🌐 LAW 0AR — A Modern, Origin-Centered View of Action–Reaction Symmetry

⭐ A New Structural Perspective on Newton’s Third Law, One of Physics’ Oldest Principles

LAW 0AR provides a clean, origin-centered formulation of action–reaction symmetry.
It introduces no new physics, no new forces, and remains perfectly faithful to Newton —
while giving us a clearer structural representation for interactions that are:

• distributed (rockets, jets, exhaust flows)

• field-mediated (EM forces)

• non-local (fluids, plasmas, pressure fields)

Where Newton applies directly, LAW 0AR behaves identically.
Where Newton becomes hard to express locally, LAW 0AR offers stability, clarity, and bounded structure.

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Note: LAW 0AR is not a new force law. It does not modify force, momentum, or Newtonian mechanics; it only provides a bounded structural representation of symmetry.

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🔑 The Core Principle (ASCII)

“Every physical interaction produces a dual, symmetric, bounded pair of structural responses originating from the same interaction source.”

This ensures:

• 🔁 perfect action–reaction symmetry

• 🔒 bounded structural behavior

• 🎯 classical recoverability (Newton preserved)

• 📉 no blow-ups, no singularities

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⚙️ The Structural Operator (SSMO-AR)

LAW 0AR is the law.
SSMO-AR is the mathematical tool used to express it.

Minimal demonstration:

from math import tanh

def SSMO_AR(F):
    Df = tanh(F)      # dissipation / scaling
    Bf = tanh(Df)     # bounded collapse
    Af = Bf           # Z(x) = identity
    return Af, -Af

print(SSMO_AR(10.0))
print(SSMO_AR(-25.0))
print(SSMO_AR(0.5))

Expected:

• values always in (-1, +1)

• perfect symmetry: A + R = 0

• smooth collapse for large forces

This matches all LAW 0AR scientific validations.

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🚀 Real-World Validation

Evaluated (observation-only) on public datasets across four domains:

• Rocket Thrust Curves — smooth bounded collapse

• Aerodynamic Pressure Fields — symmetric mappings

• Asymmetric CFD Flow — structural asymmetry aligns with lift/drag

• Metal Stress–Strain — elastic → plastic → saturation transitions captured cleanly

Across all datasets:
A + R = 0 for every sample
Bounded stability. Zero singularities.

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🧭 Why LAW 0AR Matters

Modern physics increasingly deals with:

• momentum distributed through media

• forces transmitted via fields

• non-local reaction pathways

• flux-driven interactions

• turbulent or continuum environments

Newton’s Third Law remains true — but is often not locally expressible.

LAW 0AR provides a structural, bounded, origin-centered representation of symmetry that:

• preserves Newton fully

• clarifies difficult interaction regimes

• remains mathematically stable

• adds no assumptions, no predictions, no reinterpretations

It is a neutral complement, not a replacement.

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🔍 One-Sentence Summary

LAW 0AR preserves Newton’s Third Law while extending symmetry clarity to distributed, field-mediated, and modern interaction regimes — using clean, bounded structural mathematics.

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📂 Repository

LAW 0AR — Open Standard (Observation & Interpretation Only)
https://github.com/OMPSHUNYAYA/Symbolic-Physics-LAW-0AR

Master Index — Shunyaya Symbolic Mathematics
https://github.com/OMPSHUNYAYA/Shunyaya-Symbolic-Mathematics-Master-Docs

Blogs:
https://shunyaya.blogspot.com
https://shunyaya.blog

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🌈 Closing Thought

Newton revealed what symmetry is.
LAW 0AR helps us see where symmetry originates —
directly at the interaction source, cleanly, universally, and without modifying the physics we trust.

It does not replace. It reveals.

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OMP