Manifestation Flow with Mass Partitioning in Extended Classical Mechanics

1. Pure Algebra (No Physics Yet)

We begin strictly at the algebraic level. No physical interpretation is assumed at this stage. Consider the identity:

(PEᴇᴄᴍ − ΔPEᴇᴄᴍ) + ΔPEᴇᴄᴍ = PEᴇᴄᴍ

This is a mathematical tautology. Subtracting a quantity and adding it back restores the original total. ECM assigns physical meaning only after this identity is established.

2. The Energy Identity in ECM

1️⃣ Start from your statement

PEᴇᴄᴍ = (PEᴇᴄᴍ − ΔPEᴇᴄᴍ) + ΔPEᴇᴄᴍ

In ECM, the manifested portion of potential energy is identified with manifested matter mass:

ΔPEᴇᴄᴍ ≡ ΔMᴍ_manifested c²

Hence the total matter mass satisfies:

Mᴍ = Mᵉᶠᶠ + ΔMᴍ_manifested

Short answer: yes — that identification is ECM-consistent, provided the sign meaning (manifested vs unmanifested) is kept explicit.

3. Total Vacuum-Phase Potential

1️⃣ Total Vacuum-Phase Potential (PEᴇᴄᴍ₍ᵤₙᵢᵥ₎)

The universal vacuum-phase potential represents the uneventful, pre-manifest state of existence. It is not directly observable and is globally conserved.

PEᴇᴄᴍ₍ᵤₙᵢᵥ₎ = (PEᴇᴄᴍ₍ᵤₙᵢᵥ₎ − ΔPEᴇᴄᴍ) + ΔPEᴇᴄᴍ

The residual term is identified with Unmanifested Vacuum-Phase Potential, or NAM.

4. Hierarchy of Manifested Mass

1️⃣ Hierarchy of manifested mass

ECM treats mass manifestation as hierarchical rather than absolute.

Figure 2 — ECM mass partitioning: matter mass (Mᴍ) internally redistributes into effective manifested mass (Mᵉᶠᶠ) and apparent mass deficit (Mᵃᵖᵖ ≡ NAM).

ΔMᴍ_manifested_univ ⊇ ΔMᴍ_manifested_local

The universal manifested mass contains all locally manifested structures as subsets.

5. Local Manifested Mass

1️⃣ Local manifested mass

Local manifested mass includes both baryonic matter and dark matter contributions:

ΔMᴍ_manifested_local = Mᴍ(baryonic) + Mᴍ(dark)

This locally manifested mass obeys the same ECM manifestation principles, constrained by the local termination scale r_max.

6. Universal Origin of Manifestation

1️⃣ Starting point: Unmanifested vacuum-phase potential

All manifested mass originates from the unmanifested vacuum-phase potential (NAM), governed by frequency drift:

Figure 1 — Universal ECM manifestation flow from unmanifested vacuum-phase potential (PEᴇᴄᴍ₍ᵤₙᵢᵥ₎) to observable energy and effective mass.

f₀ → f_obs = f₀ − Δf

The observed energy follows directly:

E_obs = h f_obs = ΔMᴍ_manifested c²

7. Connecting ECM Manifestation Flow to Mass Partitioning

The full ECM manifestation flow can now be summarized:

PEᴇᴄᴍ₍ᵤₙᵢᵥ₎ → ΔPEᴇᴄᴍ → ΔMᴍ_manifested → Mᵉᶠᶠ → E_obs

Local systems (planets, stars, galaxies) inherit this flow from the universal level, ensuring internal consistency across scales.

For extended discussions, see: Mass Partitioning in Extended Classical Mechanics