The Carlo Theory: A Universal Pulse‑Driven Symbolic Transformation Engine (Canonical Formula, Meta‑Engine, CVL, and ReGenesis Mapping)

This release introduces The Carlo Theory — a universal, pulse‑driven symbolic transformation framework that unifies rhythm, recursion, geometry, behaviour, and context into a single computational engine. The theory defines a minimal but expressive structure capable of generating coherent systems across visual, cognitive, narrative, and computational domains. This deposit includes the canonical formula, the full set of governing laws, the Carlo Visual Language (CVL), the meta‑engine specification, and the formal mapping into the ReGenesis Engine architecture. Core Contribution At the heart of the theory is the Carlo Constant, the irreducible formula from which all Carlo engines derive: Engine=Pulse∘Loop∘Behaviour∘Context∘Symbol This single expression encodes the entire system: Pulse — time = breath = hierarchy Loop — update → render Behaviour — phase, symmetry, recursion, rotation, breath Context — unified field: time, state, influence Symbol — instruction → geometry → behaviour → meaning Symbolic Chain (Full Equation) The Carlo symbolic pipeline is defined as: Symbol→Geometry→Behaviour→Meaning This chain allows symbols to become actions, actions to become transformations, and transformations to become interpretable meaning. Recursion Law (Three‑Layer Constraint) Carlo recursion is strictly limited to: Parent→Child→Grandchild All deeper structure is implied, not computed. This produces infinite‑feeling depth with zero computational explosion. One‑Stroke Geometry Law All geometry in the Carlo system must be expressible as: Geometry=OneStroke (s) This constraint enforces minimalism, clarity, and symbolic inevitability. Behaviour Meta‑Operator Carlo behaviour is defined as a unified operator: Behaviour=f (phase, symmetry, recursion, rotation, breath) This single operator governs all dynamic expression. Meta‑Engine Specification The Ritual Layer generalises into a meta‑engine capable of generating entire families of engines: MetaEngine=f (Pulse, Symbol, Context, Behaviour) This provides the generative backbone for the Carlo Engine taxonomy. ReGenesis Mapping (Formal Embedding) The Carlo Engine maps cleanly into the ReGenesis Engine via: ReGenesis (RitualLayer) =SymbolicPulse (Pulse) ∘StateFlow (Loop) ∘BehaviourStack (Behaviour) ∘ContextMesh (Context) ∘SymbolicRoot (Symbol) This demonstrates practical integration into a scalable engine architecture. Included Materials The Carlo Master Document (full theory) Formal definitions and governing laws Canonical formula and derived equations Carlo Visual Language (CVL) reference Meta‑engine specification ReGenesis mapping document Coherent example suite (pulse, recursion, symbolic, behaviour, ReGenesis) Implementation pseudocode Why This Matters The Carlo Theory provides a unified computational substrate for any system where symbols transform over time. It is minimal, deterministic, expressive, and domain‑agnostic — a foundation for future engines, languages, visualisers, and cognitive models. This release marks the first public availability of the complete theory. Keywords: Carlo Theory, Carlo Engine, Carlo Constant, Pulse Engine, Recursion Engine, Symbolic Engine, Behaviour Engine, ReGenesis Engine, ReGenesis Mapping, StateFlow, SymbolicPulse, BehaviourStack, ContextMesh, SymbolicRoot, Pulse = Time = Breath = Hierarchy, update → render, Instruction → Geometry → Behaviour → Meaning, One‑Stroke Geometry, Three‑Layer Recursion, Parent → Child → Grandchild, Constraint Identity, Constraint = Identity, Universality Law, Emergence Law, Rhythm + Constraint + Symbol, Carlo Visual Language, CVL, Core Engine Glyph, ⟲ ϟ ∴ → ○ → ◎ >, Spiral Operator, Breath Operator, PhaseShift Operator, Mirror Operator, Recursive Operator, Node Field, Transition Field, Pulse Field, Operator Field, Carlo Meta‑Engine, MetaEngine = f (Pulse, Symbol, Context, Behaviour), Engine Taxonomy, Rhythmic Engines, Symbolic Engines, Recursive Engines, Constraint Engines, Behavioural Engines, Field Engines, Pulse Engines, Meta‑Symbol Engines, Meta‑Operator Engines, Universal Engines, Emergent Engines, Interpretive Engines, Transformational Engines, Cognitive Engines, Aesthetic Engines, Carlo Master Document, Carlo Engine Codex, Carlo Publication Document, Carlo Example Suite, Carlo Teaching Appendix, Carlo Pseudocode, Master Publication Document Pseudocode, Document‑Engine Pseudocode, Combined Example Diagram, Pulse Phase Oscillator, Symbol → Geometry → Action, Behaviour Meta‑Operator, phase symmetry recursion rotation breath, Carlo Reset Operator, ReGenesis (RitualLayer), SymbolicPulse (Pulse), StateFlow (Loop), BehaviourStack (Behaviour), ContextMesh (Context), SymbolicRoot (Symbol), Minimal Geometry, Symbolic Transformation, Temporal Symbolic Systems, Domain‑Agnostic Engine, Computational Aesthetics, Cognitive Modelling, Generative Systems, Recursive Structures, Symbolic Grammars, Engine Architecture, Unified Engine Pattern, Universal Symbolic Substrate, Minimal Computational Grammar, Scalable Engine Framework, Carlo Research Object, Zenodo Research Deposit.