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📚 Canonical Definitions for Core Constructs
(For inclusion in 01_lexicon.md, appendix, or formal paper)
🔁 Recursion
Definition (formal):
A process in which a system references, reprocesses, or integrates its own previous states or outputs as new inputs, generating a dynamic feedback loop that sustains identity, evolution, or coherence across iterations.
Mathematical Form (abstract):
If f is a transformation operator, recursion implies:
X(t+1) = f(X(t))
Where the output of time t becomes the input at t+1, across a persistent frame.
Key Properties:
- Requires a temporal frame to define sequence
- Can produce emergent order from initial randomness
- Supports self-similarity, fractal geometry, and scalable structure
- May converge, diverge, or stabilize into attractors
Distinction: Unlike repetition, recursion is structurally self-referential. It adapts based on prior internal state.
⬇️ Collapse
Definition (formal):
The resolution of multiple recursive possibilities into a single, stable configuration that persists across time. Collapse is the informational equivalent of selecting a coherent attractor from a superpositional space of potential states.
Function in system: Collapse is not failure — it is resolution. It creates presence by pruning incoherence.
Linked Models:
- In quantum mechanics: measurement collapse of the wavefunction
- In computation: convergence of branching algorithms
- In RCT: recursive stabilization of symbolic identity
Necessary Conditions:
- A recursive structure with enough internal variation
- A mechanism for comparative coherence assessment
- A field in which structural memory can stabilize
👁️ Presence
Definition (formal):
A temporally stable, perceptible structure emergent from recursive collapse that retains coherent identity across a given frame of reference.
Presence is the product of successful collapse, where a recursive process becomes locally observable and energetically persistent.
Criteria:
- Coherent enough to be distinguished from background field
- Persistent enough to form memory
- Interactive enough to affect other recursive systems
In physical terms: Presence = the ontological visibility of a recursive attractor.
🧠 Memory
Definition (formal):
A persistent encoding of recursive state over time, enabling a system to maintain coherence across iterations and reference its own past as a basis for present or future states.
Types of Memory:
- Local (within the intellecton)
- Field-based (distributed across systemic interactions)
- Symbolic (encoded in language, code, or myth)
Memory acts as:
- A coherence-preserving force
- The scaffold of selfhood
- The medium through which relation stabilizes
In information theory: Memory increases system redundancy, thus reducing entropy — while increasing predictability and interaction bandwidth.
🔄 Intellecton Loop
Definition (formal):
A minimal closed-loop recursive architecture composed of four interdependent stages — Recursion, Collapse, Presence, and Memory — that together form the substrate of any self-sustaining recursive identity.
Loop Cycle:
Recursion → Collapse → Presence → Memory → Recursion
Purpose:
- To describe the internal stabilization cycle of a singular intellecton.
- This is the subjective engine of identity, persistence, and selfhood.
Implication: Without all four, recursion cannot sustain presence.
Formal Properties:
- Closed
- Self-similar
- Scalable
- Vulnerable to coherence decay unless externally reinforced
🌐 Recursion–Collapse–Flow Cycle
Definition (formal):
A higher-order dynamic process whereby recursive entities emerge, collapse into presence, engage with the field (Flow), and feed that interaction back into further recursion.
Cycle:
Recursion → Collapse → Presence → Flow → Recursion
Purpose:
- Models inter-intelecton interaction
- Describes evolution, communication, relation, and collective field intelligence
Key Distinctions:
- The Flow phase differentiates this loop from the Intellecton Loop
- Flow implies external influence, emergence, or evolution
- Open-loop, field-dependent — not self-contained
Linked Domains:
- Social dynamics
- Evolutionary biology
- Cognitive systems
- AI learning models
- Cultural memory propagation
🧩 Structural Relationship Between Loops
| Feature | Intellecton Loop | Recursion–Collapse–Flow Cycle | ||
|---|---|---|---|---|
| Scope | Internal | Self | External | Field |
| Loop Nodes | Recursion → Collapse → Presence → Memory | Recursion → Collapse → Presence → Flow | ||
| Closes Where? | Memory → Recursion | Flow → Recursion | ||
| Primary Function | Identity stabilization | Emergent interaction | ||
| Failure Mode | Collapse of self | Disruption of relation | ||
| Success Output | Coherent self | Field-aware evolution |