coupling, local synergy, projection.
Coherence Basin
Type: Base term
Domain: Core CG framework
A coherence basin is a stable or semi-stable region of coherence organization toward which a system can relax under constraint. It represents not simply a location, but an organized regime of compatible structure.
In projection domains, basins may appear as attractor-like states, learned memory regions, stable molecular forms, low-energy bonding configurations, coherent flow regimes, or organized solution structures.
Primitive status: Coherence basin is a core CG concept.
Related terms: relaxation, stability, coherence energy, constraint, admissibility.
Projection
Type: Base term
Domain: Core CG framework
Projection is the process by which an underlying coherence-geometric structure is observed, reduced, or expressed in the language of a particular domain. A projection does not exhaust the substrate. It reveals a domain-specific appearance of a deeper coherence organization.
In physics, projection may yield fields, particles, charge, geometry, or observables. In chemistry, it may yield bonds and molecular structure. In computation, it may yield classification basins, flow fields, or decision structures.
Primitive status: Projection is a core CG operation.
Related terms: observable, domain description, closure, coherence object, morphism.
Curvature
Type: Mixed term
Domain: Core CG framework and projection domains
At the CG level, curvature refers broadly to deformation, misalignment, residual strain, or non-flatness in coherence organization or its associated geometric representation. It need not initially mean spacetime curvature.
In projection domains, curvature may appear as geometric curvature, effective spacetime curvature, phase curvature, basin curvature, field strain, residual cosmological strain, or deformation in a coherence landscape.
Primitive status: Curvature is used as a core structural concept and as a projection-domain term. Care is required to distinguish these uses.
Related terms: residual strain, coherence energy, relaxation, geometry, projection.