First-order Functional Weight Space

.me Functional Spaces and Route-Like Semantics

This document describes the concept of first-order functional weight space in ME Calculus and how higher-order spaces naturally induce route-like semantics:
meSpace¹ ⊂ meSpace² ⊂ meSpace³ ⊂ …
me / meSquare / meSquare2
The goal is to give a precise mental model that can later be mapped to code, routing and UI.

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1. ME as a Functional Identity

In this model, .me is not a static profile object, but a callable, declarative identity:

`const me = new ME(secret, namespace)

me.instrumento("Moog Matriarch")
me.color("blue")
me.device("laptop")`

Each method call:
• uses a dynamic key (instrumento, color, device, etc.)
• attaches a value or list of values
• produces a signed declaration internally

Conceptually:

.me : (key, value) → declaration

No schema is imposed. Semantics emerge from usage.

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1. First-Order Functional Weight Space (meSpace¹)

If we consider all methods ever invoked on a given ME instance, we obtain a set of functional dimensions:

{ instrumento, color, device, ... }

For each key we can define a weight based on usage:
• frequency of use
• recency (time since last use)
• recurrency over a time window
• relevance score (any metric you choose)

This defines a first-order functional weight space, which we can denote as:

meSpace¹

Where:
• each dimension corresponds to a method/key
• each dimension has an associated weight
• ordering of methods (e.g. for UI) can follow this weighting

In other words, .method is not only an entry point; it is a weighted axis in meSpace¹.

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1. Higher-Order Spaces: meSpace², meSpace³, …

Once meSpace¹ exists, we can construct higher-order spaces as contexts built on top of the first space.
• meSpace¹ – functional surface: methods and their weights.
• meSpace² – contexts or “areas” that group and organize functions.
• meSpace³ – meta-contexts that group multiple second-order spaces, and so on.

Formally:

meSpace¹ ⊂ meSpace² ⊂ meSpace³ ⊂ …

Each inclusion means:
• meSpace² contains the functional structure of meSpace¹, plus additional structure (e.g. grouping, scoping, or contextualization).
• meSpace³ contains meSpace², and so on.

You can think of:
• meSpace¹ as the set of actions you can perform.
• meSpace² as where those actions live (contexts, rooms, domains).
• meSpace³ as how those contexts relate at a higher level (meta-graphs, workspaces, projects, etc.).

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1. From Spaces to “Squares”: meSquare, meSquare2

To keep the terminology concrete:
• meSquare can be used as a name for the first visible functional area (built from meSpace¹).
• meSquare2 can represent a second area that contains or extends the first.

Example idea:

`// base identity
const me = new ME(secret, namespace)

// first functional area – meSquare
me.instrumento("Moog")
me.device("laptop")

// second area – meSquare2 – a higher-order grouping/context
// conceptually containing the functions already declared
`

At the implementation level, meSquare and meSquare2 can be:
• explicit groupings of declarations
• contextual scopes
• mapped directly to namespaces or routes

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5. Why It Becomes Route-Like

The route-like intuition:

me / meSquare / meSquare2

emerges naturally from:
1. Identity root – me
Represents the core identity (e.g. identityRoot or namespace).
2. First area / meSquare – functional surface
A logical layer grouping methods and interactions for a given context.
3. Second area / meSquare2 – higher-order context
A container for subspaces, nested contexts, or compositions of actions.

This maps cleanly to a hierarchical path:

/me
/me/meSquare
/me/meSquare2

or, more concretely, in a system like Cleaker:

username.cleaker.me/
username.cleaker.me/meSquare
username.cleaker.me/meSquare2

Each additional layer adds context, just like nested routes:
• / → base identity
• /meSquare → first functional area for that identity
• /meSquare2 → extended or specialized area built on top of the first

Because the spaces are nested (meSpace¹ ⊂ meSpace² ⊂ …), they map naturally to nested paths.

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1. Practical Use Cases

This layered model can be used to:
1. Order functions dynamically
Use weights in meSpace¹ (frequency, recency) to prioritize actions in UI.
2. Define contextual dashboards
meSquare as the main working area for a user; meSquare2 as a different “mode” or project.
3. Generate routes from semantics
Instead of hardcoding routes, derive them from the structure of meSpace layers.
4. Attach GUI to spaces
A GUI layer (e.g. this.GUI) can “paint” each space:
• meSpace¹ → action palette
• meSpace² → contextual workspace
• meSpace³ → meta overview

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7. Summary

• First-order functional weight space (meSpace¹) is the set of all methods (keys) on ME, each with a weight derived from usage.
• Higher-order spaces (meSpace², meSpace³, …) encapsulate that functional layer into larger conceptual or contextual areas.
• This hierarchical inclusion naturally induces route-like semantics, such as:

me / meSquare / meSquare2

• **GUI **and routing layers can leverage these spaces to build navigable, identity-centered interfaces without hardcoding schemas up front.

This model keeps identity declarative, extensible, and space-aware, while remaining straightforward to implement on top of the existing ME declarative engine.