Research-Stack/6-Documentation/docs/charged_mass_braid_sieve.md

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)