---
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  "title": "OP-MAT-001 · Stable Finite-Energy Electron Solution",
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  "summary": "ASD describes the electron as a closed orientation structure in the minimal negative-charge sector. Chapter 4 supplies the orientation field, finite-energy boundary, topological current and charge matching. Chapter 5 supplies the unique positive stationary radius and radial second-derivative check of a one-parameter energy model. The scale-stabilization mechanism is analytic; the next task is the full three-dimensional electron configuration.",
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      "A radial scale minimum does not replace a full three-dimensional solution or stability against all perturbations; a 2π internal-phase label alone does not determine the three-dimensional mapping degree."
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---
## Established results

ASD describes the electron as a closed orientation structure in the minimal negative-charge sector. Chapter 4 supplies the orientation field, finite-energy boundary, topological current and charge matching. Chapter 5 supplies the unique positive stationary radius and radial second-derivative check of a one-parameter energy model. The scale-stabilization mechanism is analytic; the next task is the full three-dimensional electron configuration.

<Equation name="mat-boundary" />

<Equation name="sd-derrick" />

## Research still required

Fix the common action, target space, coefficient sources and boundary, then solve the finite-energy configuration in the minimal-charge sector. Calculate nonradial perturbations and translation/rotation zero modes, and test fission and radiation. Retained amplitude variables require an unwinding-through-zero check; periodic cores require Floquet analysis.

## The next reproducible deliverable

First deliver a reproducible electron-sector solution with equation residuals, boundary/grid convergence, vacuum-subtracted energy, topological integrals and perturbation spectra. Calculate charge, mass and rotational response from that same core–surrounding-field system, identifying calibrated parameters.

## Scope and research links

A radial scale minimum does not replace a full three-dimensional solution or stability against all perturbations; a 2π internal-phase label alone does not determine the three-dimensional mapping degree.

[stability](/en/theory/matter/stability) · [electron](/en/theory/matter/electron) · [localization](/en/theory/matter/localization) · [stability](/en/theory/matter/stability) · [master equation](/en/theory/space-dynamics/master-equation) · [matter](/en/theory/matter)

<CanonicalSource />