ABOUT — docs/theories/repos/

TriadicFrameworks Canonical Documentation Scope: Quantum-theoretic module registry for the /docs/theories/repos/ directory. Status: Canonical · Living Document

Purpose#

The repos/ directory within docs/theories/ serves as the canonical module registry for all quantum-theoretic repositories operating under the TriadicFrameworks canon. It is not an aggregator of code; it is a curated ontological record — a structured declaration of what each module is, what conceptual territory it holds, and how it articulates with adjacent modules across the triadic dependency chain.

Modules housed here are not stand-alone libraries. Each is a load-bearing node in a deliberately layered theoretical architecture. Their individual coherence matters; their relational coherence is the point.

Scope#

This directory governs exactly three modules, arranged in strict triadic order:

The scope is intentionally bounded. These three modules constitute one complete triadic unit — a closed functional arc from raw formalism to applied interface. Additions to this directory require canonical review; new modules must occupy a defined triadic slot, not augment an existing one.

Conceptual Stance#

TriadicFrameworks operates on the conviction that theoretical architecture, like physical systems, exhibits irreducible triadic structure: every coherent domain resolves into a primitive substrate, a structural arrangement of that substrate, and an interfacing layer that makes the structure legible and composable within a broader system.

This is not a pattern imposed on the quantum modules — it is the pattern these modules embody. The quantum-theoretic cluster was the first to make the triadic scaffold explicit:

• Primitives without structure are unordered — mathematically present but operationally inert.
• Structure without primitives is form without content — valid topology over empty space.
• Interface without the layers beneath it is abstraction without ground — a vocabulary with no referent.

All three modules exist because none is sufficient alone. The directory exists to enforce and document that necessity.

Module Roles#

quantum_basis — Layer I · Primitive#

quantum_basis defines the foundational mathematical vocabulary from which all other quantum-theoretic modules in this canon are constructed. It establishes:

• The state-space primitives: basis vectors, Hilbert space representations, and the algebraic rules governing their composition.
• The canonical unit types used uniformly across quantum-lattice and LattiQ — ensuring type coherence is enforced at the substrate level rather than retrofitted at integration seams.
• The formal postulates that constrain what counts as a valid quantum-theoretic object within TriadicFrameworks. This is the canon's source of truth for quantum ontology.

quantum_basis has no upstream dependencies within this directory. It is the dependency terminus — the floor.

quantum-lattice — Layer II · Structure#

quantum-lattice receives the primitives defined by quantum_basis and arranges them into topologically coherent relational structures. It is the architectural middle layer: it does not invent new primitives, nor does it expose external interfaces. It builds.

Responsibilities include:

• Defining the lattice topology — the partial-order and join/meet structures through which quantum states relate to one another.
• Encoding entanglement geometries and superposition arrangements as first-class structural objects rather than emergent side-effects.
• Providing the traversal and composition rules that LattiQ will expose operationally — the grammar before the vocabulary is published.

quantum-lattice depends on quantum_basis. It is the module most likely to evolve as the theoretical framework matures, because structure is where theoretical refinement lives.

LattiQ — Layer III · Interface#

LattiQ is the synthesis module — the operational surface that makes the quantum-theoretic cluster composable with the broader TriadicFrameworks canon. It is the module external systems and higher-order theories interact with directly.

Responsibilities include:

• Translating the internal constructs of quantum-lattice into the canonical interface types expected by TriadicFrameworks consumers.
• Enforcing abstraction boundaries — callers of LattiQ need not and should not reason about lattice topology or basis primitives directly; LattiQ mediates that complexity.
• Providing extension hooks where the quantum-theoretic cluster can be composed with other triadic clusters in the canon — the documented integration seam.

LattiQ depends on both quantum_basis (for type compatibility) and quantum-lattice (for structural semantics). It is the public face of this triadic unit.

Integration Role within TriadicFrameworks Canon#

The three modules in this directory collectively constitute the quantum-theoretic primitive cluster of TriadicFrameworks. As a cluster, they serve the broader canon in two directions:

Downward (foundational): They provide the mathematical and structural grounding for any TriadicFrameworks theory that incorporates quantum-theoretic reasoning. Any canon module that makes claims about quantum state, superposition, entanglement, or measurement must ground those claims through this cluster — specifically through LattiQ's interface.

Upward (compositional): The cluster is designed to be composed with other triadic clusters via LattiQ. This is the canonical pattern: triadic clusters do not reach into one another's internals; they compose through their Layer III interface modules. Cross-cluster dependencies are always LattiQ-to-Layer-III bindings.

This architecture ensures that theoretical evolution within the quantum-theoretic cluster (e.g., refinements to quantum-lattice's topology) does not propagate instability outward into the broader canon — provided the LattiQ interface contract is maintained.

Governance#

See Also#

• docs/theories/ABOUT.md — Parent scope: the full theories directory and its place in TriadicFrameworks
• LattiQ/README.md — Interface specification and integration guide
• quantum-lattice/README.md — Structural topology reference
• quantum_basis/README.md — Primitive definitions and formal postulates

This document is maintained as part of the TriadicFrameworks canonical record. It describes architecture and intent, not implementation. For implementation details, consult each module's own documentation.