# Charged-Mass Braid Sieve (InteractionPhysics)

> *Charged-Mass Braid Sieve transfers unstable information through a path-sensitive braid field so its charge can be separated into stable signal, useful residue, scar memory, or dischargeable noise.*

**Domain:** `axis-11-geometry`
**Secondary Domains:** `axis-07-attestation`, `axis-01-compression`, `axis-06-safety`
**Settlement:** `FORMING`

## Core Mechanism

The **Charged-Mass Braid Sieve** treats unstable information not as a static object to be judged, but as a path-sensitive entity whose identity evolves based on its exchange history within a braid field. It provides a formal mass-transfer pipeline to resolve the charge of incoming signals.

### Transfer Pipeline

1. **Injection:** Introduce unstable information packet $x_i$.
2. **Provisional Weighting:** Assign initial charged mass $M_i$.
3. **Rotation:** Route $x_i$ through the braid field $B(t)$.
4. **Instability Exposure:** Allow repeated braid interactions to separate stable phase from charge instability.
5. **Mass Transfer:** If the signal proves admissible, transfer its mass into the stable center $C(t)$.
6. **Sieve Charge Resolution:**
   - **Coherent charge:** Promoted to a stable **basin**.
   - **Partial charge:** Held as an edge survivor (**useful residue**).
   - **Unstable charge:** Sent to **FAMM scar** for quarantine.
   - **Incoherent charge:** Discharged as noise.

## Mathematical Mapping

The sieve acts as a physicalized execution of the **Mass Number** ratio:

$$ \text{Mass Number} = \frac{\text{Admissible Reduction}}{\text{Residual Risk}} $$

Through rotation, the sieve continuously updates the mass of the packet based on its interaction with the field:

$$ M_i(t+1) = M_i(t) + \Delta_{\text{admissible}}(x_i, B, C) - \Delta_{\text{risk}}(x_i, B, C) $$

The foundational **Transfer Rule** dictates that:
*Unstable charge becomes useful only if rotation lowers residual risk.*

## Topological Equivalence

This primitive bridges standard metric models and the braid-theoretic information architecture of the Sovereign Stack:

| Standard Model | Sovereign Stack Model (Charged-Mass Braid Sieve) |
| :--- | :--- |
| Static Identity | Path-Sensitive Identity (Anyon Rotation) |
| Fixed Mass | Interaction-Weighted Charge Mass Field |
| Binary Validation | Admissibility Sieve Test |
| Discarded Data | FAMM Scar / Useful Residue Phase Drift |
| Output Value | Emergent Center (Stable Basin) |