doing rounds of internal reviews

notes/01_lexicon_notes.md

@@ -0,0 +1,174 @@
+## 📚 **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                  |          |       |
+
+---